ANALOG AND LABVIEW- BASED CONTROL OF A MAGLEV … IMECE2005_paper81600_sli… · ANALOG AND...

ANALOG AND LABVIEW-BASED CONTROL OF A MAGLEV SYSTEM WITH

NI-ELVISRISHABH SINHACooling Design CenterLarge Power Systems DivisionCaterpillar Inc.Mossville, IL 61552 [email protected]

MARK NAGURKADepartment of Mechanical &

Industrial EngineeringMarquette University

Milwaukee, WI 53201 [email protected]

IMECE2005-816002005 ASME International Mechanical Engineering Congress and Exposition

November 5-11, 2005, Orlando, Florida USA

Sinha & NagurkaIMECE2005-81600 2

Marquette UniversityMarquette University

View from 5th floor of Olin Engineering Bldg, Oct 27, 2005


Outline of PresentationOutline of Presentationo Objectiveso Backgroundo Maglev Testbedo Control Strategieso Simulation Studieso Experimental Studieso Summaryo Future Work


ObjectivesObjectivesUsing a low cost maglev system for

mechatronics education:

o Develop a linearized modelo Investigate classical linear controllerso Implement controllers using analog

circuits on NI-ELVISo “Implement” controllers using LabVIEWo Compare performance of controllers


What is Maglev?What is Maglev?o Maglev = Magnetic Levitation

o Levitate objects by electro-magnetic forces to cancel effect of gravity

o Established technology : o high-speed maglev vehicleso maglev bearingso vibration isolation systems, etc.


ExamplesExamples

Maglev train (China)(speeds of 430 km/h) Maglev Bearing

Levitron


Control StrategiesControl Strategieso Linear Control

o Classical PIDo PID with gain schedulingo Phase-lead, Phase-lago LQR, LQE, LQG, H∞, µ-synthesis

o Nonlinear Controlo On-offo PWMo Fuzzy-logico Neural-network controlo Feedback linearizationo Adaptive controlo Backstepping theory


Physical TestbedPhysical Testbed


Testbed PictorialTestbed Pictorial


o Infrared emitter and detector pair

o Acts as a variable resistoro Levitated object blocks

path, changes light intensity

o Linear behavior in operating region

Infrared (IR) SensorInfrared (IR) Sensor

sv xβ=

Displacement

Sen

sor O

uput

svxβ

=

IR Emitter IR DetectorLevitatedObject


Sensor and Controls LogicSensor and Controls Logico The emitter generates constant

light intensity.o The detector signal is amplified

and compared with a reference voltage.

o Difference of signals used to adjust current to electromagnet.o If the levitated object is too close to

electromagnet (detected IR signal too small), the current is reduced.

o If the levitated object is too far (detected IR signal too large), the current is increased.

IR Emitter IR Detector


ActuatorActuatoro Actuator is electro-

magnetic coil with steel bolt core

o Electromagnet obtained commercially

o FEA performed to check for magnetic saturation

o Power supply:18 V / 3 A


Maglev Temperature Expt.Maglev Temperature Expt.

Mechatronics Laboratory, Marquette University

Thermistor mounted to coil used to

measure temperature

during levitation


( ) 1o oL xL x Lx

= +

Nonlinear ModelNonlinear Model( ) ( ) ( )2

, ,2

i t dL xf x i t

dx= −

( ) ( )( )

( )( )

2 2

, ,2o o i t i tL xf x i t C

x t x t⎛ ⎞ ⎛ ⎞

= =⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

( ) ( )2

2 , ,d x t

m mg f x i tdt

= −

( ) ( )( )

22

2

d x t i tm mg C

dt x t⎛ ⎞

= − ⎜ ⎟⎜ ⎟⎝ ⎠


Linearized ModelLinearized Model

( ) ( ) ( )2 2

2 3

2 2, , ...o o o

o o o

i Ci Cif x i t C i t x tx x x

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ ⎝ ⎠

( ) 1, , ...of x i t f f= + +

( )2

, oo

o

if x i C mgx

⎛ ⎞= =⎜ ⎟

⎝ ⎠

( ) ( ) ( )2

1 2 3

2 2, , o o

o o

Ci Cif x i t i t x tx x

⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

( )2

2

d x tm mg f

dt= −

( ) ( ) ( )2 2

2 2 3

2 2o oo

o o

d x t Ci Cim mg f i t x tdt x x

⎛ ⎞ ⎛ ⎞= − − +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠


Linearized Model (cont’d)Linearized Model (cont’d)2

oo

o

if C mgx

⎛ ⎞= =⎜ ⎟

⎝ ⎠

( ) ( ) ( )2 2

2 2 3

2 2o o

o o

d x t Ci Cim i t x tdt x x

⎛ ⎞ ⎛ ⎞= − +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

( ) ( ) ( )2

22 3

2 2o o

o o

Ci Cims X s I s X sx x

⎛ ⎞ ⎛ ⎞= − +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

( ) ( )( )

2 2

2 22 2

3 3

2 2

2 2

o o

o o

o o

o o

Ci Cix mxX s

G sI s Ci Cims s

x mx

⎛ ⎞ ⎛ ⎞− −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠= = =⎛ ⎞ ⎛ ⎞

− −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠


Block DiagramBlock Diagram

( ) ( )( )

2 2

2 22 2

3 3

2 2

2 2

o o

o o

o o

o o

Ci Cix mxX s

G sI s Ci Cis m s

x mx

⎛ ⎞ ⎛ ⎞− −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠= = =⎛ ⎞ ⎛ ⎞

− −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠


Alternate Plant Transfer FunctionAlternate Plant Transfer Functiono The electromagnet

represented as a series combination of a resistor and inductor

o Consider sensor output as the system output

o Consider voltage to the electromagnet as the system input

( ) ( ) ( ) ( ), ,di t

v x i t Ri t L xdt

= +

( ) ( )( )

2

22

3

2

2

o

oso

o

o

CimLxV s

G sV s CiRs s

L mx

β⎛ ⎞−⎜ ⎟⎝ ⎠= =

⎛ ⎞⎛ ⎞+ −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠


Block Diagram IIBlock Diagram II

( ) ( )( )

2

22

3

2

2

o

oso

o

o

CimLxV s

G sV s CiRs s

L mx

β⎛ ⎞−⎜ ⎟⎝ ⎠= =

⎛ ⎞⎛ ⎞+ −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠


Open-loop AnalysisOpen-loop Analysis

( ) ( )( ) ( )824000

232 49.5 49.5oG ss s s

=+ + −

The root-locus has a pole in the right-half plane; the system is

unstable

Unstable


Control Block DiagramControl Block Diagram

o Error signal calculated as difference of setpoint and sensor output

o Error signal is input to controllero Bias is added to controller output, amplified,

and input to “maglev plant”o Controlled output is actual output


Control StrategiesControl Strategieso Proportional Control

o Controller output is proportional to error

o Lead-Lag Controlo Adds a zero and a pole to the

open-loop system

( )P PG s K=

( )P PG s K=

( ) ( ) ( )Leads zG s K K s z ps p+

= + →∞+

( )/Lead Lags zG s Ks p+

=+

00

Lead for z pLag for p z

< << <


Control StrategiesControl Strategieso PD Control

o Adds derivative term

o PID Controlo Integral term makes steady-state

error zero

( )PD P DG s K K s= +

( ) IPID P D

KG s K K ss

= + +


Proportional ControllerProportional ControllerProportional Controller acts

as a gain; cannot move poles into left-half plane

Proportional Controller by itself cannot stabilize

open-loop unstable system

Unstable


Lag CompensatorLag CompensatorLag Compensator

cannot move poles into left-half plane

Lag Compensator by itself cannot stabilize

an open-loop unstable system

Unstable


Lead CompensatorLead CompensatorLead Compensator

moves poles into left-half plane

Lead Compensator can stabilize open-

loop unstable system

Gain Margin: 13.2 dBPhase Margin: 15.8 deg

Stable


Lead Compensator ResponseLead Compensator ResponseStep ResponseSettling Time: 0.157sSteady-State Error: 0.24

Impulse ResponseSettling Time: 0.164s

(Zero at -100 rad/s, Pole at -1000 rad/s)


PD ControllerPD ControllerPD Controller


PD Controller can stabilize open-loop

unstable systemGain Margin: 2.61 dB

Phase Margin: 7.28 deg

Stable


PI ControllerPI Controller

PI Controller cannot stabilize

open-loop unstable system

PI Controller cannot move poles into left-half plane

Unstable


PID ControllerPID ControllerPID Controller


PID Controller can stabilize open-loop

unstable systemGain Margin: 3.42 dB

Phase Margin: 8.94 deg

Stable


PID Controller ResponsePID Controller ResponseStep ResponseSettling Time: 0.354sSteady-State Error: 0


(KP=0.68, KI=3.12, KD=0.0141)


Maglev Experimental StationMaglev Experimental Station



NI-ELVISNI-ELVIS

Mechatronics Laboratory, Marquette University, Oct 27, 2005

National Instruments’Educational Laboratory Virtual Instrumentation Suite


NI-ELVIS Prototyping BoardNI-ELVIS Prototyping Board


National Instruments’Educational Laboratory Virtual Instrumentation Suite


Analog Control with NI-ELVISAnalog Control with NI-ELVIS



Lead Compensator Analog CircuitLead Compensator Analog Circuit

( ) 5 1

5 6

5 6 1

1

D

sensor

sR CVG s R RV s

R R C

+= =

++


Lead Compensator Analog ImplementationLead Compensator Analog Implementation

R11

1k

0

Coil

18V

Q22N3055

RS 276-145

0

IR PhotoTransistor

IRDiode

0

R810k

R2

33k

R1150 Ohm 25W

15V 15V

R10

15k

RS 276-143

0

D1

1N5400

-

+

U1

LM7413

26

7 14 5

15V

-15V

C1

0.1u

R5

100k

R6

11k

0


PD Analog CircuitPD Analog Circuit

SUMMER

-

+

U4

26

3

DERIVATIVE

INVERTER

Verror

RP1

00

RD

-

+

U1

26

3

RP2

R5

PROPORTIONAL

R1

R4

R2

0

Vcontrol0

CD-

+

U2

26

3

-

+

U3

26

3

R3

( ) ( )( ) ( )2

1control

errorD

P

V s RPG s RD CD sV s RP

KK

⎛ ⎞= = + ×⎜ ⎟⎝ ⎠


Sensor Output

Setpoint

Proportional

Derivative

Bias

SummationController

Output

Error

DifferenceSensor

PD Analog Circuit ImplementationPD Analog Circuit Implementation

KP=0.68, KD=0.0141


PID Analog CircuitPID Analog CircuitSUMMER

CI

-

+

U5

26

3

CD

INVERTER

Verror

INTEGRAL

RP1

0

R3

0

0

-

+

U1

26

3

RP2

R5

PROPORTIONAL

R1

R4

R2

0

Vcontrol

RI

0

-

+

U2

26

3

-

+

U4

26

3

RD

DERIVATIVE

-

+

U3

26

3

R4

( ) ( )( ) ( )2 1 1

1control

errorD

P I

V s RPG s RD CD sV s RP RI CI s

KK K

⎛ ⎞ ⎛ ⎞= = + + ×⎜ ⎟ ⎜ ⎟×⎝ ⎠ ⎝ ⎠


PID Analog Circuit ImplementationPID Analog Circuit Implementation

Sensor Output

Setpoint

Setpoint for Antiwindup

Proportional

Integral

Derivative

Bias

Summation Controller Output

Error

Difference

Difference

KP=0.68, KI=3.12, KD=0.0141


Analog ImplementationAnalog Implementation

Power Transistor

Setpoint for Anti-windup

Setpoint

Bias

Power Resistor



LabVIEW-based ControlLabVIEW-based Control

IRDiode

RS 276-145

RS 276-143IR PhotoTransistor

0

R1150 Ohm 25W

0

DA

C 0NI-ELVIS

0

18V

Coil

R233k

Q22N3055

R312k

15V

R33

180

15V D4

1N5400

AC

H 2

0

LabVIEW - Maglev.VI


LabVIEW-based ControlLabVIEW-based Control

Power Transistor

Power Resistor

Analog Output



LabVIEW VI Front PanelLabVIEW VI Front Panel


LabVIEW VI ProgramLabVIEW VI Program


Levitation of AA BatteryLevitation of AA Battery



Levitation of Thin RingLevitation of Thin Ring



Levitation of Nested WasherLevitation of Nested Washer



Levitation of 9V BatteryLevitation of 9V Battery



Levitation of Various ObjectsLevitation of Various Objects



Current ComparisonsCurrent Comparisons

N/AN/A2.27N/AN/A639.48%50.95Large Bolt

N/AN/A2.19N/AN/A587.37%47.369-Volt Battery

1.75N/A1.791.78N/A542.53%44.27Splined Ring

1.261.371.341.361.27240.93%23.49Thin Ring

1.221.301.241.291.16174.17%18.89AA Battery

1.721.721.601.681.59106.53%14.23Bolt 2

1.371.391.321.361.2954.43%10.64Bolt

1.461.491.471.491.3429.75%8.94Nested Washer

LV - PIDLV - PDA - PIDA - PDA -Lead

CURRENT (A)% VariationFrom 6.8gMASS (g)OBJECT


Addition of Second CoilAddition of Second Coil



StiffnessStiffness


PD Controller ResponsePD Controller Response


SummarySummaryo Developed nonlinear and linearized modelo Conducted simulation studies to compare

controllers and select gains o Implemented PID-type controllers using analog

circuits with NI-ELVIS boardo Developed software-based controllers using

LabVIEW o Compared "hardware” vs. "software" based

controllers o Added second coil for determining stiffness and

system responseo Tested practical differentiator and anti-windup

circuits


MovieMovie


ClosingClosingo Applied classical linear control

strategies to a linearized model of a nonlinear system

o Implemented analog controllers using NI-ELVIS

o Developed LabVIEW controllerso Can dynamically change controller

type and parameters and observe effect on system in real-time


Outline of PresentationOutline of Presentationo Objectiveso Backgroundo Maglev Testbedo Control Strategieso Simulation Resultso Experimental Resultso Summaryo Future Work


Future WorkFuture Worko Implement nonlinear and optimal control

strategies in LabVIEW & compare performance with linear control strategies

o Develop a detailed FEA model to optimize the shape of the electromagnet for maximum field strength

o Design an array of sensors to translate levitated object vertically.

o Add horizontal electromagnets for two degree-of-freedom system.


Future Work (cont’d)Future Work (cont’d)

o Add velocity sensor for controlled damping

o Develop more advanced modelo Include gyro-dynamics

o Include skin friction using a CFD model

o Test remote access to VI through internet

o Create a virtual reality model using Virtual Reality Toolbox o Visualization of simulation without actual

implementation

The EndThe End

Questions ...Questions ...


Movie of Levitated BallMovie of Levitated Ball


Backup Slides


Magnetic Field FEA ResultsMagnetic Field FEA Results

Using FEMM package


Practical DifferentiatorPractical DifferentiatorCN

-

+3

26

0

CDVin

RD

Vout

o A pole needs to be added to differentiator circuit for “roll-off” of high frequency response.

o Without additional pole, differentiator circuit just amplifies any high frequency noise signals.

o Need to filter high frequency signals from signal going to the differentiator.

o Capacitor, CN, added in the differentiator circuit

( )( )

( )( ) 1

out

in

V s RD sV s RD CN s

=× +


Anti-windup CircuitAnti-windup Circuito The integral circuit

integrates the error with respect to time

o If error is large & constant, e.g., when the object is not present, integral action will continuously increase until saturation

o Need an “anti-windup” circuit


System IdentificationSystem Identification

Transistor constantβF

V/mSensor gainβ

HCoil inductanceL

ΩCoil resistanceR

N-m2/A2Force constantC

AEquilibrium currentio

VVoltage supplied to electromagnetVin

mEquilibrium distancexo

kgMass of the objectm

SI UNITSDESCRIPTIONSYMBOL


SISO Design ToolSISO Design Tool


PD Controller ResponsePD Controller ResponseStep Response

Settling Time: 0.157sSteady-State Error: 2.15


(KP=0.68, KD=0.0141)


PID Controller ResponsePID Controller Response


Margin Plots for PD ControllerMargin Plots for PD Controller


Margin Plots for PID ControllerMargin Plots for PID Controller

ANALOG AND LABVIEW- BASED CONTROL OF A MAGLEV … IMECE2005_paper81600_sli… · ANALOG AND...

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