Diss. ETH No. 13065

Planar High Speed Linear Direct Drivewith Submicron Precision

Bernhard Sprenger

Swiss Federal Institute of TechnologyETH Zurich

1999

Diss. ETH No. 13065

Planar High Speed Linear Direct Drivewith Submicron Precision

Dissertation submitted to theSWISS FEDERAL INSTITUTE OF TECHNOLOGY

ZURICH

for the degree ofDoctor of Technical Sciences

presented byBernhard SprengerDipl. El.-Ing. ETHborn July 15, 1967citizen of Germany

accepted on the recommendation ofProf. Dr. G. Schweitzer, examinerProf. Dr. J. Hugel, co-examiner

Prof. Dr. R. Siegwart, co-examiner

Zurich, 1999

Acknowledgments

andof

foree-

orart-theful

em-liza-

ndand

This thesis is based on my research work performed between 19941999 at the Institute of Robotics (IfR) at the Swiss Federal InstituteTechnology (ETH), Zurich.

I would like to thank my supervisor, Professor Dr. G. Schweitzer,enabling me to work in a liberal environment and for providing the frdom to conduct my research in an independent way.

I would like to thank Prof. Dr. R.Y. Siegwart and Prof. Dr. J. Hugel fbeing my co-examiners. I am grateful to Prof. Dr. R.Y. Siegwart for sting the project and for his supervision during the time, he was withInstitute of Robotics, and I am grateful to Prof. Dr. J. Hugel for his helpcomments on this thesis.

Many other people have contributed to this thesis in various ways, mbers of the IfR as well as students that helped me throughout the reation of this thesis. Specially, I would like to thank Martin Adams aShao Jü Woo for correcting my thesis; Silvia Alegro, Ladislav KuceraFelix Moesner for their expertise and encouragements.

ˆ

Table of Contents

4

Abstract v

Kurzfassung vii

1 Introduction 11.1 Motivation 1

1.1.1 Microelectronics 21.1.2 Micro-Electromechanical Systems

1.2 State of the Art 51.3 Objectives 91.4 Thesis Outline 10

2 Concept and Basic Design Principles 132.1 Actuator Arrangement 142.2 Suspension Technique 172.3 Summary 19

i

Table of Contents

3 Actuator Design 213.1 Basics of Voice Coil Actuators 223.2 Actuator Configuration 263.3 Electromagnetic FEM Simulation 273.4 Mechanical FEM Simulation 353.5 Electrical Model and Eddy Currents 373.6 Realization 413.7 Summary 44

4 Experimental Setup and Its Components 454.1 Mechanical Configuration 464.2 Air Bearing 494.3 Sensor System 51

4.3.1 Position Sensors 514.3.2 Accelerometers 54

4.4 Controller Hardware 554.5 Realized Experimental Setup 574.6 Conclusions 59

5 Control Design 615.1 Plant Modeling 62

5.1.1 Single Rigid-Body Model 625.1.2 Linear State-Space Model 685.1.3 Summary 74

5.2 PD-Controller 745.2.1 Control Structure 745.2.2 Filter 755.2.3 Trajectories 775.2.4 Performance 78

5.3 LQG Controller 845.3.1 Control Structure 84

ii

5.3.2 Performance 865.4 Conclusions 92

6 Conclusion 956.1 Summary 956.2 Outlook 97

References 99

Curriculum Vitae 105

iii

Table of Contents

iv

Abstract

anyelrder

reaseave to

beenver,

com-ave

isasedt and

ov-ear-ept

The need for fast and accurate positioning devices is increasing in mfields of technology, particularly in the field of manufacturing novadvanced products emerging from micro- and nano-technology. In oto reduce the mounting costs of such novel products and thus, to inctheir chance of a possible market success, the employed machines hwork not only at high speed, but also with high precision.

Many concepts of high speed or high precision manipulators haveproposed in the literature and have been realized in industry. Howeonly a few of these concepts can actually serve to obtain high speedbined with high precision positioning. Even these concepts still hsome inherent limitations and unsolved technical problems.

A new design of a planar linear drive with three degrees of freedomintroduced and its realization is detailed in this thesis. The design is bon a novel concept, using ideas in the fields of actuator arrangemensuspension. It consists of an arrangement of three identical modified ming coils attached to the slide, which is supported by one planar air bing and glides on a granite plate. It will be shown that this conc

v

Abstract

ary-ts.

m xs upr-

veralries,

lera-sesnsesnmset-ofele-

mpli-Thend a

izedsientilar

ctor 4

eliminates many problems connected with other solutions, such as ving natural frequencies caused by angular guides, and frictional effec

The experimental setup occupies a workspace of approximately 60 m60 mm, a sensor resolution of approximately 10 nm and accelerationto 30 ms-2, limited only by the employed power amplifiers. The perfomance has been verified in the whole workspace by carrying out setranslational tracking movements along sinusoidally shaped trajectoe.g. it allows movements of 30 mm within 94.8 ms, reaching an accetion of 25.5 ms-2. During the first tenth of a second the transient responshow overshoots of approximately 200 nm. Afterwards, the respotransform into decaying oscillations with a maximal amplitude of 650and a frequency of 11 Hz. Their amplitudes reduce to 200 nm after atling time of 1 sec. These oscillations result from the flexible mountingthe granite plate to a bench, which has been carried out by rubberments. For slower movements, the transient overshoots and the atudes of these decaying oscillations reduce to below 100 nm.stationary positioning noise is smaller than 60 nm peak-to-peak aroustationary offset of approximately 25 nm.

Compared to other known industrial and academic solutions optimfor fast and accurate positioning, the realized setup excels at a tranbehavior, which shows an at least four fold enhanced precision at simaccelerations. This precision has the potential to be increased by a fawithout requiring essential modifications of the setup itself.

vi

Kurzfassung

rhöhtuarti-

dieinesschi-win-

menor-ich,hen.lösteein-

rmo-aufam-

t aus

Der Bedarf an schnellen und genauen Positioniermechanismen esich in vielen technischen Bereichen, besonders in der Fertigung neger Produkte, welche der Mikro- und Nanotechnik entstammen. UmProduktionskosten zu verringern und so die Wahrscheinlichkeit eMarkterfolges zu erhöhen, müssen die eingesetzten Produktionsmanen nicht nur mit hoher Präzision, sondern auch mit grosser Geschdigkeit arbeiten.

Viele Konzepte für Hochgeschwindigkeits- und Präzisions-Mechanissind in der Literatur vorgeschlagen oder in der Industrie verwirklicht wden. Jedoch ist es nur mit wenigen dieser Konzepte wirklich möglgrosse Geschwindigkeiten zusammen mit hoher Präzision zu erreicAuch diese weisen jedoch immer noch Beschränkungen und ungetechnische Probleme auf, die die allgemeine Anwendbarkeit starkschränken.

In dieser Dissertation wird ein neuartiges Design eines ebenen Lineators mit drei Freiheitsgraden vorgestellt und realisiert. Es basierteinem Konzept, das auf einer neuartigen Antriebskonfiguration zusmen mit einer kontaktlosen Lagerung basiert. Das Design besteh

vii

Kurzfassung

littenirderenger

un-leu-nzenrmi-genabeie-

200voniner200der

ng-imaletio-pitze

henreali-

dendie

ern,

einer Anordnung dreier identischer Tauchspulen, die an einen Schmontiert sind, der luftgelagert auf einer Granitplatte gleitet. Es wgezeigt, dass dieses Konzept viele Probleme beseitigt, die mit andLösungen verbunden sind, wie Reibungseffekte und durch Winkellaverursachte veränderliche Eigenfrequenzen.

Der realisierte experimentelle Aufbau weist einen Arbeitsbereich vongefähr 60 x 60 mm2, eine Sensorauflösung von 10 nm und eine Beschnigungsfähigkeit von bis zu 30 ms-2 auf, die nur durch die verwendeteLeistungsverstärker begrenzt ist. Die Leistungsfähigkeit wurde im ganArbeitsbereich mittels translatorischer Bewegungen entlang sinusföger Beschleunigungsprofile verifiziert. Das System erlaubt Bewegunüber eine Distanz von 30 mm innerhalb von 94.8 ms und erreicht dBeschleunigungen von 25.5 ms-2. Das Einschwingverhalten dieser Bewgungen weist in der ersten Zehntelsekunde ein Überschwingen vonnm auf, welche in eine abklingende Schwingung mit einer Frequenz11 Hz und einer maximalen Amplitude von 650 nm übergeht. Nach eSekunde hat sich die Amplitude der Schwingung bereits wieder aufnm reduziert. Diese Schwingung rührt von der elastischen LagerungGranitplatte her, die mittels Gummielementen realisiert wurde. Für lasamere Bewegungen reduziert sich das Überschwingen und die maxAmplitude der abklingenden Schwingung auf unter 100 nm. Das stanäre Positionsrauschen des Systems ist kleiner als 60 nm Spitze-Sum einen stationären Offset von ungefähr 25 nm.

Verglichen mit anderen bekannten industriellen oder akademiscLösungen für schnelle und genaue Positionierung zeichnet sich dassierte System durch ein Einschwingverhalten aus, welches eine umFaktor vier erhöhte Genauigkeit aufweist. Zudem bietet das SystemMöglichkeit die Genauigkeit nochmals um den Faktor 4 zu verbessohne dass wesentliche Änderungen am System notwendig wären.

viii

1 Introduction

assfore,matedeld-the

rerg-ring

ssescus

The

Everything should be made as simple as possible, but not simpler.

Albert Einstein

1.1 Motivation

Automation is an ongoing process, which enables the cost effective mproduction of many products even in high wage countries, and therealso enabling their possible market success. Examples are the automanufacturing processes in the automotive industry (e.g. car body wing), in electronic consumer industry (e.g. assembly of telephones), inwatch industry (e.g. assembly of theSwatch) and in the semiconductoindustry. However, the manufacturing of novel advanced products, eming from micro- and nano-technologies, requires novel manufactutechnologies.

The specific fields of interest are the assembly and connection proceused for the manufacturing of such novel advanced products with foon microelectronics and micro-electromechanical systems (MEMS).

1

Introduction

idualThe

andand, the

with

con-lec-

hichthatle attimes

fall

prox-d toeM,tely

g ahnol-ips,

ding.hipere-nce

assembly and connection technologies are assigned to combine indivcomponents and subsystems into a function-oriented total system.employed manufacturing processes largely affect the reliability, sizeprice of an appropriate product. In order to reduce the mounting coststherefore, to increase the chance of a possible market successemployed machines have to work not only with high speed, but alsohigh precision, delivering a large throughput rate.

In the subsequent sections, the need for advances in assembly andnection technologies are discussed with focus on the field of microetronics and micro-electromechanical systems (MEMS).

1.1.1 Microelectronics

The dynamics of the developments in semiconductor technology, wwill continue also in the next years, are characterized by the factevery ten years, device complexity increases by a factor of 100, whithe same time an appropriate manufacturing plant becomes tenmore expensive. The prices however, related to the bit or the circuit,down to 1%. Still in 1971, the typical chip size was approximately 9 mm2,consisting of less than 4000 transistors while the feature size was apimately 10 µm. By 1990, the leading edge chip size had increaseapproximately 100 mm2, consisting of up to 6 millions transistors and thchip had a feature size of approximately 0.8 µm. The 1 Gbit-DRAwhich is scheduled for the year 2001, will already measure approxima500 mm2, consisting of approximately 1.2 billion transistors and havinfeature size of 0.18 µm. Thus, the future assembly and packaging tecogies are confronted with substantially larger and more complex chrequiring substantially more I/O pins [VANZANT97].

Currently, most dies are connected to the package leads by wire bonHowever, TAB (tape automated bonding) and in particular the flip-ctechnology provide better electrical and thermal characteristics. Thfore, wire bonding has been declared suboptimal from a performa

2

Motivation

itsforondreol-logyandads

downwillearswillonalace

r theging

point of view for years. However, the advantage of wire bonding isflexibility - wiring changes are easily accomplished without the needextensive tooling and material changes, by simply teaching a new “bprogram”. This flexibility, together with steady improvements in wibonding and difficulties with the chip attachment in the flip-chip technogy, has enabled wire bonding to remain the predominant methodofor packaging. An example of a bonded chip is shown in Figure 1.1aan enlarged view of the connection of the bond wires with the bond pon the die is shown in Figure 1.1b.

In recent years, the bond pad pitch has been reduced from 120 µmto currently 70 µm. But in order to meet future requirements the pitchbe reduced down to 45 µm by the year 2000 and even further a few ylater. Currently, most chips use inline pad pitches, but future chipsalso utilize staggered bond pad configurations, resulting in an additireduction of the effective bond wire pitch and in even less free spbetween the individual wires.

Consequently, this leads to an increased precision requirement fonext generation wire bonding machines. In order to keep the packa

Fig. 1.1: Wire Bonding (ESEC SA, Switzerland)

(a) Low Loop Wire Bonding (b) Bond Balls

3

Introduction

theh an

sultsith

ili-on

ac-, and

mer-s)-

d, thepro-large

and

oas-cision,otorotor

costs low, the bonding cost of one pin has to be reduced by factor 4 innext few years, which can only be achieved by faster machines witincreased throughput [REICHL98].

1.1.2 Micro-Electromechanical Systems

Recent research in micro- and nanotechnology has delivered initial rein the form of many prototypes of microsystems, e.g. micro-motors wgears [GUCKEL92], micro-actuators [BENECKE94], micro-optical systems[M OTAMEDI97], micro-pumps [RICHTER92], micro-valves [LISEC94], andmicro-sensors [EATON97]. Many of these microsystems are based on scon technology emerging from microelectronics, others are basedLIGA (Lithographie-Galvanik-Abformung) technology [BRUECK95],FAB (Fast Atom Beam) etching [HATAKEYA 95] or ultra precision cuttingtechnique [YAMAGATA 96]. Many of these microsystems can be manuftured without the need of any assembly processes in automatedtherefore, cost-effective batch processes. Good examples are the comcially available iMEMS® (integrated micro-electromechanical systemaccelerometers fromAnalog Devices, which are based on surface micromachining. Because standard integrated circuit technologies are useprocess can be incorporated well into the standard wafer fabricationcesses. This allows the consistent and repeatable production ofquantities of devices at low cost.

But microsystems, such as the micro-optical disk pickup [LIN96B] (someparts employed in this micro-optical system are shown in Figure 1.2aFigure 1.2b) or the microchemical analysis system [MENZ97], which con-sist of a combination of several microparts, require one or more micrsembly processes. These assembly processes may require high prewhich can be derived from the assembly requirements of a microm[GUCKEL92], featuring a difference between the shaft diameter and rhole of 0.5 µm, and thus, a bearing clearance of 0.25 µm.

4

State of the Art

t bye, isemscomeolsging, and

beenes ofr thehighofwith

Presently, the assembly of such microsystems is mostly carried oumanually-operated micrometer screw mechanisms and thereforrestricted to experiments only. However, in order for such microsystto succeed on the open market, their mass production has to beaffordable. Therefore, significant improvements in manufacturing toare required, in particular the assembly, connection and packamachines have to be automated, reach high precision and be fastthus, they have to be optimized for high throughput.

1.2 State of the Art

Many concepts of high speed or high precision manipulators haveproposed in literature or have been realized. The most significant onthese concepts are now discussed with respect to their suitability fodesign of mechanisms, which allow to reach both high speed andpositioning precision. However, it will be demonstrated that only fewthese concepts can actually serve to obtain high speed in conjunction

Fig. 1.2: Micro Machined Optics ([L IN96A] and[L IN96C])

(a) Micro Machined Fresnel Lens (b) Tunable Fabry-Perot Etalon

5

Introduction

ome

cha-

ashing,

ts aausethese

onaller-

reci-w

dingbe

arges).ctse or

Thiselera-outthelowtheult

high positioning precision. Nevertheless, these few ones still have sinherent limitations and unsolved technical problems:

• Lead screws and ball screws are often used in high precision menisms that require a large workspace [OTSUKA97]. Because backlashleads to chattering vibration and long positioning time, zero backlbetween the screw and the nut is required for precise positionwhich results in large frictional forces. However, for fast movemencertain degree of backlash is required, because frictional forces cnoise, produce heat and increase wear. There are ways to solveinconsistent requirements for the backlash [SATO-K97]. On the otherhand, there are still mechanical design limitations, such as torsiwindup and large inertia, which limit the attainable speed and acceation.

• Piezo electric actuators allow the achievement of fast and high psion motions, but their range of motion is usually limited to a femicrometers but can reach approximately one millimeter, depenon the size of the device. However, this limitation of workspace canovercome by the inchworms or the impact drive principle [ZESCH95].These devices allow the achievement of a high resolution over a lworking area, but only with very low speed (in the range of mm/Their main fields of application are the manipulation of small objeunderneath microscopes (e.g. the manipulation of cells in medicinbiology) and the near field microscopy.

• Fast parallel drives, similar to the Delta-Robot [CLAVEL 88], have theadvantage that their motors are fixed and don’t have to be moved.reduces the moved mass and allows the achievement of high acctions. They use ball bearings for the joints, which have radial run-of several µm. The inaccuracy accumulates with each joint ofrobot arranged in a chain-like structure. Other problems are thestiffness of these structures, the frictional forces in the joints andcomplex kinematics and dynamics. All these effects make it diffic

6

State of the Art

ayimitpro-

withreasretheinginn-

highro”-ticu-

struc-

ved,hetionof

heire.ulars,

tiond ins, thener.

to achieve high precision combined with large acceleration. This mbe improved when using direct visual feedback, however, the lcycles resulting from the frictional forces and the speed of imagecessing will still be limiting factors.

• Studying human arm motion shows that the upper arm, togetherthe forearm, is used for coarse and low-bandwidth motions, whethe light weight fingers together with the light weight hand aemployed for fine and high-bandwidth motions, and to reduceoverall errors. This biologically motivated principle suggest creatmini/macro manipulators [KHATIB91]. This idea has also been used[HODAC97] for a micro/macro manipulator design. The main advatage of this approach is that not all actuated joints have to deliverprecision, because the overall error can be eliminated by the “micpart. Nevertheless, still more research has to be carried out, parlarly in the areas of control structures for optimal performance.

• Steel cables or steel belts as transmission elements allow the contion of high performance manipulators [FÄSSLER90]. Their mainadvantage is that their motors are fixed and don’t have to be moleading to minimal inertia of all moving parts, and thus, allowing tachievement of high accelerations. However, the attainable resoluis limited due to their vibrational properties, the complex deflectioncables/belts and frictional forces.

• Linear drives achieve high performance and good resolution, but tconfiguration for multiple degrees of freedom is difficult to realizThey are often arranged into parallel structures by the use of angguides [OKAMURA 88]. The friction can be eliminated by air bearingleading to enhanced precision [MEISSER88]. Unfortunately, air bear-ings have the detrimental behavior that their stiffness varies in relato the applied load. Because the air bearings, which are employethe angular guide, are exposed to tensile and compressional stresnatural frequencies of the entire system vary in a nonlinear man

7

Introduction

am-outare

lting

uchsys-

erota-

eehichsys-tionom;ersters,

heters

mmethegn a

tillross

-ess

These varying natural frequencies limit the attainable system dynics because control theory still has problems in treating them withthe loss of bandwidth. Further disadvantages of these solutionstheir complex designs (e.g. 3 planar air bearings) and mass resufrom the angular guides, which is to be moved.

• Planar Magnetic Levitators are a promising technique, but still mresearch remains to be done. They also require a more complextem design, but they can offer more degrees of freedom.The system described in [KIM97] and [KIM98] uses three capacitancgap gauging systems to measure the vertical displacement andtional angles around theX- andY-axis. TheX- andY-position, and therotational angle around theZ-axis are measured by means of thrlaser interferometers. The usage of these laser interferometers, ware quite expensive system components, leads to relatively hightem costs. Furthermore, the goal of achieving nanometer resoluwhile measuring the movements of the rotor (6 degrees of freedworkspace 50 mm x 50 mm x 0.5 mm) with laser interferometrequires a measurement surface quality in the range of nanomewhich is difficult to realize. Therefore, the effective precision of tproposed sensor system is probably in the range of micromeinstead of nanometers. Additionally, the results presented in [KIM98]are based on movements along translational trajectories of 20with an acceleration of 10 ms-2. However, the transient behavior of thexperiments is presented in a confusing manner, it shows only“fine settling behavior”, which are the movements after a settlintime of 0.1 s, but the effective transient behavior is not shown ocorrect scale. Even at the beginning of the presented“fine settlingbehavior”, which is 0.1 s after the endpoint should be reached, it sshows a decaying error of approximately 10 µm and a decaying ccoupling error of 0.5 µm.The setup described in [MOLENAAR98] is based on an interesting principle, but its performance is currently limited to accelerations of l

8

Objectives

rtude

, real-andout

ces ahus,

e the

wscou-ngsrriedicu-limittemen-entsnal

ithr to

the

than 2 ms-2. The usability of this principle still has to be verified fohigher accelerations, which are more than one order of magnilarger.

1.3 Objectives

The basic goal of the research presented in this thesis is the designization and control of a high performance planar manipulator for fastprecise movements. The objective of such a manipulator is to carryhighly precise positioning tasks at high speeds. In this sense, it produdegree of precision far beyond human motor capabilities, and tachieves task performance, impossible for human beings.

In order to develop a successful solution, it is necessary to investigatfollowing related issues:

• Mechanical configurationA suitable configuration has to be found and realized, which allofast and precise planar movements. This includes the effective depling of the system from floor motions, the arrangement of beariand the design of all mechanical parts. The design has to be caout taking special care of its natural frequencies. Low and, in partlar, varying natural frequencies have to be avoided, because theythe attainable system performance. The decoupling of the sysfrom floor motions introduces some unavoidable low natural frequcies. However, their values and corresponding damping coefficican be influenced by the mechanical design. Furthermore, frictioforces have to be avoided, as they tend to lead to limit cycles.

• Actuator designAn actuator type has to be chosen, modified and optimized wrespect to its application for fast and precise movements. In ordeachieve high precision in conjunction with high accelerations,

9

Introduction

angelsohys-e andcedwith

truc-nce,

ran-rol-

toon-ivedentalbe

eve-ighecha-sionovel

arch,

tors.iththe

actuators need to have a large electromechanical dynamic rtogether with a high stiffness of their mechanical structure. It is apreferable that they have a linear actuation characteristic with noteresis effects, which increases the attainable system performancfacilitates the controller design. Furthermore, the ratio of the produforce in relation to the accelerated mass has to be maximizedrespect to the requirements mentioned earlier.

• Control SystemIn order to achieve a high performance system, several control stures have to be investigated, regarding their attainable performatheir required computing power and their transient behavior. The tsient behavior is an important condition while starting up the contler, due to limitations of the manipulated variables and duelimitations of the workspace. The design and simulation of the ctroller requires an exact model of the system, which has to be derfrom the measurement of the frequency responses. An experimsetup will be built, and the most promising control structures willimplemented and tested in the experimental setup.

1.4 Thesis Outline

The design of a high performance manipulator, which allows the achiment of high accelerations in conjunction with high precision, makes hdemands on the mechanical and electromagnetic properties of the mnism. However, many known concepts for high speed or high precimanipulators are not feasible to achieve both together. Therefore, a nconcept is derived in Chapter 2, which has been realized in the resedetailed in this thesis.

Chapter 3 is dedicated to the design of the employed voice coil actuaIt starts with an explanation of their physical principle and continues wthe realized actuator configuration. The next two sections deal with

10

Thesis Outline

EMy to

f theed insys-.

siveere-

d per-ter

elop-

optimization of the actuators by electromagnetic and mechanical Fsimulations. An electrical model is then derived, which is necessarevaluate an appropriate power amplifier.

The experimental setup is described in Chapter 4. First an overview omechanical setup is given. The design of the air-bearing is discussthe next section, followed by a description of the employed sensortems. The chapter ends with a discussion about the control hardware

The controller design is discussed in Chapter 5. It starts with an intenmodeling of the plant, which is needed for good controller design. Thfore, two different models are derived in this section. Afterwards, aPD-controller is discussed and its results are presented. The design anformance of aLQG-controller is detailed in the next section. The chapfinishes with a comparison of these controller designs.

Chapter 6 summarizes the thesis and gives an outlook on future devment potential.

11

Introduction

12

2 Concept and Basic DesignPrinciples

vinguts

anypro-mon-btainstill

lator,signtor

solu-rcial

itionaltech-

d for

The realization of a high performance manipulator, capable of achiehigh acceleration in conjunction with a high precision positioning phigh demands on its mechanical and electromagnetic properties. Mconcepts of high speed or high precision manipulators have beenposed in the literature or have been realized. However, it has been destrated in Section 1.2, that only few of these concepts can serve to ohigh speed in conjunction with high precision positioning, and thesehave some inherent limitations or unsolved technical problems.

Therefore, this chapter discusses a novel concept for a planar manipuon which the design detailed in this thesis is based. The first basic deidea is in the field of actuator arrangement. An intelligent actuaarrangement eliminates many problems, inherent to other designtions, during the initial design phase, and enables the use of commesensor systems. Subsequently, the problems associated with a tradarrangement of bearings are explained and a well known suspensionnique is suggested, which eliminates these problems and is well fittethe successful design of a fast and accurate manipulator.

13

Concept and Basic Design Principles

gularhese

ichracy-like

tionntalad.ed topletetem

f anyg a

ofed in

rs to

e pla-hasabil-ecificmea-

ithableussed

2.1 Actuator Arrangement

It has been demonstrated in Section 1.2, that rotational joints and anguides limit the attainable system performance. The reasons for tstatements can be summarized as follows:

• Rotational joints use ball bearings or rotational plain bearings, whalready have a radial run-out of several µm. Therefore, the inaccuof a mechanism accumulates with each joint arranged in a chainstructure.

• The use of angular guides only makes sense if utilized in conjuncwith air bearings. Unfortunately, air bearings have the detrimebehavior that their stiffness varies in relation to the applied loBecause angular guides, and thus, also air bearings, are expostensile and compression stress, the natural frequencies of the comsystem vary in a nonlinear manner, which limits the attainable sysdynamics.

Therefore, a solution has to be found that does not require the use orotational joints or angular guides. This implies the idea of deployinslide that can freely move in the plane and is actuated by some formcontactless linear actuators. The fact that a planar object can be placa plane with three degrees of freedom (theX- andY-position, and the ori-entation are free) leads to the requirement of at least three actuatoenable the controlled planar positioning of the slide.

There are many actuator arrangements possible that are usable for thnar positioning of the slide. However, an important condition, whichto be met in order to enable a successful implementation, is the availity of a usable sensor system, which can be used together with a spactuator arrangement. Due to the lack of a sensor system capable ofsuring both theXY-position as well as the rotational orientation angle wthe demanded accuracy, a combination of two commercially availtwo-coordinate measuring systems has been selected, as will be disc

14

Actuator Arrangement

ndx 98ause

thenoxi-

in Section 4.3.1. Each of these sensor systems can measure aXY-Positionwithin a workspace of 68 mm x 68 mm with a resolution of 10 nm, aeach consists of a grid plate, having the outside dimension of 98 mmmm, and a sensor head, having two flexible cables connected. Bectwo of these sensor systems are used, the rotational angle aroundZ-axis can be obtained from the twoXY-positions and the distance betweethe two sensor systems, resulting in a rotational resolution of apprmately 1 µrad.

F1

F2

F3

F1

F2F3

F1

F2

F3

F4

y

xϕ

Fig. 2.1: Possible Actuator Arrangements

a) Triangular Triple ActuatorArrangement

b) Rectangular Triple ActuatorArrangement

c) Rectangular Quadruple ActuatorArrangement

15

Concept and Basic Design Principles

pos-

ct incom-f two

blethe

hus,sued

ngu-tan-

This, itsunt-

em-

Fig-ipleancy

of afor-

thiss of

nge-y there is

ce is

However, there are still many different actuator/sensor arrangementssible. The most reasonable ones are shown in Figure 2.1.

In Figure 2.1a, the triangular triple actuator arrangement (the forces aa triangular sense) is shown. This arrangement could lead to a verypact system design. However, the employed sensor system consists oincremental two-coordinate grid plate encoders made byHeidenhain,each requiring a square space of approximately 100 cm2 for the mountingof its grid plate, which is approximately 2.1 times larger than the usaworkspace. Because the two grid plates would have to be fitted intotriangle, the size of the triangle would become relative large, and twould lead to a heavy slide. Therefore, this arrangement is not purany further.

The rectangular triple actuator arrangement (the forces act in a rectalar sense), shown in Figure 2.1b, allows an optimal coverage of its recgular area with the sensor grid plates, without wasting any area.leads to a relatively small, and thus, a lightweight slide. Furthermorestructure is application-oriented, because it allows the unhindered moing of a tool on its free side, which is required for carrying out any assbly or mounting tasks.

The rectangular quadruple actuator arrangement, which is shown inure 2.1c, is basically a more symmetrical version of the rectangular tractuator arrangement, but with redundancy in actuation. This redundcan easily be compensated by the controller design. The advantagemore symmetrical structure is an increased controllability and permance. However, the area of application for a mechanism based onconfiguration is strongly limited, because of the restricted possibilitiemounting a tool.

Because of the promising advantages of rectangular actuator arraments, their realization has been pursued in this thesis. However, onltriple actuator configuration has been realized, because its structumore application-oriented and because the achieved performan

16

Suspension Technique

signould

ura-

liza-of aar

of a-nce.used inric-icaltateeci-ign.ces,fric-

beude.ion,

iza-basedsion.

, air

already quite impressive, as will be shown later in Chapter 5. The dehas been carried out in such a way that a fourth actuator, if needed, cbe added with minimum effort, leading to a quadruple actuator configtion.

The employment of modified voice-coil actuators, whose design, reation and advantages are explained in Chapter 3, allows the realizationdirect drive configuration, in particular, the realization of a planar linedirect drive with three degrees of freedom.

2.2 Suspension Technique

Another important issue that may limit the attainable performancemechanism, is the friction [ÅSTRÖM98]. Friction appears in most mechanical systems and has a significant impact on the achievable performaFrictional forces are complicated nonlinear dynamical effects becathey are caused by a multitude of different physical mechanisms, anaddition also may lead to time-varying dynamic behavior. Therefore, ftional forces can lead to a substantial deterioration in precision. Typfrictional effects occurring in controlled mechanisms are steady serrors and limit cycles. Their influences on the system’s positioning prsion are difficult to eliminate or to compensate by the controller desThere are mainly two promising techniques to reduce these influenone is acceleration feedback and the other is adaptive model basedtion compensation. Unfortunately, the influence of friction can noteliminated completely, but it can be reduced by an order of magnitHowever, for devices that are fast and provide high positioning precisthis is often not sufficient.

Therefore, frictional forces should be reduced substantially by the utiltion of an advanced contactless suspension technique, such as thoseon air bearings, active magnetic bearings and electrostatic suspenDue to their simplicity, compactness and favorable characteristics

17

Concept and Basic Design Principles

lized

sms,ilartedns,letelyof air

roper-g asd by

ble toy any

non-inthe

havethee ford assign

ment,rying

g onether

cu-

bearings are selected for providing contactless suspension in the reasetup.

Air bearings allow the design of contactless and frictionless mechaniwhich is advantageous for high precision devices. The only effect simto friction derives from aerodynamic drag, but it can usually be neglecexcept at high flow rates of the air or at large velocities. For applicatioas the one described in this thesis, aerodynamic drag can be compneglected because it can not be detected during operation. The usebearings results in wear-free designs because of their contactless pties. Therefore, no oil or any other lubricant is required. Thus, as lonthe provided air is clean, there is no danger of contamination, causeother mechanical bearings. For this reason, air bearings are applicaclean room applications. In special cases, the air can be replaced bother gas, which may be inert.

Unfortunately, air bearings have the drawback that their stiffness is alinear function of the applied load. Accordingly, varying loads resultvarying natural frequencies. These varying natural frequencies limitattainable system dynamics, because existing control methods stillproblems in treating them without loss of bandwidth. Therefore,design of the complete system has to be carried out with special carthe loads of the air bearings - varying load forces have to be avoidemuch as possible. However, this problem is not present in the dedescribed in this thesis, because of its special actuator arrangewhich does not require any angular guides that are exposed to vatensile and compressional stresses.

The thickness of the air cushion measures only a few µm, dependinthe design aspects. Because of the required polished surfaces togwith this thin air cushion, air bearings are sensitive to dirt, oil and partilarly to filings.

18

Summary

nted,sus-

lemsaliza-sionma-

ctu-slideded

l be

2.3 Summary

In this chapter, a concept for a planar manipulator has been presehaving basic design ideas in the fields of actuator arrangement andpension. It has been shown, that this concept eliminates many probassociated with other solutions. As such, this concept enables the retion of a high performance manipulator, which can achieve high precipositioning in conjunction with high speed. This concept can be sumrized as follows:

A mechanism is employed, which is based on a rectangular slide, aated by three or four voice coil actuators, which are attached to thewithout the use of any joints or angular guides. The slide is suspenby a planar air bearing allowing contact free, frictionless actuation.

The realization of a planar manipulator based on this concept, wildescribed in the following chapters.

19

Concept and Basic Design Principles

20

3 Actuator Design

on-the

ntrolple

e for

mag-eenator-coilnge-

ed

tionan-

ons.

Electromagnetic linear drives are known in DC and multiple phase cfigurations. Multiple phase devices can be built to a smaller size thanequivalent DC devices. However, their design, manufacturing and cois more complicated. DC linear drives, on the other hand, have a simconstruction and are easy to control. These two factors were decisivtheir choice.

Several DC linear actuator designs have been evaluated by electronetic FEM simulations and the two most promising designs have brealized as laboratory prototypes. However, the most practical actudesign yielding a good performance was found to be based on voiceactuators and is detailed in this chapter. It consists of a merged arrament of two commercially available stators/cores fromETEL togetherwith a novel developed coil, whose coil former is made of fiber reinforccomposites.

The coils are optimized by FEM simulations [ANSYS95] to achieve maxi-mal actuation force and small mechanical deformation in conjuncwith minimal weight and large electromechanical dynamics. The mechical deformation properties are obtained from mechanical simulati

21

Actuator Design

ons.esti-

ich isller.ua-sim-

ofichon auceard, to

icetor/la-

osi-coilntrols forirror

The current-force relationship is obtained by electromagnetic simulatiThe electrical transfer function is measured and the eddy currents aremated to assess the dynamics of the electromagnetic system, whessential for selecting the power amplifier and designing the controThe following sections focus on the basic principles of voice coil acttors, the actuator configuration, the electromagnetic and mechanicalulations, the electrical modeling, and the realization.

3.1 Basics of Voice Coil Actuators

Voice coil actuators allow linear movements over a limited rangemotion. Originally, they are derived from radio loud speakers after whthey are named. Voice coil actuators are direct drive devices basedpermanent magnet field and current-carrying coil windings, and proda force, which is directly proportional to the applied current (lineforce-current characteristic). Therefore, they are easy to understanbuild, to apply and to control [BLACK93][STUPAK89][MCLEAN88].

In the field of fast and precise positioning, the main advantage of vocoil actuators is that only the light coil moves, whereas the heavy stacore is fixed. Thus, it is possible to obtain high accelerations with retively little power. Another great advantage is that the actuation is ption insensitive, resulting in a simpler system design. Thus, voiceactuators are widely used in high speed and accurate positioning coactuators, such as magnetic disk drives and vibration isolation systemspace applications, or in optomechanical devices, such as multiple mtelescopes and large binocular telescopes.

22

Basics of Voice Coil Actuators

the

netichefield

existstionsusing

Their electromechanical energy conversion process is based onLorentz Forceprinciple, which is illustrated in Figure 3.1. This lawexpresses that if a current-carrying conductor is placed in a magfield, a force will act upon it, which is proportional to the current and tmagnetic flux density. Based on the assumptions that the magneticbetween the pole shoes is homogeneous and static, that no fringingat the pole shoes, that no flux-leakage occurs, and that no field variaare caused by the DC conductor current, this force can be calculatedthe following equation:

(3.1)

where:

: Force vector: Current vector: Magnetic flux density vector: Conductor length in the magnetic field

Fig. 3.1: Force Acting on a Current-Carrying Conductor

F

i

LS

N

B

F L i B×( )⋅=

FiBL

23

Actuator Design

por-ted

theat thetord by

In the case that the conductor moves in a magnetic field, a voltage protional to its velocity is induced across the conductor, which is illustrain Figure 3.2. This voltage is known as the induced voltage. Based onsame assumptions made before and the additional assumption thflux density vector, velocity vector and orientation vector of the conducare orthogonal, the magnitude of the induced voltage can be calculate

(3.2)

where:

: Induced voltage: Current: Velocity of the conductor: Magnetic flux density: Conductor length in the magnetic field

Fig. 3.2: Back Electromotive Force (back EMF) Generation

Ui L v B⋅ ⋅=

UiivBL

24

Basics of Voice Coil Actuators

s ahetiza-heonged to

rce

amealcu-

In its simplest form shown in Figure 3.3, a linear voice coil actuator itubular coil of wire placed within a radially orientated magnetic field. Tfield is generated by a tubular permanent magnet with radial magnetion, which is mounted on the interior of a hollow soft iron cylinder. Tmagnetic circuit is completed by an inner soft iron core positioned althe centerline of the coil. This core and the permanent magnet are fixthe soft iron cylinder, jointly forming the shell of the actuator.

Applying a current through the coil windings generates an axial fobetween the coil and the shell. This force also arises from theLorentzForce principle, as discussed before, and thus, with respect to the sassumptions made before, this force and the induced voltage can be clated by

(3.3)

(3.4)

Fig. 3.3: Conventional Voice Coil Actuator Configuration(1-Soft Iron Core; 2-Soft Iron Cylinder; 3-Permanent Magnet; 4-Coil)

1

3

42

F

F N L i B⋅ ⋅ ⋅=

Ui N L v B⋅ ⋅ ⋅=

25

Actuator Design

urensted.pla-Sec-

ign,

where:

: Number of coil windings: Length of one coil winding

3.2 Actuator Configuration

The conventional voice-coil actuator configuration, as shown in Fig3.3, has only a limited range of motion - it effectively allows only motioalong its centerline; movements in other directions are strongly restricTherefore, this actuator design is not suitable for the realization of anar linear direct drive with three degrees of freedom, as discussed intion 2.1. However, this limitation can be overcome by a modified des

NL

Fig. 3.4: Realized Voice-Coil Actuator Configuration(1-Coils, 2-Permanent Magnets, 3-Cores/Stators)

1X

Y

Z

23

26

Electromagnetic FEM Simulation

ricalmod-theare

losedlosedningthe

cedn beatord tofromtes

r isss, itthis

:ers.ype

therol-e, allded.

which uses cuboid coil and core geometries instead of the cylindones. Furthermore, the sidewalls of the housing are removed. Theseifications allow a large translatory and rotational range of motion inhorizontal plane. Such voice-coil configurations are well known andcommercially available.

On the other hand, in order to achieve a more compact design, a cactuator configuration is preferable. The disadvantages of such a cconfiguration are the electromagnetic field displacement and weakeat the coils when applying a coil current. This effect corresponds toarmature reaction known for DC motors. This results in a reduforce-current ratio and will be discussed in Section 3.3. This effect careduced by the introduction of an air gap, which divides the core/stinto two separate parts. In conclusion, the optimal design was founconsist of a merged arrangement of two commercial stators/coresETEL in combination with a newly developed former, which incorporatwo separate coils and is shown in Figure 3.4.

Detailed information about the practical realization of this actuatogiven in Section 3.6. However, since the design was an iterative proceis necessary to provide some information about the realization atpoint, in order to increase the understanding of the following sections

• Each of the two coils consists of 101 windings arranged in 3 layThe FEM simulations, however, have been carried out for a prototconfiguration consisting of 116 windings.

• The maximum force is reached when applying a coil current of 8 A

3.3 Electromagnetic FEM Simulation

Magnetic saturation effects lead to a nonlinear characteristic offorce-current transfer function. However, in order to facilitate the contler design, and thus, to increase the obtainable system performancthe nonlinearities resulting from saturation effects have to be avoi

27

Actuator Design

con-thealso

o berob-EM

twoions

andld isaps.

thanthe

Therefore, extensive electromagnetic FEM simulations have beenducted to ensure that the force-current relation remains linear inrequired operating area. Furthermore, the efficiency of the devices isoptimized on basis of the simulations, allowing higher accelerations treached while using the same power amplifiers. In addition, heating plems related with the power dissipation are reduced. The employed Fsimulation software isANSYS 5.3.

The electromagnetic FEM simulations have been carried out using adimensional modeling of the actuator. The usage of 2D FEM simulatis applicable, because the magnetic flux density outside of the coresair gaps is relative small and, thus, the force produced by this stray fieneglectable small compared to the force produced inside of the air gThe expected error resulting from this reduced modeling is smallerthe error resulting from the variance of the magnetic properties ofemployed magnets, which is approximately ± 5%.

Fig. 3.5: Two Dimensional Electromagnetic Simulation Model(1-Cores/stators, 2-Permanent Magnets, 3-Coils)

28

Electromagnetic FEM Simulation

h isppliedetic

by athe

theu-

eeninging

tro-twot ansityher-hannted

hey3.6c,

bethe

nesx linen theure

arewing

Applying a coil current causes a field displacement in the cores, whicdependent on the clearance between the two cores/stators and the acurrent. This field displacement introduces a weakening of the magnflux density through the coils. Because the resulting force producedcertain coil current is also a function of the magnetic flux throughcoils, it is also affected by the clearance. This effect corresponds toarmature reaction known for DC motors and is pointed out by FEM simlations, which are carried out for different sizes of the clearance betwthe two cores together with an applied coil current of 8 A. The resultmagnetic flux densities are shown in Figure 3.6 while their correspondflux lines are shown in Figure 3.7.

These simulations illustrate the effects of the coil current on the elecmagnetic field in relation to the size of the clearance between thecores. In Figure 3.6a, which shows the magnetic flux density withouclearance between the two cores, it can be observed that the flux deat the coils on the left side is smaller than that on the right side. Furtmore, it can be noticed that the flux density in the left core is larger tin the right one. These effects are reduced in the configuration presein Figure 3.6b, showing the flux density for a clearance of 14 mm. Tare reduced even more in the configuration presented in Figureshowing the flux density for a clearance of 60 mm.

The effect of the reduced magnetic flux density at the coils can alsoobserved in Figure 3.7, because the flux density corresponds withspacing between the flux lines. In Figure 3.7a, which shows the flux liwith zero clearance between the two cores, it can be seen that the fluspacing at the coils on the left side is larger than the one at the coils oright side. This effect is reduced for the configuration presented in Fig3.7b, showing the flux lines for a clearance of 14 mm, while theyreduced even more in the configuration presented in Figure 3.7c, shothe flux lines for a clearance of 60 mm.

29

Actuator Design

e

(a) Clearance of0 mm

(b) Clearance of14 mm

(c) Clearance of60 mm

Fig. 3.6: Magnetic Flux Density in Tesla with Respect to the Size of thClearance between the Cores when applying a Coil-Current of 8 A

30

Electromagnetic FEM Simulation

(a) Clearance of0 mm

(b) Clearance of14 mm

(c) Clearance of60 mm

Fig. 3.7: Flux Lines with Respect to the Size of the Clearancebetween the Cores when applying a Coil-Current of 8 A

31

Actuator Design

mag-en-mumelyranceated.m

met-nse-ores

thethe

tinghefi-

ucediffer-

forcecoil

nlin-lus-tween

thatof 0is 14

Because the generated force of the actuator is proportional to thenetic flux going through the coils, this force of the actuator is also depdent on the size of the clearance between the two cores. The maxiforce-current propagation coefficient would be obtained for an infinitsized clearance between the two cores. However, an enlarged cleaalso leads to a bigger coil with more mass, which has to be accelerAn important limiting constraint for the size of the actuator results frothe bounded space available for its mounting, which is due to the georical properties of the slide, as will be seen in Chapter 4. As a coquence, a rough estimation of the optimal distance between the two cwas found to be 14 mm, which is approximately twice the height ofgap (including the height of the magnets, which have approximatelysame permittivity as air) in which the coil moves. The simulated resulforce of 250 N at a coil current of 8 A is approximately 16% below tsimulated theoretical maximum, which would be obtained with an innitely sized clearance between the two cores. The effect of a redmaximal force has also been pointed out by measurements for two dent actuator configurations in [KUEMM96].

The dependency between the size of this clearance and the resultingis also evaluated by FEM simulations and shown in Figure 3.8 for acurrent of 8 A.

As mentioned earlier, magnetic saturation phenomena result in a noear characteristic of the force-current transfer function. Figure 3.9 iltrates the nonlinearity caused by these phenomena for an air gap bethe two stators/cores of 0 mm and 14 mm, respectively. It can be seenthe magnetic saturation has indeed a large influence for an air gapmm, whereas no influence can be seen in the case that the air gapmm, even for large coil currents.

32

Electromagnetic FEM Simulation

0 20 40 60 80 100 120235

240

245

250

255

260

265

270

275

Gap Size [mm]

Res

ultin

g M

ax. F

orce

[N]

- Simulated Points

Fig. 3.8: Clearance-Force Dependency

0 10 20 30 40 50 60 70 800

500

1000

1500

2000

2500

Current [A]

Forc

e [N

]

- 0 mm Gap- 14 mm Gap

xo

Fig. 3.9: Current-Force Relationship for DifferentAir Gap Separations

33

Actuator Design

f theandn airetic

esis

guredear

actu-ion,norr torre-im-the

lizedcoil

rityed inruc-com-

ned.r tonotould

As demonstrated above, introducing an air gap causes a reduction oinfluence of the coil currents on the magnetic flux density in the gapcores. As a result, hysteresis effects are also reduced. Already at agap separation of 14 mm, the coil currents only influence the magnflux density in the gap and cores slightly, and, thus, allow hystereffects to be neglected.

Based on these observations, the realized actuator design is confiwith a 14 mm clearance between the two cores, delivering a linforce-current characteristic for a coil current range of 0 to 8 A.

It has to be noted that these simulations have been carried out for anator design incorporating 116 coil windings. The realized configurathowever, uses only 101 coil windings, resulting from several midesign modifications during the manufacturing. Therefore, in ordeobtain the correct driving force, the coil current has to be scaled cospondingly. In other words, the realized configuration delivers only a sulated force of approximately 218 N at a coil current of 8 A instead of250 N obtained for the design with 116 coil windings.

In addition, it has to be noted that measurement shows that the reaactuator design delivers a reduced force of approximately 178 N at acurrent of 8 A, which is 18% below the simulated 218 N. This disparesults from the inaccuracies present in the material parameters usthe FEM simulation - the properties of the materials used for the consttion of the stators could only be estimated, because these stators aremercial products and their exact properties could not be obtaiObviously, the material properties could have been “tuned” in ordeobtain more accurate simulation results, but this tuning wouldincrease the positioning performance of the realized system and whave no consequences for the subsequent chapters.

34

Mechanical FEM Simulation

ted.mer.terialon-gapke

ther-ontrolThis

ddi-

thef then the

3.4 Mechanical FEM Simulation

Upon applying a coil current, a force acting on the coil itself is generaThis force results in mechanical stress and deformation of the coil forClearly, the mechanical stress should remain below admissible mastress levels while the deformation should not violate geometrical cstraints. One important geometrical constraint is the height of the airin which the coil moves. The coil and its former are not allowed to mamechanical contact with the core/stator, even at maximum force. Furmore, high natural frequencies are desirable, because they ease the cdesign and largely increase the attainable system performance.implies that the coil former is required to posses a high stiffness. Ationally, minimal weight is required to enable large accelerations.

For this reason, mechanical FEM Simulations are used to optimizemechanical design. This leads to a design in which the thickness ocoil former is enhanced at the end plates, since these do not move i

Fig. 3.10:Mechanical Simulation Model

35

Actuator Design

one

im-

oxyratebricto

lingcoilend3.6).gyani-ring

ane aner,rifiedim-trial

tions

in

air gap. The deployed FEM simulation software is the same as theused for the electromagnetic simulations in Section 3.3, which isANSYS5.3. The employed three dimensional model of the mechanical FEM sulations is shown in Figure 3.10.

However, the use of composite technology, and in particular epresin-glass fabric-prepreg laminate, makes it difficult to achieve accusimulation results. In order to achieve accurate results, each fiber falaminate layer would have to be modeled individually while taking inaccount its fiber orientation. This would lead to an enormous modeproblem since the bottom plate and the cover plate of the realizedformer consist of approximately 20 fiber fabric layers each and theplates consist of approximately 35 layers each (refer to SectionAnother major problem is that the employed lamination technololargely affects the achievable material properties. Moreover, the mechcal properties of the cured resin depend largely on the employed cuprocess and temperature.

Therefore, the applied mechanical FEM simulations only provideapproximation of the real mechanical behavior, however, they providindication on the location of possible design problems of the coil formand how they can be solved. Nevertheless, each design has to be veand improved by evaluating prototypes, however, with the support of sulations the number of design iterations is far less than when a pureand error approach is chosen. It should be noted that the simularevealed the need for an enhanced thickness of the end plates.

Applying a load of 250 N results in the simulated deformation shownFigure 3.11.

36

Electrical Model and Eddy Currents

pli-atornicalarac-

el istricalentsostlyping

antedreas-cies.

of

3.5 Electrical Model and Eddy Currents

For the design of the controller and for the evaluation of the power amfier, it is essential to know the electromagnetic dynamics of the actuand the operating range over which a reasonable electromechaenergy conversion takes place. Therefore, the locked impedance chteristic of the actuator is measured and an equivalent circuit modderived from these measurements. It should be noted that the elecexcitation of the actuator produces not only a force, but also eddy currin the core/stator and even inside the wires. Eddy currents are munwanted losses, however, they could be used to implement a dameffect. In the design described, the eddy currents are treated as unwlosses. The effect of eddy currents on the system increases with incing excitation frequencies, leading to huge losses at high frequenThus, eddy currents constitute a major factor limiting the dynamics

Fig. 3.11:Mechanical Deformation of the Coil Former

37

Actuator Design

cur-on-

d bysure-d outarey anynical

theces,

ver,of the

electromagnetic devices. For this reason, an estimation of the eddyrents is obtained from a closer examination of the locked electrical cductance characteristics.

The impedance characteristics of the moving coil actuator are obtaineusing a precision LCR meter with a bias current source. For the meaments the coil is fixed to its core/stator. The measurements are carriefor several bias currents (0 A, 0.5 A, 1 A, 1.5 A, 2 A and 2.5 A) andshown in Figure 3.12. It can bee seen that the bias current has hardlinfluence on the impedance characteristic. Due to some mechamodes of the coil structure and the temporary attachment of the coil tocore/stator, the electrical transfer function shows four slight resonanthat is, two at approximately 120 Hz and two around 400 Hz. Howethese resonances have no impact on the electromagnetic propertiesdevice and for this reason are left out in the following considerations.

Fig. 3.12:Electrical Transfer Function

Am

plitu

de z

[Ohm

]

0

5

1 2 3 4 5 6

1 2 3 4 5 6

10 10 10 10 10 1010

10

10 10 10 10 10 10100

50

0

50

100

Phas

e z

[Deg

ree]

Frequency [Hz]

Frequency [Hz]

38

Electrical Model and Eddy Currents

hasetiveil

ase ~medalent

ing

veandher-oulde for

The complex impedance of the actuator shows an ohmic behavior (p~ 0) for low frequencies, due to the resistance of the wires, an inducbehavior (phase ~π/2) for frequencies up to 100 kHz, due to the coinductance, a resonance at 100 kHz, and a capacitive behavior (ph-π/2) for frequencies above 100 kHz, due to the capacitance forbetween the windings. On the basis of these observations, an equivelectrical circuit of the coil can be derived consisting of a resistorR, aninductanceL and a capacitorC as shown in Figure 3.13.

The impedance of this equivalent circuit is expressed by the followequation:

(3.5)

where:

The values forR, L andC are obtained by least square fitting the aboequation with the measured curve. Obviously, the equivalent circuitequation are only valid for the case that the coil is fixed to the core. Otwise, a voltage source, representing the back electromotive force, whave to be added. Furthermore, the equivalent circuit is only accurat

Fig. 3.13: Equivalent LCR Circuit

R

L

C

zR jωL+

1 ω2LC– jωRC+

--------------------------------------------=

R 4.8Ω=L 4.9mH=C 0.36nF=

39

Actuator Design

fectsd par-con-, the

lim-citiveltagearge

the

weren-

fre-d totudesusly

coil

lec-in thetionrac-out

ected

eringationhisuen-kHz,

frequencies below 300 kHz. For higher frequencies, the capacitive efbetween the windings and the layers have to be treated separately anasitic inductances have to be added, leading to an equivalent circuit,sisting of several resistors, inductances and capacitors. In additioninfluence of eddy currents would also have to be included.

Beside mechanical limitations, the usable bandwidth of the device isited by its electromagnetic properties. Because of the inherent capabehavior of the actuator for frequencies greater than 100 kHz, any voexcitation with a frequency above 100 kHz produces almost only chexchange currents. Therefore, the electromagnetic bandwidth ofdevice is limited to 100 kHz.

In the power range, required for the planar manipulator, switching poamplifiers are mostly used because of their efficiency. However, the mtioned capacitive behavior at high frequencies limits the switchingquency to 100 kHz. Switching frequencies above 100 kHz would lealarge charge exchange currents, as mentioned before, with amplimuch larger than the desired coil current magnitude. This effect serioimpedes the measurement requirements set for a good control of thecurrent.

Eddy currents are another main effect that can limit the dynamics of etromagnetic actuators. At high frequencies they cause huge lossescore and even inside the wires. In the shown electrical transfer func(Figure 3.12) dominating eddy currents below 500 kHz would be chaterized by exhibiting a strong damping of the natural frequency at ab120 kHz. The weak damping reveals that eddy currents can be neglat least up to 500 kHz.

It is easier to make an assessment about the eddy currents by consida loss function, which was measured by using a sweep sine excitwith an effective voltage of 1 V and which is shown in Figure 3.14. Tfigure shows that the loss function decreases monotonically for freqcies up to 200 kHz. Eddy currents can be neglected at least up to 100

40

Realization

asingainlyshortthe

instry.tiontlywithty of

because dominating eddy currents would be represented by increlosses. The increasing loss for frequencies above 200 kHz results mfrom the capacitance formed between the windings, which acts as acircuit at high frequencies, but part of it could already result frombeginning influence of eddy currents.

3.6 Realization

The application of fiber reinforced composites is strongly increasingvarious industrial fields, such as aerospace and the automotive induFiber reinforced composites are materials, which consist of a combinaof long continuous fibers and a matrix of plastic materials, mosthree-dimensionally cross-linked thermosetting resins. Comparedmetals the specific strength and stiffness with respect to the densi

Fig. 3.14:Loss Function @ 1V r.m.s.

10 10 10 10 10 10

10

10

10

10

10

10

1 2 3 4 5 6

-5

-4

-3

-2

-1

0

f [Hz]

P[W

]

41

Actuator Design

theamidn orelyhigh

pre-

rcedgoodro-assplifyte isas ach,

thodnd-at-

asedenercoil

d byepbyalina-

lu-ted

fiber reinforced composites are up to four times higher. Nowadays,most common materials for reinforcement are glass, carbon, and ar(aromatic amides) fibers. The fibers are oriented either in one directioin two or more directions as a woven or stitched fabric. The most widused, economical reinforcement in composites is E-glass. Whenstrength and toughness are required, carbon and aramid fibers areferred materials [STESALIT].

Based on these considerations, the coil former is made of fiber reinfocomposites. Carbon fiber has been discarded due to its relativelyconductivity, which could lead to eddy currents. The difficulties in pcessing aramid, which is difficult to cut, resulted in the selection of glfiber, which is more economical and easier to process. In order to simthe construction even further, epoxy resin-glass fabric-prepreg laminaused, which is easier to handle. Finally, a design is obtained, which hplate and coping consisting of approximately 20 fiber fabric layers eaand end plates consisting of approximately 35 layers each.

Several experiments have been carried out in order to find the best meto implement the coil windings. It has been tried to create the coil wiings during the lamination process of the coil former, by simply lamining them into the former. However, this approach leads to an incredifficulty in fabricating the coil. Furthermore, problems occur whremoving the finished coil former from the inner mould, as the formtends to be damaged. In addition, it is almost impossible to create awith well structured windings. The best results have been achievefirst producing the coil former without any coil windings. In the next stthe grooves for the coils are milled. Afterwards, the coils are woundusing a winding machine and glued to the coil former, delivering optimmanufactured coils. This procedure simplifies and speeds up the lamtion process.

The attachment of the coil former to the slide was first tried by using aminum inlets, which were laminated into the coil former and moun

42

Realization

und,en-as

e bych is

is

iretwo

dingeal-

are

onto a connecting piece. However, an alternative solution was fowhich simplified the realization and also yielded higher natural frequcies. In this realization, one of the two end plates of the coil former wmilled to obtain a flat surface. Afterwards, the attachment was madusing a linkage part, which covers almost the entire end plate and whimounted to the coil former by 9 screws.

One of the realized coil formers in conjunction with its linkage partshown in Figure 3.15.

The two coils of each coil former consist of 101 windings of copper wwith a diameter of 0.84 mm each, which are arranged in 3 layers. Thecoils are electrically connected, either in parallel or in series, depenon the characteristics of the employed power amplifier. In the actual rization they are connected in series.

One of the built actuators is shown in Figure 3.16. Its stators/corescommercially available fromETEL.

Fig. 3.15:Realized Coil Former

43

Actuator Design

asedbeennts

fiberab-ittle

ed as

A

3.7 Summary

The design and realization of a high performance actuator, which is bon voice coils, have been presented in this chapter. The design hasoptimized while taking special care to avoid nonlinearities, eddy curreand hysteresis effects. Furthermore, the coil former was made ofreinforced composites, more specifically, epoxy resin-glass fric-prepreg laminate, resulting in a structure with high stiffness and lweight.

The characteristics of the realized actuator design can be summarizfollows:

• Capable of delivering a force of approx. 178 N at a coil current of 8• Allows translational movements of up to 64 mm• Lightweight coil (coil former and windings) of approximately 800 g• First natural frequency at approximately 365 Hz• Linear force-current relationship

Fig. 3.16:Realized Actuator

44

4 Experimental Setup andIts Components

dingw theented,ree

bo-coilined,

uatorf theThe

s ande-in

ibed

Following the actuator design, which has been detailed in the precechapter, this chapter discusses the experimental setup. It shows hoconcept and basic design ideas, presented in Chapter 2, are implemresulting in a high performance planar linear direct drive, with thdegrees of freedom.

At the beginning of this chapter the mechanical configuration of the laratory prototype is presented in Section 4.1. It is shown how the voiceactuators, whose realization has been detailed in Chapter 3, are combin order to realize a system which is based on the proposed actarrangement outlined in Chapter 2. Subsequently, the structure oemployed air bearing is shown and briefly discussed in Section 4.2.chapter continues with a description of the employed sensor systemuncovers important limitations, resulting from their utilization. Subsquently, a description of the employed controller hardware is givenSection 4.4. Afterwards, the entire experimental setup is briefly descrin Section 4.5.

45

Experimental Setup and Its Components

, ther 2.reesnted,ctua-

t onlyve-beeneencon-aineaseveore,-cur-

upled inof ae isse of

reci-ove-

he

thets of

4.1 Mechanical Configuration

This section details the mechanical setup of a planar manipulatorunderlying concept of which has previously been derived in ChapteThis approach is based on a planar linear direct drive with three degof freedom, supported by a planar air bearing. Two setups are presewhich are based on the suggested rectangular triple and quadruple ator arrangement, respectively.

These two arrangements require a special actuator design, which noallows movements in the actuated direction, but which also allows moments perpendicular to it. Therefore, a special actuator design hasdeveloped, the principle, realization and properties of which have bdetailed in Chapter 3. This design consists of an arrangement of twoventional voice coils. In the field of fast and precise positioning the madvantage of voice coils is that only the lightweight coil moves, wherthe heavy stator/core is fixed. Therefore, it is possible to achiextremely high accelerations with relatively small forces. Furthermthe advantages of a position insensitive actuation and a linear forcerent characteristic ease the controller design.

These actuators are combined to implement the triple or the quadrplanar linear direct drive arrangements, which have been discusseSection 2.1. The coils are attached to a slide, which is moving on topgranite plate, while the stators are fixed to this granite plate. The slidsupported by a planar air bearing, as suggested in Section 2.2. The uan air bearing results in frictionless guidance, and thus, yields high psion movements. The employed planar air bearing permits free mments in theXY-plane, whereas movements inZ-direction and rotationsaround theX-/Y-axis are prevented. A more detailed insight into tdesign of this air bearing is given in Section 4.2.

The resulting triple actuator system configuration, which embodies alldesign aspects mentioned above, is shown in Figure 4.1. It consis

46

Mechanical Configuration

vingorefree

et-by ane per-

etryangu-ctua-f theily beation

three identical moving coil actuators, which are attached to the moslide. The advantage of this configuration is that its structure is mapplication-oriented as it allows the easy mounting of a tool at theside of its slide. The disadvantage of this configuration is its non-symmrical structure, the consequences of which have to be compensatedadvanced controller design. Despite this disadvantage, the achievablformance is still rather impressive, as will be shown in Chapter 5.

In order to avoid torsional stress and to increase the degree of symmof the structure, a fourth actuator can be added. This leads to the rectlar quadruple actuator arrangement shown in Figure 4.2. Since four ators are employed to control the three planar degrees of freedom oslide, this is a redundant system, however, this redundancy can eascompensated by the controller design. The advantage of this configuris the increased symmetry, leading to an increased controllability.

The cross-section of both configurations is shown in Figure 4.3.

Fig. 4.1: Triple Actuator System Configuration

47

Experimental Setup and Its Components

Fig. 4.2: Quadruple Actuator System Configuration

Fig. 4.3: Cross-Sectional View of the Entire System(1-Cores/Stators, 2-Moving Coils, 3-Slide, 4-Air Bearing,

5-Granite Plate)

432 51

48

Air Bearing

truc-such

um

nceearsms.rrorsthentalrd-us,s the-mentand

ionalatedforce,

-

ring

Only the triple actuator configuration has been realized, because its sture is more application-oriented. The design has been carried out ina way, that a fourth actuator, when needed, can be added with minimeffort, leading to a quadruple actuator configuration.

4.2 Air Bearing

The most important factor limiting the attainable precision performaof mechanisms is friction. Frictional forces have complicated non-lindynamic effects; they are caused by many different physical mechaniTypical frictional effects of controlled mechanisms are steady state eand limit cycles. However, frictional forces can largely be avoided byuse of air bearings. Unfortunately, air bearings exhibit the detrimebehavior that their stiffness varies in relation to the applied load. Accoingly, varying loads result in varying natural frequencies and thdegrade the attainable system dynamics. The design described in thisis avoids this serious problem by using a special actuator arrangeexcluding angular guides, which would be exposed to varying tensilecompressional stresses.

The planar air bearing is integrated into the slide, whose cross-sectview is shown in Figure 4.4. It consists of pressurized and evacuzones; evacuated zones are used to generate a defined preloadeddelivering high suspension stiffness in theZ-direction and about the rotational X-/Y-axis.

The lower surface of the slide along with some details of the air beadesign is shown in Figure 4.5.

49

Experimental Setup and Its Components

Fig. 4.4: Cross-Section of the Slide(1-Air Gap, 2-Grid Plates, 3-Compressed Air, 4-Vacuum,

5-Sensor Heads, 6-Slide, 7-Granite Plate)

21 3 4

7

6

5 5

Fig. 4.5: Bottom View of the Slide(1-Air Nozzles, 2-Vacuum Zones, 3-Grid Plate,

4-Pressure Zones)

1

43 3

2

50

Sensor System

signhisfor-

.2.

sen-stem.reci-com-

men-

ctioneoller

ationsed.oders-corre-ring

educ-

The realization of the air bearing is based on an existing reliable defrom ESEC SAand was implemented with experienced help from tcompany. In order to preserve the intellectual properties, no further inmation about this design can be given.

With respect to the general properties reference is made to Section 2

4.3 Sensor System

The essential elements in any controlled system are its sensors. Thesors largely determine the attainable performance of the complete syTherefore, they have to be chosen carefully. In order to obtain high psion and fast dynamics, the sensors need to posses high bandwidthbined with a high resolution and low noise.

The experimental setup employs two different sensor systems. Incretal two-coordinate grid plate encoders manufactured byHeidenhainareused as position sensors for the controller and are described in Se4.3.1. Acceleration sensors fromPCB Piezotronicsare used to analyze thsystem and to obtain the transfer functions necessary for the contrdesign. Furthermore, they are used in the feed-forward path of thestate-spacecontroller, as described in Section 5.3.

4.3.1 Position Sensors

Due to the unavailability of a sensor system delivering both theXY-posi-tion and the rotational angle with the demanded accuracy, a combinof two commercially available two-coordinate measuring systems is uThese sensor systems are incremental, two-coordinate grid plate encmanufactured byHeidenhain. Due to their interferential measuring principle, no mechanical contact exists between the sensor head and thesponding grating. The advantages of this two-coordinate measusystem, compared to using two separate linear encoders, include r

51

Experimental Setup and Its Components

an

s and. Theshiftola-

ofpro-ns ofh of

ulting

tinyndnals

tion of the Abbe error and the orthogonality errors. This results inoverall more accurate measuring device.

Each of these measuring systems provides a pair of sinusoidal signalone reference mark output as output for each measurement directiontwo sinusoidal signals of each pair have a 90 degree relative phaseand have a signal period of 4 µm. They are processed by digital interption electronics, resulting in a theoretical measurement resolutionapproximately 4 nm. However, because of both noise in the signalcessing electronics of the sensor systems and manufacturing limitatiothe gratings, the effective resolution is reduced to 10 nm. Thus, eacthese sensor systems provides an accurate measurement of theXY-posi-tion with a resolution of approximately 10 nm, as suggested byHeiden-hain. The rotational angle around theZ-axis is obtained from these twoXY-positions and the distance between the two sensor systems, resin a rotational measurement resolution of approximately 1 µrad.

Due to their underlying physical principle, these sensors allow only arotational displacement (about theZ-axis) between the sensor head athe grid plate. The relation between the amplitudes of the sensor sig(sinusoidal form) and the rotational displacement about theZ-axis isshown in Figure 4.6.

52

Sensor System

latese ofited

ctedd bye the

stem

ase

lide

This amplitude-rotation relationship is quite similar to a sinc2-function.Its generation can be explained by the Moiré effect between the grid pand the reference grid caused by the rotational displacement. Becauthe zeros in this function, the usability of these sensor systems is limto rotational displacements of less than ±1.5 mrad (±0.1°). This restriworking range implicates that the set point of the rotational angle, usethe control system, has to be kept to a constant value of 0°. Thereforcontrolled system allows only free positioning in theX- andY-directions(2 degrees of freedom), whereas the controller has to deal with a syhaving essentially three degrees of freedom.

The amplitude information is easily extracted from these 90° phshifted encoder signals (cos2(θ)+sin2(θ)=1). Consequently, it will be usedon-line by the controller to trigger an emergency stop in case the sgoes outside the allowed rotational range.

Fig. 4.6: Amplitude-Rotation Sensitivity

-0.6 -0.4 -0.2 0 0.2 0.4 0.60

100

200

300

400

500

600

700

Rotation [Degree]

Sig

nal A

mpl

itude

[mV

]

Noise

53

Experimental Setup and Its Components

tion,sis.

theiezo-“to

, dis-mea-

alizedver,ationargealtedrder

of thelow

earityrlye aatio)

rkiveesehich

nsi-s.

4.3.2 Accelerometers

The accelerometers have been chosen specifically for their applicawhich is not only for control purposes, but mainly for system analyThe employed modal analyzerSCADAS II[SCADAS91] used to obtain thetransfer functions, is optimized for piezoelectric sensors, which arestate of the art sensors for modal testing. These devices rely on the pelectric effect, as their name indicates (“Piezo” is greek and meanssqueeze”). If piezoelectric elements are strained by an external forceplaced electrical charge accumulates on the opposing surfaces. Thesurement of these ensuing charge variations requires some specielectronics, more specifically, it requires a charge amplifier. Howeonly dynamic events can be measured because of the limited insulproperties of piezoelectric materials and the input resistance of the champlifier. While step inputs will cause an initial output, this output signwill slowly decay according to the piezoelectric material or associaelectronic's time constant. This time constant corresponds to a first-ohigh-pass filter and is determined by the capacitance and resistancedevice and signal conditioner. This high-pass filter determines thecut-off frequency and measuring limit of the device [PCB].

Piezoelectric sensors are rugged devices and feature excellent linover a wide amplitude range. In fact, when coupled with propedesigned signal conditioners, piezoelectric sensors typically havdynamic amplitude range (maximum measurement range to noise rin the order of 100 dB.

The chosen accelerometers are instrumentational gradeICP® devicesfrom PCB Piezotronicswith a bandwidth of 1 to 3000 Hz. The trademaICP® denotes sensors with built-in microelectronics, which can drsensor signals over long cables without any loss in signal quality. Thdevices are based on a shear configuration of the piezo crystals, woffers a well balanced blend of wide frequency range, low off axis setivity, low sensitivity to base strain, and low sensitivity to thermal input

54

Controller Hardware

arethe

. Forectlyheirards

thisas onl con-ghlinearh isace

adyfor

tinghine

s aces

inule,

on-bushisliver-

Six of these accelerometers are embedded in the setup, threeemployed for measuring the movements of the granite plate whileremaining three are used for measuring the movements of the slidethe purpose of the system analysis, their output signals are fed dirinto the modal analyzer. For the purpose of controlling the system, toutput signals are sent to an additional signal conditioner and afterwdigitized for further usage by the controller.

4.4 Controller Hardware

The realization of a high performance system, as that described inthesis, places high demands on the mechanical configuration as wellthe control system. Despite the simple appearance of the mechanicafiguration, the requirement of high precision in conjunction with hiacceleration leads to a demanding control system. For this reason, astate space controller 40th order is chosen, the treatment of whicdeferred to Section 5.3. The digital implementation of this state spcontroller, which runs at a sampling frequency of 2500 Hz, alrerequires a continuous computing power of approximately 10 MFlopsimplementing the controller itself. This excludes any overhead, resulfrom the real-time operating system, not optimally generated macinstruction code, time required for converting the analog inputs, etc. Aconclusion, the realization and control of the planar linear drive plahigh demands on the employed controller hardware.

A schematic overview of the employed controller hardware is givenFigure 4.7. The controller hardware consists of a processor modencoder interpolation/counter card, signal conditioner including A/D-cverters, D/A-converters, and power amplifiers. It is based on a VMEsystem, which is equipped with a MVME 2305 processor module. Tprocessor module employs a 300 MHz 604e PowerPC processor, de

55

Experimental Setup and Its Components

300

van-iz-ith

er

dersuntern

n ofec-am-

ondi-higheenoise.ncur-me,be

rs,als

earto

oxi-

ing a peak computing power of 540 MIPS, respectively more thanMFlops.

The software development has been carried out withXOberonas real-time cross development system, which is easy to use. However, its adtage of simplicity in use conflicts with the disadvantage of a poor optiming compiler, leading to a waste of valuable computing power, and wthe disadvantage of incompatibility withMatlab (Matlab offers the possi-bility of direct generation ofC-code, which would speed up the controlldesign process, if the generated code could be used on the target).

The sensor signals of the incremental two-coordinate grid plate encoare evaluated by the use of a special encoder interpolation and cocard from Heidenhain, capable of performing a thousandfold positiointerpolation and therefore, delivering a theoretical sensor resolutioapproximately 4 nm (effective resolution is 10 nm), as mentioned in Stion 4.3.1. This interpolation and counter card allows the concurrent spling of the position signals, supplied by all four encoders.

The sensor signals of the accelerometers are amplified by a signal ctioner, as mentioned in Section 4.3.2, and afterwards digitized byprecision 16-bit analog/digital converters. The 16-bit resolution has bchosen in order to avoid any problems associated with quantization nEach sensor signal has assigned its own converter, allowing the corent sampling of all channels without wasting valuable processing tiwhich would happen, if multiplexed analog/digital converts wouldused instead.

The gating of the actuators is done by utilizing modified HiFi-amplifiewhich have been altered in order to allow the amplification of DC-signand to include a current control. They excel in delivering a highly lintransfer function. Unfortunately, their output drive capability is limited4 A and 40 V. Therefore, they limit achievable accelerations to apprmately 30 ms-2.

56

Realized Experimental Setup

en, itmentlide,r air

d air,seen

4.5 Realized Experimental Setup

The realized experimental setup is shown in Figure 4.8. As can be seconsists of an arrangement of three voice coil actuators, the developof which was detailed in Chapter 3. These actuators are fixed to the swhich glides on top of a granite plate and is suspended by a planabearing. The flexible tubes, required for the vacuum and compresseand the wires, which are connected to the voice actuators, can also bein this figure.

Fig. 4.7: Control Hardware

D/A-Converter

Signal Conditionerand A/D-Converter

Encoder Interpolationand Counter

Power Amplifier

ProcessorModule

AccelerometerSignals

Incremental EncoderSignals

CoilCurrents

57

Experimental Setup and Its Components

fromon-nly,

islica-

tu-of

dis-orcetheirve-rfor-

In order to achieve optimal performance and to decouple the systemthe floor, it would be best to mount the granite plate on top of a large ccrete block, however, this solution is realizable for laboratory use oi.e. not for use in a production line. Therefore, the granite platemounted onto a bench by rubber elements instead, which is more apption orientated but with reduced vibration isolation capabilities. Unfornately, this approach introduces some low natural frequenciesapproximately 11 Hz. The use of these rubber elements results in aplacement of the granite plate of more than 1 mm when applying a fof approximately 200 N. Another disadvantage of these mountings isnonlinear damping, which makes it difficult to compensate the moments of the granite plate. Therefore, this decreases the overall pemance of the complete system as will be seen in Chapter 5.

Fig. 4.8: Triple Actuator Experimental Setup

58

Conclusions

sys-rads tolim-

),

beenas thatthreelatewellith

It should be pointed out that due to the fact that the employed sensortem allows only small rotational displacements of less than ±1.5 m(±0.1°), the set point of the rotational angle, used by the controller, habe kept at a constant value of 0°. As a result, the controlled system isited to free positioning in theX- andY-directions (2 degrees of freedomwhereas the controller has to deal with the full 3 degrees of freedom.

4.6 Conclusions

In this chapter, the experimental setup of the planar manipulator haspresented. This setup is based on the concept and basic design idehave been discussed in Chapter 2. It consists of an arrangement ofvoice coil actuators, attached to a slide, which glides on a granite pand is supported by a planar air bearing. Therefore, this setup issuited for applications, that require high precision in conjunction whigh speed.

59

Experimental Setup and Its Components

60

5 Control Design

flu-llers

The

. Infore,Sec-

own.

pre-ancesug-

The attainable system performance of the linear drive is largely inenced by the employed control system. Two types of discrete controwere realized in this thesis. The first one is an enhancedPD-controller,which employs a decoupling part in order to linearize the system.second one is astate-spacecontroller incorporating aKalmanestimator.The PD-controller is mainly used to compare thestate-spacecontrollerwith, which delivers, as expected, an improved performance.

The design of a control system relies on the knowledge of the systemother words it demands a good analytical model of the system. ThereSection 5.1 presents a detailed model of the plant. Subsequently, intion 5.2 the design and implementation of the discretePD-controller isdescribed and the obtainable closed-loop system performance is shIn Section 5.3, the realization of the discretestate-spacecontroller isdetailed and again the obtainable closed-loop system performance issented. This chapter ends with the conclusions, in which the performof both controllers is compared and some possible improvements aregested.

61

Control Design

ve athelvethe

ody,ionbasiseledcon-

odel,onox-fromvan-

ity,tionplic-del,lies

instem

rigid

nd,

5.1 Plant Modeling

In order to achieve optimal system performance, it is necessary to hagood analytical model of the plant. Three different ways to modelrealized system have been investigated in detail - the first two invoparametric models while the third one involves a numerical model. Infirst model the slide and coils are modeled together as one rigid bwhich is moving relative to an inertial frame. This is described in Sect5.1.1. The parameters of this model can be estimated on-line on theof an adaptation law. In the second model the slide and coils are modas separate rigid bodies, which are connected by flexible joints, eachsisting of a spring and a damper. This leads to a large nonlinear mmaking it difficult to identify the model parameters, and for this reasthis model was not investigated further. The third possibility is to apprimate the system as a linear state-space model, which can be derivedthe measurement of its transfer functions. This model has several adtages and is detailed in Section 5.1.2.

5.1.1 Single Rigid-Body Model

The main advantage of the single rigid-body model is its simplicwhich enables the implementation of an on-line parameter identificaalgorithm in order to evaluate its parameters. However, due to its simity, no natural frequencies of the system are contained in this mowhich limits the attainable performance, if the controller design reonly on this model. Instead, the single rigid-body model will be appliedthe feed forward path of the controllers to increase the obtainable syperformance, as will be shown in Section 5.2 and Section 5.3.

The slide and the coil formers are modeled together as one singlebody having a massm and inertiaJ (center of mass:S, position: (xs, ys),orientation:ϕs). The granite plate is considered as an infinite mass athus, is treated as the inertial frame. The active force vectors (F1, F2, F3),

62

Plant Modeling

rel-d byche-

rentver,rpo-thedif-have

eci-theratedns:

generated by the voice coil actuators, act on the rigid body and drive itative to the granite plate (inertial frame). Because the slide is supportea planar air bearing, no frictional effects need to be considered. A smatic representation of this model is given in Figure 5.1.

The employed voice coil actuators excel due to their linear force-curcharacteristics, facilitating the modeling and controller design. Howevariations in the magnetic properties of the magnets, which are incorated into the actuators, combined with the nonideal effects ofemployed power amplifiers and digital-to-analogue converters lead toferent stationary offsets and gains for each actuation channel. Theseto be included in the model in order to achieve higher positioning prsion. Now, by assuming infinite fast current control capabilities ofpower amplifiers, the absolute values of the forces, which are geneby the voice coil actuators, can be expressed by the following equatio

Fig. 5.1: Rigid-Body Model

F1

F2

F3

lx lx

ly m,J

x

ySj s (x , y )s s

0

63

Control Design

ulated

ody

(5.1)

(5.2)

(5.3)

where:

, , : Absolute values of the generated forces [N]

, , : Output voltages of the D/A converters [V]

, , : Offset voltages of the D/A converters [V]

, , : Gain factors of the power-amplifiers [A/V]

Based on these equations, the corresponding force vectors are calcby:

(5.4)

(5.5)

(5.6)

The Newton’s equations and the Euler’s equation of the single rigid bmodel are given by the following three equations:

(5.7)

f1 k1 u1 o1+( )⋅=

f2 k2 u2 o2+( )⋅=

f3 k3 u3 o3+( )⋅=

f1 f2 f3

u1 u2 u3

o1 o2 o3

k1 k2 k3

F1f1x

f1y

f1ϕssin

ϕscos⋅==

F2f2x

f2y

f2ϕscos

ϕssin⋅==

F3f3x

f3y

f3–ϕssin

ϕscos⋅==

f1x f2x f+ +3x

m xs··⋅=

64

Plant Modeling

17pli-

5.7tions

oth-i-

tion

and

am-

(5.8)

(5.9)

The allowable range of rotational motion is limited to ±0.1° (±0.00rad), due to the employed sensor system. Therefore, the following simfications are applicable, with almost no loss of precision:

(5.10)

After applying these simplifications to the Newton’s equations (Eq.and Eq. 5.8) and Euler’s equation (Eq. 5.9), the resulting set of equacan be easily solved to obtain the following dynamic equations:

(5.11)

(5.12)

(5.13)

Some of the parameters of this solution can be evaluated easily, whileers, such as the inertiaJ, require more effort in determining them. Addtionally, the massm and inertiaJ in particular, vary with almost everymodification of the experimental setup. Thus, an automatic identificaor an adaptive parameter estimation algorithm would be desirable.

There are many identification algorithms shown in the literatureresearch continues in this area. TheDynaNet-algorithm [BURDET97] wasfound to be a practical choice for the implementation of an on-line par

f1y f2y f+ +3y

m ys··⋅=

f1

l x xs+

ϕscos---------------⋅– f2

ly ys–

ϕscos--------------⋅– f3

lx xs–

ϕscos--------------⋅– J ϕs

··⋅=

ϕs 1 ϕscos⇒« 1 ϕssin 0≅,≅

u1

J– ϕs··

m ys ly–( ) xs··

m lx xs–( ) ys··⋅ ⋅+⋅ ⋅+⋅

2 k1 l x⋅ ⋅-------------------------------------------------------------------------------------------------------- o1–=

u2mk2----- xs

··⋅ o2–=

u3

J– ϕs··

m ys ly–( ) xs··

m– xs lx+( ) ys··⋅ ⋅⋅ ⋅+⋅

2 k3 lx⋅ ⋅----------------------------------------------------------------------------------------------------- o3–=

65

Control Design

nothmrmed

ans-:

is lin-onfol-

eter identification method due to its recursive nature, which doesrequire a large amount of computing power. However, this algoritrequires that the dynamic equations (Eq. 5.11-Eq. 5.13) are transfointo a single equation, which is linear in the parameter vectorw, which isgoing to be adaptively learned. In order to carry out the mentioned trformations, the solution (Eq. 5.11-Eq. 5.13) is first rewritten as follows

(5.14)

(5.15)

(5.16)

where:

These equations can now be expressed as a matrix equation, whichear in the parameter vectorw, as required for a successful implementatiof the DynaNet-algorithm. This matrix equation can be expressed aslows:

(5.17)

u1 w1 ϕs··

w2

ys ly–( ) xs··

l x xs–( ) ys··⋅+⋅

2 l x⋅---------------------------------------------------------------

w7–⋅+⋅=

u2 w5 xs··⋅ w7–=

u3 w3 ϕs··

w4

ys ly–( ) xs··

xs l+x

( )– ys··⋅⋅

2 l x⋅-------------------------------------------------------------

w8–⋅+⋅=

w1J

2 k1 l x⋅ ⋅---------------------–= w2

m2 k1⋅------------=

w3J

2 k3 l x⋅ ⋅---------------------–= w4

m2 k3⋅------------=

w5mk2-----= w6 o1=

w7 o2= w8 o3=

τ Ψ q q· q··, ,( ) w⋅=

66

Plant Modeling

tion,. A

ning

glers,

andted in

where:

The above modifications have led to a notation of the dynamic equawhich can be used directly to realize the adaptive learning algorithmsimple nonlinear adaptive controller has been implemented for obtaithe parameter vectorw. After successful learning the parameter vectorw,this parameter vector will be employed in conjunction with the sinrigid body model in the feed-forward path of the designed controllewhich will lead to a better system performance.

However, it has to be mentioned that the influence of the elasticdamped suspension modes of the granite plate itself has been neglec

w w1 w2 w3 w4 w5 w6 w7 w8

T=

q xs ys ϕs

T=

τ u1 u2 u3

T=

Ψ

ϕs··

0 0

ys ly–( ) xs··⋅ xs lx–( )– ys

··⋅2 lx⋅

------------------------------------------------------------- 0 0

0 0 ϕs··

0 0ys ly–( ) xs

··xs l+

x( )– ys

··⋅⋅2 lx⋅

-------------------------------------------------------------

0 xs··

0

1– 0 0

0 1– 0

0 0 1–

T

=

67

Control Design

thengle,sys-hanram-

trolcel-

mea-pace.in anter

tem.d lin-atorneds of

func-ela-

MO

iderm-s a

uralncies

the model. Furthermore, in order to learn the inertia, an excitation ofsystem is necessary, which also involves the rotational angle. This ahowever, has to be kept below ±0.1°. Because of this small range oftem excitation, the estimation of the inertial term needs more time tthat of the other parameters. As a result, a good estimate of all the paeters is obtained after a learning period of approximately 30 minutes.

5.1.2 Linear State-Space Model

In this section a continuous-time linearstate-spacedescription of the sys-tem will be derived. Therefore, the transfer functions between the convariables (input voltages of the power amplifiers) and the resulting acerations (translatory and rotational) of the slide and granite plate aresured. These measurements are obtained in the center of the worksThis results in the elimination of some position dependent terms andlinearization of the remaining position dependent terms around the ceof the workspace, which becomes the operating point of the sysAfterwards, these measured transfer functions are approximated anearized as linear transfer functions (consisting of a polynomial numerand denominator) in the frequency domain. Since the slide is positiorelative to the granite plate, the reduced order linear transfer functionthe granite plate are then subtracted from the appropriate transfertions of the slide, in order to obtain the transfer functions of the slide rtive to the granite plate.

The resulting relative transfer functions are composed into a linear MI(Multiple-Input-Multiple-Output) transfer function. Because of thestate-spacecontroller realization, a model describing the position of the slrelative to the granite plate is required, which can be obtained by perfoing a double integration of the previous MIMO model. This serves agood model for the planar manipulator.

The main advantage of this model is that most of the important natfrequencies of the system are included. Some of these natural freque

68

Plant Modeling

therssionoller,

per-

with-etersove-

g theunc-sfersfer

sing

in

trans-n in

ncystic-o thee 350orsove-andtheden-owl-

are due to the elasticity of the suspension of the granite plate, while oare due to the limited stiffness of the coils, slide and stators. The incluof the natural frequencies into the model allows the subsequent contrdesigned on the basis of this model, to achieve an enhanced systemformance.

The measurement of the open loop transfer functions is carried outthe aid of the modal analyzerSCADAS IIcombined with the accelerometer signals, which have been discussed in Section 4.3. Six acceleromare embedded in the setup: three are employed for measuring the mments of the granite plate while the other three are used for measurincorresponding movements of the slide. This leads to nine transfer ftions for the granite plate and another nine for the slide. These tranfunctions are approximated as high order continuous-time linear tranfunctions in the frequency domain, which has been carried out by utheFrequency Domain System Identification Toolboxof Matlab®. Subse-quently, their insignificant poles and zeros are removed, resultingreduced order linear transfer function representations.

Examples of the measured and approximated acceleration-voltagefer functions, describing the movements of the granite plate, are showFigure 5.2 (translatory) and Figure 5.4 (rotational). The low frequepoles and zeros at approximately 11 Hz and 30 Hz arise from the elaity of the rubber elements, which are used to attach the granite plate tbench. The sources of the higher frequency poles and zeros (abovHz) are difficult to identify, but they are probably caused by the statand the bench. The corresponding transfer functions describing the mment of the slide are shown in Figure 5.3 and Figure 5.5. The poleszeros at approximately 360 Hz result from structural oscillations incoils. The exact sources of the other poles and zeros are difficult to itify. The design of a control system, however, does not require any knedge of the source of a natural frequency.

69

Control Design

Fig. 5.2: Transfer Function of Actuator 1→ Translatory Accelerationin Y-Direction of the Granite Plate

10 100 1000

-40

-20

0

10 100 1000

-12

-10-8-6-4-2

0

Frequency [Hz]

Phas

e [r

ad]

Am

plitu

de [d

B]

ApproximationMeasurement

Fig. 5.3: Transfer Function of Actuator 1→ Translatory Accelerationin Y-Direction of the Slide

10 100 1000

-20

0

10 100 1000

-2

-

0

20

Frequency [Hz]

Phas

e [r

ad]

Am

plitu

de [d

B]

ApproximationMeasurement

70

Plant Modeling

Fig. 5.4: Transfer Function of Actuator 1→ Rotational Accelerationof the Granite Plate

10 100 1000

-40

-20

0

10 100 1000

-12-10

-8-6-4-2

0

20

Frequency [Hz]

Phas

e [r

ad]

Am

plitu

de [d

B]

ApproximationMeasurement

Fig. 5.5: Transfer Function of Actuator 1→ Rotational Accelerationof the Slide

10 100 10000

20

10 100 1000-2

-

0

40

Frequency [Hz]

Phas

e [r

ad]

Am

plitu

de [d

B]

ApproximationMeasurement

71

Control Design

thef thee toThe...)uts

c-MOown

As mentioned earlier the reduced order linear transfer functions ofgranite plate are subtracted from the appropriate transfer function oslide, in order to obtain the linear transfer functions of the slide relativthe granite plate, since the former is positioned relative to the latter.resulting relative acceleration-voltage transfer functions ( , ,are then composed into a linear MIMO transfer function with three inp(the input voltages of the amplifiersu1, u2, u3) and three outputs (theaccelerations , , ) as expressed by:

(5.18)

where:

The continuous-time linear relative position-voltage MIMO transfer funtion can be obtained from the linear relative acceleration-voltage MItransfer function (eq. 5.18), by performing a double integration, as shbelow:

(5.19)

where:

Gx''u1Gx''u2

xs··

ys·· ϕs

··

p'' Gacc s( ) u⋅=

p''

xs··

ys··

ϕs··

= Gacc s( )

Gx''u1Gx''u2

Gx''u3

Gy''u1Gy''u2

Gy''u3

Gϕ''u1Gϕ''u2

Gϕ''u3

=

u

u1

u2

u3

=

p G s( ) u⋅=

G s( ) 1

s2

---- Gacc s( )⋅=

72

Plant Modeling

q.The

ing

erosreci-wn

bberr ele-when

The continuous-time linear position-voltage MIMO transfer function (E5.19) is transformed into a state space representation of order 39.resulting model is illustrated in Figure 5.6, which shows the resultapproximated relationship betweenu1 (actuator 1) and the resultingY-position.

It should be noted that the modeling of the low frequency poles and zat approximately 11 Hz determines to a great extent the reachable psion, even if their effect seems insignificant in the transfer function shoin Figure 5.6. These pole-zero pairs arise from the elasticity of the rumountings between the granite plate and the bench. These rubbements cause a displacement of the granite plate of more than 1 mmapplying a force of approximately 200 N.

Fig. 5.6: Approximated Transfer Function Actuator 1 -> Positionof the Slide relative to the Granite Plate

10 100 1000

-150

-100

-50

-

0

Frequency [Hz]

Phas

e [r

ad]

Am

plitu

de [d

B]

10 100 1000

73

Control Design

ved,sys-th

n-

a-ford bysys-

ve.cking

ableper-a-

ired

5.1.3 Summary

In this section two models of the planar linear drive have been deriwhich are indispensable for the design of a high performance controltem. Thesingle rigid-bodymodel is used in the feed-forward path of bocontrol systems (PD-controller, state-spacecontroller). Thestate-spacemodel is used in the design of thestate-spacecontroller, layout of theKalmanfilter, and the gain-matrix. In the following sections, the two cotrol systems are detailed.

5.2 PD-Controller

The first realized control system is based on aPD-controller. The mainadvantage ofPD-controllers is their simplicity in design and implementtion. However, their achievable performance is limited, particularlynonlinear and coupled systems. Often, this limitation can be reducethe introduction of linearization and decoupling components into thetem.

This section details the design and implementation of an enhancedPD-controller, having the capability to control the planar linear direct driThe closed-loop performance is presented by discussing various tramovements along sinusoidally shaped translatory trajectories.

5.2.1 Control Structure

PD-controllers require linearization and decoupling components to enthe successful control of a nonlinear and coupled system. This isformed by theDecouplingblock, which is based on the dynamic equtions of a single rigid-body model (Section 5.1.1).

Furthermore, the utilization of aFeed-Forwardblock, which incorporatesthe dynamic equations of the single rigid-body model and the desacceleration of the slide ( , , ), allows a reduction of the deviationxd

··yd·· ϕd

··

74

PD-Controller

nts).

ion,car-

ionion

ur-ar in

nals.

oopr alimit

between the real and desired trajectories (especially for fast movemeThus, an improvement in the overall control performance is achieved.

The velocity of the slide has to be obtained by numerical differentiatsince the employed sensor system delivers only its position. This isried out by theFilter block, which will be discussed in Section 5.2.2.

The control structure of the complete enhancedPD-controller, shown inFigure 5.7, was implemented as a discrete control system.

5.2.2 Filter

As mentioned earlier, the velocity is obtained by numerical differentiatof the position of the slide. However, the differentiation of the positsignal also amplifies any noise (including the quantization noise). Fthermore, the structural natural frequencies of the coils and slide appethe position signals and, thus, also appear enlarged in the velocity sig

These effects lead to an oscillation or even instability of the closed-lsystem for large values ofP andD. These large values are necessary fogood control performance, and thus, the mentioned effects strongly

Fig. 5.7: PD-Controller with Feed-Forward Path

PD-Controller

+

+

ϕx, y,.. .

x, y, ϕ,

Σ

Decoupling

Plant

Filter

FeedForward

x, y, ϕu , u , u1 2 3

x ,d d dy , ϕ. ..x ,d y ,d dϕ

x ,d y ,d dϕ.. .. ..

75

Control Design

t theese

s fil-th.

his

the attainable performance. Consequently, it is indispensable to limibandwidth of the differentiation, in order to reduce the impact of theffects.

Therefore, the velocities are obtained by using a first order high paster, which calculates the derivative of the position with limited bandwidThis filter has a cut off frequency of 100 Hz. The transfer function of tcontinuous time filter is shown in Figure 5.8.

The continuous-time transfer function of this filter is expressed by:

(5.20)

Fig. 5.8: Transfer Function of the Filter used for the Derivative

1 100 1000

40

20

0

1 100 1000

/2

0

Frequency [Hz]

Phas

e [r

ad]

Am

plitu

de [d

B]

0.1

0.1 10

10

60

GFilter

628.31s--- jω⋅ ⋅

628.31s---⋅ jω+

---------------------------------=

76

PD-Controller

nta-

tep-to-andby

step

tingon-

theed byow-vior,ecifi-zeded byult-

outThe

This continuous-time filter had to be transferred into thez-space (discrete-time), because of the time quantization caused by its digital implemetion.

5.2.3 Trajectories

In general, the design of a controller can be optimized for smooth sresponses with no overshoot, but with limited ability to follow trajecries, or for fast transient behaviors with small steady state errorsimproved trajectory tracking. The latter is, however, accompaniedlarge overshoots for excitations containing high frequencies (e.g.responses) and increased positioning noise.

The intended use of the system for wire-bonding or assembly/mountasks, requires the ability to follow fast trajectories. Therefore, the ctroller design has to be optimized for fast transient behaviors, despiteassociated disadvantages. The excitation of overshoots can be reducusing trajectories, that are optimized for a low-frequency spectrum. Hever, generating such trajectories displaying a time-optimal beharequires an advanced path-planner. Therefore, only a simple, not spcally time-optimal trajectory generation algorithm has been realiinstead. The trajectories are generated as sinusoids, which are filterlow-pass filters of second order with a cutoff frequency of 100 Hz, resing in low-frequency trajectories.

The discussion of the closed-loop system performance will be carriedfor five trajectories, which are generated by the above algorithm.main features of these trajectories are shown in Table 5.1.

77

Control Design

entsable

-ndhichmtlingthents,

an-f theajec-

ng

5.2.4 Performance

The performance of the system achieved with thePD-controller is illus-trated in Figure 5.9 to Figure 5.16, showing the responses for movemalong the sinusoidally shaped and low-pass filtered trajectories of T5.1, either inX- or in Y-directions, and the steady-state behavior.

A 5 mm translational movement in theY-direction along the desired trajectory of typeB is shown in Figure 5.9. During the first tenth of a secothe transient response shows an overshoot of approximately 1 µm wlater turns into a decaying oscillation with an initial amplitude of 2 µand a frequency of 11 Hz. Its amplitude reduces to 0.5 µm after a settime of 1 sec. This oscillation ensues from the flexible mounting ofgranite plate to the bench. This mounting, realized by rubber elemeresults in the natural frequency of 11 Hz. The magnified view of the trsient behavior, shown in Figure 5.10, indicates that, at the end-point odesired trajectory, the real trajectory lags 24 ms behind the desired trtory.

Figure 5.11 shows a 30 mm translational movement inY-direction alongthe desired trajectory of typeC. The transient behavior shows a decayi

Tab. 5.1: Trajectory-Types

Trajectory-Type

Distance TimeMax.

Acceleration

A 1 mm 28.3 ms 16.7 ms-2

B 5 mm 46.6 ms 22.8 ms-2

C 30 mm 94.8 ms 25.5 ms-2

D 30 mm 122 ms 13.0 ms-2

E 30 mm 500 ms 0.77 ms-2

78

PD-Controller

Itsnd-

ire

y ofootyingm.jec-

ure

cilla-al

ion0 nmtion-ideated

on-ffsetnetion.more

oscillation with an initial amplitude of 6 µm and a frequency of 11 Hz.amplitude reduces to 0.8 µm after a settling time of 1 sec. At the epoint, the real trajectory lags 20 ms behind the desired trajectory.

In Figure 5.12 a movement is shown, which is representative for wbonding applications. It constitutes a 1 mm translational motion inY-direction along a sinusoidally shaped and low-pass filtered trajectortypeA. During the first tenth of a second the resulting transient overshis less than 350 nm, however, afterwards it transforms into a decaoscillation of 11 Hz with a starting amplitude of approximately 450 nAt the end-point, the real trajectory lags 27 ms behind the desired tratory.

Motions with smaller acceleration are shown in Figure 5.13 and Fig5.14. These figures show 30 mm translational motions in theY- and X-direction respectively, along trajectories of typeD. Both movements showquite similar behaviors. The transient overshoot shows a decaying ostion of 11 Hz with an initial amplitude of 3 µm. At the end-point, the retrajectory lags 30 ms behind the desired trajectory.

A slow 30 mm translational motion in theY-direction along the trajectoryof type E is shown in Figure 5.15. No overshoot or decaying oscillatcan be observed, except for some positioning noise of less than 12peak to peak and a stationary offset of approximately 60 nm. The staary offset results from the stiffness of the flexible pipes, which provthe vacuum and compressed air for the air-bearing. This can be eliminby the introduction of an integrator into the controller design.

Figure 5.16 shows the steady-state behavior of the system. It demstrates a positioning noise of 55 nm peak-to-peak and a stationary oof approximately 5 nm. The stationary offset is different from the oshown in Figure 5.15, because this plot was derived at a different posiThe positioning noise is smaller, because the transient effect hadtime to decay and also because of the different position.

79

Control Design

Fig. 5.9: Translatory Motion of 5 mm in Y-Directionalong a Trajectory of Type B

0 0.5 1 1.5 2 2.5-3

-2

-1

0

1

2

3

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.52.497

2.498

2.499

2.5

2.501

2.502

2.503Zoomed:

3

Desired TrajectoryMeasured Trajectory

Fig. 5.10:Magnified View of the Translatory Motion of 5 mmin Y-Direction along a Trajectory of Type B

0.54 0.56 0.58 0.6 0.62 0.64

2.498

Time [s]

Y-Po

sitio

n [m

m]

2.501

2.5

2.499

2.503

2.502

2.497

Desired TrajectoryMeasured Trajectory

80

PD-Controller

Fig. 5.11:Translatory Motion of 30 mm in Y-Directionalong a Trajectory of Type C

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.514.992

14.994

14.996

14.998

15

15.002

15.004

15.006

15.008Zoomed:

3

Desired TrajectoryMeasured Trajectory

Fig. 5.12:Translatory Motion of 1 mm in Y-Directionalong a Trajectory of Type A

0 0.5 1 1.5 2 2.5-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.50.4994

0.4996

0.4998

15

0.5002

0.5004

0.5006Zoomed:

3

Desired TrajectoryMeasured Trajectory

81

Control Design

Fig. 5.13:Translatory Motion of 30 mm in Y-Directionalong a Trajectory of Type D

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.514.996

14.997

14.998

14.999

15

15.001

15.002

15.003

15.004Zoomed:

3

Desired TrajectoryMeasured Trajectory

Fig. 5.14:Translatory Motion of 30 mm in X-Directionalong a Trajectory of Type D

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

X-Po

sitio

n [m

m]

0.5 1 1.5 2 2.514.996

14.997

14.998

14.999

15

15.001

15.002

15.003

15.004Zoomed:

3

Desired TrajectoryMeasured Trajectory

3

82

PD-Controller

Fig. 5.15:Translatory Motion of 30 mm in Y-Directionalong a Trajectory of Type E

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

Y-Po

sitio

n [m

m]

3

1 1.5 2 2.514.9994

14.9998

15

15.0002

15.0006Zoomed:

3

Desired TrajectoryMeasured Trajectory

15.0004

14.9996

Fig. 5.16:Steady-State Behavior

Time [s]

Y-Po

sitio

n [n

m]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-40

-30

-20

-10

0

10

20

30

40

83

Control Design

es.av-

ionhmsign

llhas

f lin-s.ntlyce is

ationtory

ain-back

These plots show that the improvedPD-controller is strongly limited inits ability to follow fast trajectories (large lag) and to reject disturbancHowever, thePD-controller excels at offering a good steady-state behior.

5.3 LQG Controller

In contrast toPD-controllers, linearstate-spacecontrollers are able tocontrol coupled systems (MIMO) without demanding the implementatof any additional decoupling components. Furthermore, many algoritare known that facilitate the design of such controllers. The desdescribed in this section has been realized as aLQG-controller (LinearQuadratic Gaussian), whose underlying design algorithms are wedescribed in the literature and which deliver good results. The designbeen carried out by using theControl System Toolboxfor Matlab®.

It has to be mentioned that, generally, the obtainable performance oear state-spacecontrollers is also limited by unmodelled nonlinearitieHowever, due to the fact, that the nonlinearities are not predominapresent in the dynamics of the linear drive, the reachable performanstill high.

This section presents the design and implementation of such astate-spacecontroller. Similar to the discussion of thePD-controller, the achievedclosed-loop performance is evaluated on the basis of a closer examinof several tracking movements along the sinusoidally shaped translatrajectories, which have been characterized in Section 5.2.3.

5.3.1 Control Structure

Thestate-spacecontroller consists of aKalmanestimator (Kalmanfilter)and a gain-matrix (state-feedback regulator). The design of the gmatrix was carried out as a discrete-time linear quadratic state-feed

84

LQG Controller

was

gleeenuch,

ranite

atingrollerThetheardsust-

ty. If

regulator with output weighting. The required state-space observerdesigned as aKalmanestimator.

TheFeed-Forwardblock incorporates the dynamic equations of the sinrigid-body model and contributes to a reduction of the deviation betwthe real and desired trajectories (especially for fast movements). As sit increases the overall performance of the control system. TheFeed-For-ward block uses the desired acceleration of the slide ( ,, ), set bythe trajectory generator, and the measured accelerations of the gplate ( , , ).

The control structure of the completestate-spacecontroller is shown inFigure 5.17.

The inaccuracy of the state-space representation caused by approximthe nonlinear system as a linear state-space model, turns the contdesign into a play off between the transient and stationary behavior.more the transient behavior (lag and control accuracy) is weighted indesign process, the further some of the closed-loop poles move towthe right half plane in the pole-zero map, resulting in decreased robness and in increased stationary positioning noise or even in instabili

xd··

yd·· ϕd

··

xg··

yg·· ϕg

··

Fig. 5.17:Linear State-Space Controller with Feed-Forward Path

x , y , ϕd d d

. ..x ,d y , ϕd d

Gain-Matrix

++

x

Σ Plant

KalmanEstimator

Feed-Forward

x, y, ϕu , u , u1 2 3

Σx ,g y , ϕgg

.. .. ..

x ,d y ,d dϕ.. .. ..

++

85

Control Design

e sta-nd a

fornsla-e

-nseyingHz.dis-thed inctory

e-

nsesnsesnmset-veryling

the transient behavior is weighted less, the robustness increases, thtionary positioning noise decreases, leading to an increased lag alarger stationary offset.

5.3.2 Performance

Similar to the presentation of the performance reached by thePD-control-ler, the achieved performance of the system with theState-Spacecontrol-ler is illustrated in Figure 5.18 to Figure 5.26, showing the responsesmovements along the sinusoidally shaped and low-pass filtered tratory trajectories of Table 5.1 in theY-direction along with the steady-statbehavior.

A 5 mm translational movement in theY-direction along a desired trajectory of typeB is shown in Figure 5.18. The resulting transient resposhows an overshoot of approximately 350 nm and turns into a decaoscillation with a starting amplitude of 280 nm and a frequency of 11Its amplitude is reduced to 200 nm after a settling time of 1 sec. Ascussed earlier this oscillation originates from the flexible mounting ofgranite plate. The magnified view of the transient behavior, depicteFigure 5.19, indicates that the measured trajectory and desired trajeare a close match, showing no detectable lag.

Figure 5.20 and Figure 5.21 show 30 mm translational motions in thY-direction along trajectories of typeC. The difference between the two figures is that Figure 5.20 shows a movement in theY-direction forX=0 mm,whereas Figure 5.21 shows a movement in theY-direction forX=-25 mm.In both cases, during the first tenth of a second the transient resposhow overshoots of approximately 200 nm. Afterwards, the respotransform into decaying oscillations with a maximal amplitude of 650and a frequency of 11 Hz. Their amplitude reduces to 200 nm after atling time of 1 sec. The measured and desired trajectories matchwell, showing no detectable lag. The corresponding cross coup

86

LQG Controller

s

ire

ancay-xi-ore,

ure

ionand

-ningroxi-the

andby

ing arox-25,oiseand

between movements along theX- andY-axes displayed in Figure 5.21, iless than 1.5 µm and is shown in Figure 5.22.

In Figure 5.23 a movement is shown, which is representative for wbonding applications. It is a 1 mm translational motion in theY-directionalong a trajectory of typeA. The resulting transient response exhibitsovershoot of approximately 220 nm, which also transforms into a deing oscillation of 11 Hz, however, with a starting amplitude of appromately 170 nm and a stationary offset of approximately 30 nm. As befthe measured and desired trajectories match well.

A movement with less acceleration is shown in Figure 5.24. This figshows a 30 mm translational movement in theY-direction along a desiredtrajectory of typeD. The transient behavior shows a decaying oscillatof 11 Hz with a maximal amplitude of 280 nm. Again, the measureddesired trajectories match quite well.

A slow 30 mm translational motion in theY-direction on a sinusoidallyshaped and filtered trajectory of typeE is shown in Figure 5.25. No overshoot or decaying oscillation can be observed, except for the positionoise of less than 100 nm peak to peak and a stationary offset of appmately 20 nm. As already mentioned, the stationary offset results fromstiffness of the flexible pipes, which are needed to deliver vacuumcompressed air required by the air-bearing. It could be eliminatedintroducing an integrating part into the controller design.

Figure 5.26 shows the steady-state behavior of the system, indicatpositioning noise of 55 nm peak to peak and a stationary offset of appimately 25 nm. The stationary offset is different to that in Figure 5.because this plot was derived at a different position. The positioning nis slightly smaller, because the transient effect had more time to decayalso because of the different position.

87

Control Design

Fig. 5.18:Translatory Motion of 5 mm in Y-Directionalong a Trajectory of Type B

0 0.5 1 1.5 2 2.5-3

-2

-1

0

1

2

3

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.52.4994

2.4996

2.4998

2.5

2.5002

2.5004

2.5006

3

Zoomed:

Desired TrajectoryMeasured Trajectory

Fig. 5.19:Magnified View of the Translatory Motion of 5 mmin Y-Direction along a Trajectory of Type B

0.54 0.56 0.58 0.6 0.62 0.64

2.4992

Time [s]

Y-Po

sitio

n [m

m]

2.4998

2.4996

2.4994

2.5004

2.5002

2.5

2.499

Desired TrajectoryMeasured Trajectory

88

LQG Controller

Fig. 5.20:Translatory Motion of 30 mm in Y-Directionalong a Trajectory of Type C

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.514.9992

14.9994

14.9996

14.9998

15

15.0002

15.0004

15.0006

15.0008

3

Zoomed:

Desired TrajectoryMeasured Trajectory

Fig. 5.21:Translatory Motion of 30 mm in Y-Direction alonga Trajectory of Type C, but with an X-Offset of -25 mm

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.514.9992

14.9994

14.9996

14.9998

15

15.0002

15.0004

15.0006

15.0008

3

Zoomed:

Desired TrajectoryMeasured Trajectory

89

Control Design

Fig. 5.22:Cross-Coupling for a Translatory Motion of 30 mm inY-Direction along a Trajectory of Type C with an X-Offset of -25 mm

Time [s]

X-Po

sitio

n [m

m]

-25.002

-25.001

-25

-24.999

-24.998

0 0.5 1 1.5 2 2.5 3

Desired TrajectoryMeasured Trajectory

Fig. 5.23:Translatory Motion of 1 mm in Y-Directionalong a Trajectory of Type A

0 0.5 1 1.5 2 2.5-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.50.4994

0.4996

0.4998

0.5

0.5002

0.5004

0.5006

3

Zoomed:

Desired TrajectoryMeasured Trajectory

90

LQG Controller

Fig. 5.24:Translatory Motion of 30 mm in Y-Directionalong a Trajectory of Type D

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

Y-Po

sitio

n [m

m]

3

0.5 1 1.5 2 2.52.4994

2.4996

2.4998

2.5

2.5002

2.5004

2.5006

3

Zoomed:

Desired TrajectoryMeasured Trajectory

Fig. 5.25:Translatory Motion of 30 mm in Y-Directionalong a Trajectory of Type E

0 0.5 1 1.5 2 2.5

-15

-10

-5

0

5

10

15

Time [s]

Y-Po

sition[m

m]

3

1 1.5 2 2.514.9994

14.9996

14.9998

15

15.0002

15.0004

15.0006

Zoomed:

3

Desired TrajectoryMeasured Trajectory

91

Control Design

lag

on-

eing

All of these plots show, that thestate-spacecontroller excels at achievingan improved performance compared with thePD-controller. Its mainadvantage is the ability to follow fast trajectories almost without anyand to reject disturbances. Furthermore, it shows an improvedsteady-statebehavior.

5.4 Conclusions

In this chapter, the design and implementation of two discrete-time ctrol systems have been presented, namely a discretePD-controller and adiscretestate-spacecontroller combined with a discreteKalmanestima-tor. Their designs are based on two models, thesingle rigid-bodymodeland thestate-spacemodel.

The performance of thePD-controller is strongly limited, in particularwhen tracking trajectories possessing high dynamics (large lag) and b

Fig. 5.26:Steady-State Behavior

0 0.1 0.2 0.25 0.3 0.35

-80

Time [s]

Y-Po

sitio

n [n

m]

40

20

0

100

80

60

-100

-40

-60

-20

0.05 0.15

92

Conclusions

kingd atrs is

me aer,e,

subjected by external disturbances (oscillation). In contrast, thestate-spacecontroller delivers an enhanced performance; it excels at tractrajectories possessing high dynamics with nearly no time lag, anrejecting disturbances. The closed-loop performance of both controllesummarized in Table 5.2.

The performance of both controllers can be increased, if theFeed-For-wardblock is modified to include the natural frequencies originating frothe flexible mounting of the granite plate. However, this would requirnew analytical model and a modified identification algorithm. Howevthe time-lag of thePD-controller, constituting its main disadvantagremains unchanged.

Tab. 5.2: Performance Comparison(- denotes a small, undetectable difference)

Tra

ject

ory-

Type

PD Controller State-SpaceController

Max

.Ove

rsho

ot

Max

.Am

plitu

deof

Dec

ayin

gO

scill

atio

n

Tim

e-La

g

Max

.Ove

rsho

ot

Max

.Am

plitu

deof

Dec

ayin

gO

scill

atio

n

Tim

e-La

g

A 450 nm 450 nm 27 ms 220 nm 170 nm < 1 ms

B 2 µm 2 µm 24 ms 350 nm 280 nm < 1 ms

C 6 µm 6 µm 20 ms 650 nm 650 nm < 1 ms

D 3 µm 3 µm 30 ms 280 nm 280 nm < 1 ms

E - - < 1 ms - - -

93

Control Design

trol-nts,lop-lim-

The performance achieved by thestate-spacecontroller could beincreased, if an intelligent switching scheme between different conlers, which are optimized for different operating points and movemewould be implemented. However, this would require a real-time devement system, generating faster (more optimized) code and not beingited to approximately 1600 constants in one software module.

94

6 Conclusion

hasased

nge-manyuen-ceptcan

n ofationand

cur-fiberlown the

ple-

6.1 Summary

A new design of a planar linear drive with three degrees of freedombeen introduced and realized in the described project. The design is bon a novel concept using design ideas in the fields of actuator arrament and suspension. It has been shown that this concept eliminatesproblems connected with other solutions, such as varying natural freqcies, due to angular guides, and frictional effects. Therefore, this conenables the realization of a high performance manipulator, whichachieve high precision in conjunction with high speed. The realizatioa system, emerging from this concept, required the design and realizof a high performance actuator. This design is based on voice coilshas been optimized with special care in avoiding nonlinearities, eddyrents and hysteresis effects. Furthermore, the coil former is made ofreinforced composites, resulting in a structure with high stiffness andweight. The achievable performance of the system depends also oemployed control system. This dependence has been illustrated by immenting two different discrete control systems, namely aPD-controllerand astate-spacecontroller together with aKalmanestimator. It has been

95

Conclusion

tur-ut

x 60has

onalries,

lera-sesnsesnmset-ofg thethelesssientelowk to

narypti-bethe

ized

ichions.fac-

shown, that the performance of thePD-controller is strongly limited,especially for fast trajectories and disturbances. In contrast, thestate-spacecontroller delivers an enhanced performance; it excels by its disbance rejection and its ability to follow fast trajectories almost withoany time lag.

The experimental setup occupies a workspace of approximately 60mm2 and a sensor resolution of approximately 10 nm. Its performancebeen verified in the whole workspace by carrying out several translatimovements along sinusoidally shaped and low-pass filtered trajectoe.g. it allows movements of 30 mm within 94.8 ms, reaching an accetion of 25.5 ms-2. During the first tenth of a second the transient responshow overshoots of approximately 200 nm. Afterwards, the respotransform into decaying oscillations with a maximal amplitude of 650and a frequency of 11 Hz. Their amplitudes reduce to 200 nm after atling time of 1 sec. These oscillations result from the flexible mountingthe granite plate to the bench, which uses rubber elements. Increasinweight of the granite plate can reduce the maximum amplitude ofoscillation enormously. The cross coupling of these movements isthan 1.5 µm. For slower movements and smaller strokes the tranovershoots and the amplitude of the decaying oscillations reduce to b100 nm. The stationary positioning noise is smaller than 60 nm peapeak around a stationary offset of approximately 25 nm. The statioperformance could be increased, if the controller design would be omized for slower movements and if a vibration isolation system wouldused instead of rubber elements in order to decouple the system fromfloor.

Compared to other known industrial and academic solutions optimfor fast and accurate positioning ([KIM98], [MEISSER88], [OKAMURA 88]and [WAVRE98]), the realized setup excels at a transient behavior, whshows an at least four fold enhanced precision at similar acceleratThis precision has the potential to be increased further by more than a

96

Outlook

thes dueisola-

re arefur-

ys-ntlytheldtor

alsoter

herrfor-e ofils,

gs)ct,

us,

, thatur-

tor 4 without requiring essential modifications of the setup itself. Inliterature setups are known that are more precise for slow movementto the use of more precise sensor systems and advanced vibrationtion systems.

6.2 Outlook

Despite the impressive performance, which has been achieved, thestill many possibilities to enhance the positioning performance eventher. Some of those possibilities are now summarized:

• A simple possibility for increasing the precision of the complete stem would be to increase the weight of the granite plate (curre~100 kg). This would reduce the frequency and the amplitude ofdecaying oscillation. A granite plate with a weight of 400 kg woureduce the amplitude of the oscillation approximately by the fac2.5. The frequency would also be reduced. Furthermore, it wouldimprove the decoupling from the floor, which would lead to a betstationary behavior.

• An increased stiffness of the slide and the coils would lead to hignatural frequencies, and thus, would also lead to an enlarged pemance of the complete system. This could be obtained by the usaramid fiber instead of glass fiber for the manufacturing of the coand by a modified structure of the slide.

• The introduction of some damper windings (short circuited windininto the voice coil actuators would lead to a linear damping effewhich would increase the controllability of the system, and thwould also increase its performance but with increased losses.

• The use of an advanced control algorithm, such as H∞, could increasethe performance substantially. However, experiments have showna H∞-controller tends to exceed the rotational limitation of ±0.1° d

97

Conclusion

o aom-ifi-

erthetate

ing its start up. This requires, that the control structure is split intgain matrix and an observer part, which can settle, before the cplete H∞-controller is enabled. Unfortunately, this requires a modcation of theµ-Analysis and Synthesis Toolboxof Matlab®, whichwould require an in-depth analysis.

• Another possibility is an intelligent distribution of the windings ovall three coil formers in such a way that, at the operating point,control variables are independent of each other. This would facilithe controller design and increase the obtainable performance.

98

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104

Curriculum Vitae

Personal DataName: Bernhard Sprenger

Date of Birth: July 15, 1967Place of Birth: Altstaetten, SwitzerlandNationality: German

Education03/74 - 02/80: Elementary School, Heerbrugg & Widnau03/80 - 02/82: Junior High School, Widnau

03/82 - 09/86: Senior High School, Heerbrugg,Degree: Matura Type C (Mathematics)

10/87 - 05/93: Swiss Federal Institute of Technology, ZurichDegree: Dipl. Electr. Eng. ETH (M.Sc.)Awards: - ETH-Medal 1993

- Swiss SEV/IEEE Prize 1993 for final yeardissertation

10/94 - 02/99: Institute of Robotics, Swiss Federal Institute ofTechnology, Zurich

105

Curriculum Vitae

Professional Experience (most essential assignments)11/86 - 06/87: Union Bank of Switzerland, Altstaetten (SG)

Software developments and IT training of employees03/90 - 10/90: Mechatronics AG, Widnau

Soft- and hardware developments

04/93 - 09/94: Leica Geosystems, HeerbruggDevelopment engineer

106