H, Hovering and Guidance Control For

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Proceedings of 2004 IEEElRSJ International Conference onIntelligent Robots and SystemsSeptember 28 -October 2,2004, Sendai, Japan

H , Hovering and Guidance Control forAutonomous Small-scale Unmanned Helicopter

Daigo Fujiwara,Jinok Shin, a nd Kensaku Hazawa

Gra dua te School of Science and TechnologyChiba University, Chiba 263-8522, Japan

Abstruct-This paper describes autonomous hoveringcontrol and horizontal guidance control with H , controllerand performancc vcrification with flight experimental re-sults for ih e hobh>--class mall-scale unmanned helicopter.A simple black-box system identificdon method wasapplied, and single-inputjsingle-output SISO) non-cross-coupling stable models were obtained. Cross-validationresults showed close agreement in the respective outputsignals obtained by simulation and by experiment. At-titude control was designed as a minor feedbxk loopof praportional-integral (PI) blocks with a feed-forwardcompensator for improvement of referencefollowing per-formance. An H horizontal velocity control system wasconstructed as an outer feedback loop of an attitudecontrol. The H , controllers were designed in the frequencydomain using four closed-loop control specificalions andwere repeatedly tuned according to the time domain specifi-cations. Position control was constructed by a proportional-derivative PD) controller serving as an outer feedback loopof If, horizontal velocity control. In the flight experiments,hovering performance within a 1-m diameter circle and 15-m square point- twpoint horizontal guidance control wereachieved. Good consistency between experimental data andsimulation data demonstrates the high accuracy of themodels and the adequacy of the modeling method.

I. Introduction

A small-scale unmanned helicopter offe rs many a d-vantages, including low weight and the ability t o flywithin a narrow space. From the viewpoint of flightoutside the operator's range of direct observation andreduced labor: autonomous control technolom is indis-pensable, and research of this type has been popular inrecent years. Our research group has been conductingresearch on autonomo us flight control of a hobby-classsmall-scale unmanned helicopter (shown in Fig.1) forfour years, and we have already completed developmentof basic control system hardware [ l ] . n this paperwe describe autonomous hovering control and guidancecont rol of the above-mentioned small-scale unmannedhelicopter by identified mathematical model-based H ,

control theory.Modeling methods are roughly classified into threecategories: 1) the anall-tical approach, 2) the systemidentification approach, and 3) the numerical approach.Eac h of th e above-described approaches has advantagesand disadvantages. In addition to modeling, manymethods for control system synthesis exist which arebased on mathematical models. A good autonomous

Kenzo NonamiFaculty of Engineering

Chiba University, Chiba 263-8522, JapanEmail: nonamiC?faculty.chiba-u.jp

control method for small-scale helicopters has notyet been established, and several research groups arecurrently trying to establish various modeling andautonomous control methods.

Few studies have successfully verified control perfor-mance through flight experiments. For example, syste midentification and H , control around the yawaxis has

been described for a large-scale helicopter in [3]. Six-degree-of-freedom modeling by analytical formulationassisted by system identification and pro portional-integral-derivative PID) control has been describedfor a 43 kg helicopter in [4 ] ; [5]. In addition, H,control and gain-scheduled control h ave been de scribedin separate reports [6],[7]. The low number ofsuccessfulflight experiments illustrates the difficulty in modelingand control design. Especially, in the case of pplyingadvanced control theories, control performance is w n -sidered to depend so heavily on modeling accuracy thatmost trials of advanced horizontal guida nce control ofsmall-scale helicopters have resulte d in failure. Stabi-lizing such helicopters is inherently difficult because ofthe complex dynamics and low inertia of small-scale

helicopters.This study aims at performance verification withflight experimental re sults, applying H , control theoryto horizontal guidance control, with models given bythe simplest methods possible. First, the modelingprocess a,nd its verificat.ion are shown: a simple black-box system identification method without any hcli-copter dynamics structure was applied, which can beeasily applied to various systems, and four-degree-of-freedom DOF) sirrgle-input/single-output SISO)models including t,wo attitude models and two horizon-tal movement models were obtained. Second: controlsystem design is explained: after a minor feedbackloop of proportional-integra-derivative (PID) attitudecontrol ms designed, an H horizonta l velocity control

system was constructed as an outer feedback loop.The H , controllers were designed in the frequencydomain using four closed-loop control specificationsand were repeatedly tuned according to the timedomain specifications. Position control was constructedby a proportional-derivative PD) controller serving asan outer feedback loop of H , horizonta l velocity con-trol. Finally, control performance verification through

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flight experiments is explained: hovering performancewithin a I-m diameter circle and square point-tc-point horizontal guidance control were achieved. Goodconsistency betae en experimental data and simulationdat a demonstrates the high accuracy of the models andthe adequacy of the modeling method.

Fig. 1. HlROBO SF40 autonomous helicopter and bodyfixedcoordinates: main rotor diameter = 1 790 mm, maximum lift =17.5 kgf, quipped with 4 k c asoline engine.

11. Mathematical modeling by system identificationmethod

A. Attitude modelsInputJoutput signals of the identified model P,,

are to be assigned to the control command for aservomotor U ( U # , u g ) and a ttit ude angular velocity 4,4 espectively. The relation between att itu de angularvelocity and attitude angle was assumed to be that ofan integrator 11s.Fint ly, input/output signals shouldbe obtained by the identification flight experiment.

Since nonlinearity of th e servo motor s is consideredsufficient to prevent the excitation of the dynamicmodes of the helicopter, a chir plike frequency-changingsignal has been selected as an input signal rather thana binary signal such as hf-series pulses. Because thefuselage should be as stable and stationary as possibleduring an experim ental flight of long duratio n, humanoperation assisted safety flight of the helicopter. Iden-tification results are shown below. Fig.Z(a) representsthe frequency domain componerit of both the input andout put, and shows tha t excitation was Sufficient in theband up to 5 [ H i ] . n addition, Fig.P(b) shows a highcoherence of u p to 5 [ H z ] ,which is sufficient for theidentification of the model in this band.

Second, acquired input/output data should be pre-

processed. As seen in Fig.l(a), the frequencpdomainresponse of the ou tput sig nal has a large peak a t 2.5[ H i ] which seems to be caused by the 1st resonancemode. Therefore, the signals have been passed throug ha low-pass filter having a c ut-o ff frequency of 5 [Hz](to provide a sufficient margin for 2.5 [ H z ] ) ,as wellas trend removal. Next, an appropriate identificationalgorithm should be chosen: a simple auto-regressive

,....I . I

a) Spectrum (b) Coherence

Fig. 2. Analysis of the attitude identification data.

exogenous Am) lgorithm was applied. An identifiedmodel obtained through an autwregressive exogenous

ARX) algorithm is normally represented as a polynwmial eq uat ion of the following form:

A(q)y(I;) = B ( q M I ; - 7 ~ h - ) (1)

Now.

A(q) = 1 +alq-' +. +a,,q-B(q) = 1 +biq-' + +bn,q- b (2)

q is a time-shifting operator. I is the time, y isthe output (= 4; 8). U is the input, r is the timelatency, and is white noise. In this case, the value5 was assigned to both n, and nb, and the valuecorresponding to four times the unity sampling timewas assigned to by estimat ing the time latencyincluded in the control system loop. P,,, was derivedas follows, in continuonstime domain, for the 4 axis:

3)655.4

s3 + 1 9 2 0 ~ ~ 307.2s + 4096=for t he 8 axis :

(4)166.4

P -a ~ s3 + 14.308*+ 157.3s 1331

These Pm.s are also shown in Fig 3

1 0 -

\

Fig. 3 .

Fig.4 shpws the result of crossvalidation with theidentified 4 axis of Pa,, and close agreement is observedin the respective output signals obtained by simulationand by experiment. U indicates that the value *600is equivalent to maximum control input in manualoperation.

Bode plot of the identified attitude models A,.

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10 20 10 40 50T m s I S 4

Fig. 4. Time historical zesult of crasbvalidation (for the attitudemodel Po,,).

B . Horizontal motion models

A helicopter moves horizontally by tiltin g i ts main

rotor (or attitude). The horizontal model to be iden-tified Pa) as attitude angle 8, 4 as input and hori-zontal acceleration x , y as output, because existenceof dynamics between this input and this output isconsidered possible; specifically, rotor-head dynamics ,aerodynamic effects, and so forth. An acceleration-tn-velocity model Pu) and a velocity-to-position model(Pd) are both given as a 1st order integrator l / s ) . nthis case; maintaining stable and safe flight conditionsduring the identification experiment is difficult, anda serious xcident could occur if the helicopter uvereexcited slightly. Therefore, without particular identi-fication experime nts, identification da ta were selectedfrom the mass record of past flights that had highcoherence values: in this case the selected da ta show

high coherence from 0.05 to 0.5 [ H z ] .Auto-regressiveexogenous (A RX) method mas selected as the identi-fication algorithm, and the parameters na, b: and rin Eqs.(l) and (2) were assigned the values 5, 5, and0, respectively. Pa s derived as follows, in co ntinu oustime domain, for the x axis :

0 . 3 0 8 ~ 2+0.243s 0.629pa = - 3 3 + . 4 w +3 . ~ 9 ~1.65 (5)

for the j i axis :

6 )0 . 2 ~ 0 ~ 20.0524s +0.337

= - s3 +1 . 0 3 ~ ~1.94s+ 1.01Th e model P, for the f &xis is also shoum in Fig.5; solid-line shows the model represented as Eq.(6) without the2nd resonance mode, which was eliminated from theinitially identified %order model shown by dashed-line.

Fig.6 shows the re sults of cross-validation wit h theidentified axis of Pa, and these results show closeagreement between the output signal obtained bysimulation and that obtained by experiment.

Fig. 5 .the $ axis).

Bode plot of the identified acceleration model Pa lor

2D I O O 100TI_ I-

Fig. 6. Time historical result of crossvalidation (lor theacceleration model Pa).

111. Control designA. Control system

A s shown in Fig.7, the guidance control system con-sists of att itud e control, horizontal velocity control, and

horizontal position control. Two control system areprovided; one for leftward-rightwrd motion concernedwith #, U, etc., and the other for forward-backwardmotion concerned with 8 , x , tc., and the two systemsare completely independent from each other. Blockswhose names are prefixed by IC are controllers, andA . . D are satura tion blocks.

Since an on-board small CPU executes control cal-culations , control blocks should be of as small order aspossible. Fu ture long-distance flight seems to requirethe elimination of horizontal position control; thehelicopter can maintain stable Right by employment ofgood horizontal velocity control. Therefore , H , controltheory is applied only for horizontal velocity control,and other control is based on the proportional-integral-

derivative (PID) method.B. Attitude cont.rol

Attitude angles 4 and 0 are controlled by aproportional-integral (PI) feedback loop with a notch-filtered derivative D) feed-forward block. Each gainN ~ S djusted by trial and error through numericalsimulation. Reference-following performance can be

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I - I

Fig. 7. Block diagram of the control sys tem

improved by the feed-forward block. K,, (notch filter)is a 2nd-order transfer f unction and its para meter s wereadjusted so that overshoot became small when lookingat t he bode plot of the closed loop transfer function.Control blocks have been derived as follows, for the daxis:

s2 +4.2s + 142s' 28s + 142ap = 15: K,i = 20 K,,d = 5 , K,, =

(7)for the B axis :

sz +5.4s +92s2 18s +9'K,, = 19; K,, = 24; Kod = 5 , K,, =

8 )\ I

Limiting values of satu rati on blocks A and B were givenas 3300 and * B O , respectively. Reference-followingcontrol can be achieved for reference signals up to 2[ H i ] under disturbance-free conditions.

C . Horizontal velocity controlThe block K , in Fig.7 co ntrols horizon tal velocity x

or y using attitude angle reference T O or T I as controlinput. H m ontrol theory was applied to control design.This section describes mainly the system for the ydirection.

Kv was designed by the closed loop frequency s h a ping method. Firstly, the generalized plant, which isequivalent to evaluation functions in H , design, wasset up as a four-block structure including two inputswj and two outputs zi i >j = 1 or Z , shown in Fig.8,that could evaluate four typical closed-loop transferfunctions. Blocks prefixed with I< ' re weightingfunctions. Each function J,j is considered to be aclosed-loop transfer function from wj t o z excluding

weighing functions. Scalar number y is normally anumber less than unity. The evaluation functions ofH , design could be represented as follows :

Secondly, the frequency domain design specificationfor each J, j should be given as follo~r-s:

i: To suppress infection by step disturbance, h ishould be shaped as 20 [dB/dec] below IO [radls],and /hl 0.1 at any point below lo-' [ rad ls ] .

2: To supprcss following error for referencc signal, 5 1 2should be shaped as 20 [dB/de c] below 10 [ rad ls ] , ndlJ121 < 0.01 at any point below lo- [ r a d l s ] .

press down the peak around 10 [radls], and at thesame time the gain of 5 2 1 should be small above 10'[ rad l s ] n order to ensure stabi lity in the high frequencyband.522: To ensure stability in the high frequency band , 5 2 2should be shaped as -20 [dB/dec] above IO [radls].

Thus, Jij are clearly classified into J l j , which yieldlower hand side specifications, and J z j , u-hich yieldhigher band side specifications. The border frequencywas determined around the first peak of Pa mentionedin t,he previous section; therefore,were both given as frequency-dependent weightingfunctions, and others W,,,I and 1Vinz were givenas constants. In addition, time domain specificationshould be given as follows:A t unity step reference: the peak of control inpu tshould be less than 4 [deg] and overshoot less than30 [ I, the time until that response crosses over thercfcrence should be about 3 [SIand the convcrgcncctime about 10 [SIAt unity ste p disturbance: t,he time at which controlinput reaches -1 [ d e g ] should be about 3 [S and theconvergence time about 10 Is], and the maximumvelocity error should be less t.han 0.3 [mls] .

Weighting functions were adjusted repeatedly untilthe closed-loop system achieved the above specifica-tions (y was adjusted to about 0.9). Equations ofweighting functions are as follows :

21. . .o suppress overshoot, JZ1 hould be shaped to

and

W,,i = 0.5, I,V


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so trial-and-error t,uning was abandoned even if thecontrol system couldn't achieve those specificationscompletely.

The bound of control command (block C n Fig.7)was given as + l o [deg] . n addition, an anti-windupfilter was also designed, which suppresses a controlcommand that exceeds the range 5 8 [deg](details areomitted from this paper).

D. Horizontal position control

A posit,ion controller controls horizontal position xor y while using horizontal velocity reference r, or ry ascontrol in put. The proportional-derivative PD) designmethod xis applied. Gain values were derived as Kpp= 0 .3 and Pd = 0.2 (see Fig.7 ), by trial-and-error

through numerical simulation. Satur ation of ~i and ~shown in Fig.7 as block D as given as *1.5 [ m / s ] .

IV. Verification of control performance by flightexperiments

Performance of the designed control system xmsverified by flight experiments of traveling control alonga 15 x 15 [ m ]horizontal square and hovering controlat the corners of the square.

Fig.10 shows the flight trajectory as viewed fromabove. Reference signals were giwn as target posi-tions at only four cornem of the square, without anywaypoints on the lines. No problems v ere encounteredin hori zontal point-tc-point movement. Cross-couplingeffects and altitude variations are considered to have

affected straggling from each s traigh t line of the square.Control precision during hovering at each corner waswithin a circle of about I-m diameter; this constitutesgood performance, as the helicopter appears to becompletely stationary when viewed from a distance of10 m. Fig.11 shows positions in time domain. Eachtransient response after reference change fits that ofnumerical simulation very well: the only difference

ISs .io -15 -1; -5 0

Longitude Iml

Fig. 10.contml flight).

Horizontal trajectory experimental result of guidance

T m l r i l

Fig. 11.position latitude) and eat- wes t position longitude).

Time historical experimental rsults of north-south

_ mi

Fig. 12. Time historical experimental results of horizontalYelocity.

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6 1

. . . Im 3m- r B

Fig. 13. Time historical experimental results of attitude angle.

between them is found in oscillatory response while thercference is maintaincd const ant. Fig.12 shows the re-sults of H , horizontal velocity control. Slow reference-following speed and large overshoot are some of thefactom that deteriorate position control performance.Long sampling hold and time delay included in globalpositioning system (GPS) d at a as well as disturbancesare considered to be the reasons why overshoot isgreate r in the experime nt tha n in numerical simulation.Improvement of the H , horizontal velocity controlsystem is indispensable for further improvement ofposition performance. The result of attitude control,shown in Fig.13, is very good. D urin g simulation: quasi-disturbance d (dv+ r d,,), which was calculated by theequation below, was added t o the input of the att itud emodel, for the axis :

becomes a n improper function and is unrealizable,his has been substituted for low band constant gain

of the actual one, with a low pass filter 1/(0.5s + 1)for ignoring high band components. d denotes thedifference of actual response from modeled dynamicsPa, , which is considered the true representation ofactual dynamics: 2 ~ as added for adjustment ofthe di sturbanc e gain, since the value of d calculated bythis equation usually becomes small.

V. Conclusions

In this paper, horizontal guidance control per-formance was verified experimentally, in the casewhere H , theory was applied to a hobby-classsmall-scale unmanned helicopter with models givenby the simplest possible methods. A simple system

identification method was applied to obtain singleinput/single-output SISO) mathema tical models with-out cross-coupling terms, and cross-validation resultshave proved that the models are good representationsof the actual dynamics. A control system was con-structe d from three nested loops: proportional-integral-derivative (PID) attitude control, H , horizontal ve-locity control, and proportional-derivative (P D) hori-

zontal position control. The H , closed-loop frequencysha ping meth od achieved low sensitivity in th e lowerband and low gain and overshoot suppression in thehigher hand, and the controller was tuned repeatedlyaccording to specifications given in tim e dom ain. Good

experi mental results were produced by a flight of point-topoint movement on a square trajectory and hover-ing at the corners. Furthermore, the similarity withresponse of numerical simulation has corroborated theadequacy of th e modeling method. For furth er improve-ment of control performance, referencsfollowing timeof Hm horizontal velocity control should be shortened,by tuning of the controller. In order to make use ofthe advantages of If, theury, further studies are t o beconducted to cnsure robust stability of thc helicopterby quantitative estimation of model uncertainty andthe H , robust stabilization design method.

Acknowledgements

Th e authors would like to express their deepest grat-itude to t he Futaba Corporation and Hirobo Corpora-tion fo r providing technical cooper ation and assistance.

References

[I] Fujiwara D., et al. Autonomous Flight Control ofHobby-Class Small Unmanned Helicopter (Report 1:Hardware Development and Verification Experimentsof Autonomous Flight Control System), Journal ofRobotics and hlechatronics, Vo1.15, No.5, Japan S-ciety of Mechanical Engineers, 2003, pp.537-545.

[2] Hazawa K., et al. Autonomous Flight Control ofHobbyclass Small Unmanned Helicopter (Report 2:Modeling Based on Experimental Identification andAutonomous Flight Control Experiments), Journal ofRobotics and hlechatronics, \b1.15, No.5 Japan Soci-e t y of Mechanical Engineers, 2003, pp.546-554.

131 Adachi S., et al. Antonomous Flight Control for aLargeScale Unmanned Helicopter - System Identifi-cation and Robust Control Systems Design -, Transac-tions oI I,he Institute oi Electrical Engineers of Japan,Society I), \b l . 121: No. 12 2001, pp.1278-1283.

[4] Mettler U.F., t al. Attitude Control Optimization for aSmall-Scale Unmanned Helicopter, Proceedings of theAlA.4 Guidance, Navigation and Control Conferenceand Exhibit, Denver, CO, August 14-17, 2000, AIAApaper 2000-4059.

151 Mettler B.F., Identification Modeling and Character-istics of Miniature Rotorcraft. K h e r Academic Pub-lishers, 2003.

[6] La Civita M.; et a l. Design and Flight Testing of a High-Bandwidth H Loop Shaping Controller for a RoboticHelicoptsr, Proceedings of the AIAA Guidance, Navi-gation and Control Conference, hlonterey, CA, August2002, Vol.2, pp.1478-1488, .41AA paper 2002-4836.

i] La Civita M., et al. Design and Flight Testing of aGain-Scheduled H Loop Shaping Controller for Wide-Envelope Flight of a Robotic Helicopter, Proceedings ofAmerican Control Conference, Denver, CO, June 4-6,2003, pp.4195-4200.

[SI Gavrilets V., t al. Nonlinear Model for a Small-SizeAcrobatic Helicopter, Proceedings of AIAA Guidance:Navigation and Control Conference and Exhibit, Mon-treal, Cimada, August 6-9, 2001, AIAA paper 20014333.

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