Design and real-time implementation of a multivariable gyro-mirror line-of-sight stabilization...

Fuzzy Sets and Systems 128 (2002) 81–93www.elsevier.com/locate/fss

Design and real-time implementation of a multivariable gyro-mirrorline-of-sight stabilization platform

K.C. Tana ; ∗ , T.H. Leea, E.F. Khora, D.C. AngbaDepartment of Electrical & Computer Engineering, National University of Singapore, 10 Kent Ridge Crescent,

Singapore 119260, SingaporebSeagate Technology International, 63 The Fleming, Science Park Drive, Singapore Science Park, Singapore 118249, Singapore

Received 5 January 2000; received in revised form 19 April 2001; accepted 15 May 2001

Abstract

Gyro-mirror line-of-sight stabilization platform is a nonlinear, multivariable and highly coupled system. It forms the basisof a wide range of practical instruments used for the purposes of sighting and targeting in both surface and airborne vehicles,which is capable of maintaining the sightline of a mirror when it is subjected to external disturbances. However, a spinninggyro has a property known as precession such that when a torque is applied to one axis, it will contrary to the intuitionof mechanics, and results the rotation in the direction of another axis. This behavior poses a problem in controlling theline-of-sight since movement about one axis will cause a coupled movement in the other. In this paper, an e9cient full-matrixfuzzy logic controller is designed and implemented for a practical nonlinear gyro-mirror line-of-sight stabilization platform.Both simulation and real-time experimental results demonstrate the e;ectiveness of the designed full-matrix fuzzy gyroscopecontrol system, which o;ers an excellent closed-loop response for the transient and tracking performances, with signi<cantreduction in the coupling e;ect against cross-axis interactions. c© 2002 Elsevier Science B.V. All rights reserved.

Keywords: Fuzzy control; Gyro-mirror; Genetic algorithms; Engineering applications

1. Introduction

Electro-optical (EO) sensors that are mounted onvehicles such as aircraft, helicopter and tanks areoften subjected to vibrations introduced by theseplatforms. These vibrations cause the line-of-sight(LOS) of the EO sensors to shift and resulting in se-rious degradation of the obtained image quality. The

∗ Corresponding author. Tel.: +65-874-2127; fax: +65-779-1103.E-mail address: [email protected] (K.C. Tan).

problem is even more pronounced for systems withhigh magni<cation property. One way of overcom-ing this drawback is to use a gyro-stabilization [1,7],which is capable of maintaining the sightline of a mir-ror when it is subjected to external disturbances. Theimage obtained is then reGected onto the lens of acamera that is less blurred because of the directionalstability provided by the gyroscope.Fig. 1 shows a schematic diagram of the gyro-mirror

LOS stabilization system. There are generally threemain components in the gyroscope:

1. A Gywheel and its motor and controller;

0165-0114/02/$ - see front matter c© 2002 Elsevier Science B.V. All rights reserved.PII: S 0165 -0114(01)00161 -0

82 K.C. Tan et al. / Fuzzy Sets and Systems 128 (2002) 81–93

Fig. 1. The schematic diagram of a passive line-of-sight stabiliza-tion platform.

2. Two gimbals that provide two-degree-of-freedomto the Gywheel. Inner gimbal provides movementalong the yaw axis and outer gimbal providesmovement along the pitch axis. Two torque mo-tors are used to control the pitch axis and the yawaxis;

3. A mirror that is geared to the inner gimbals througha 2 : 1 reduction drive mechanism.

As can be seen, the controllers in the gyroscopedrive the torque motor in the gimbals for tracking ap-plications. The Gywheel is driven by an AC motorand the angular velocity is kept as constant as possi-ble. To provide position=coordinate information, twosensors are used to measure the yaw and pitch anglein a two-degree-of-freedom con<guration. Before thegyro-mirror LOS system is used to track a speci<ctarget, it must be directed from the original startingposition to the desired direction. After that the systemshall be capable of maintaining the tracking even when

disturbances exist in the platform because of the gy-roscopic principle [16]. However, the same principleapplies when one wants to set the gyroscope from itsoriginal position to a desired position. The plant has atendency to return to the original starting position andthus makes the two angles highly coupled and hard tocontrol. Moreover, although an approximated mathe-matical model of the rigid-body dynamics is available,it does not include the e;ect of unmodeled dynam-ics or practical imperfections (non-parametric uncer-tainty) [7], which adds more challenges to the controlof such a multivariable nonlinear system.Concerning these di9culties and constraints, this

paper designs and implements a full-matrix fuzzy logiccontroller for a practical gyro-mirror LOS stabiliza-tion platform. Fuzzy logic control (FLC) is one ofthe emerging intelligent control techniques, which hasbecome increasingly popular and has gained consid-erable interest in the control community since early90s [5,18,21]. With the ability to provide high-levelreasoning of expert systems, FLCs are nonlinear con-trollers and are robust against plant uncertainties anddisturbances. In addition, it o;ers various advantagessuch as the ability to incorporate uncertainty and ab-stract nature inherent in human decision making intointelligent control systems. Unlike conventional con-trol schemes, FLCs are based on natural language andmake the most from all the available information onthe system such as human experts or sensors that pro-vide numerical measurements of the key variables.Since the <rst industrial application of cement-kilnprocess control [6], FLCs have been successfully ap-plied to many real-world control problems such as therobot control [17], motor control [10], automatic trainoperation [23], servo-loop control [8], crane control[20], aircraft control [2] and etc.The control performance of a FLC system is,

however, largely dependent on the selection of anoptimal fuzzy sets and fuzzy rule-bases that repre-sent the human expert’s interpretation of linguisticvariables. Di;erent membership functions determinedi;erent extent to which the rules a;ect the con-trol signal and hence the closed-loop responses. Foroptimal fuzzy control performance, the fuzzy setsand rule-bases for the FLCs are automatically deter-mined via a genetic algorithm (GA) [3]. Emulatingthe Darwinian–Wallace principle of “survival-of-the-<ttest” in natural selection and genetics, genetic

K.C. Tan et al. / Fuzzy Sets and Systems 128 (2002) 81–93 83

algorithms have been found to be very e;ective ande9cient in searching a poorly understood, irregularand complex space for optimization and machinelearning. Such an algorithm evaluates performancesof candidate controllers at multiple points simultane-ously leading to several globally optimized solutions,which is naturally well suited for the nonlinear andmultivariable fuzzy controller design optimizationin an usually multi-modal multi-dimensional searchspace [4,16,22].The rest of the paper is organized as follows: a

physical gyro-mirror LOS stabilization platform isstudied and a nonlinear gyroscope model is derivedin Section 2. Section 3 designs a full-matrix fuzzylogic controller for the nonlinear multivariable gyro-scope model via a genetic algorithm as well as thecomparisons with other control techniques. Section 4presents the real-time fuzzy control implementationresults upon a physical gyroscope platform, whichshows an excellent transient and tracking performancewith only minor coupling e;ect for both of the outputchannels. Conclusions are drawn in Section 5.

2. Gyro-mirror line-of-sight stabilization platform

2.1. Principle of the gyroscopic

As mentioned in the Section 1, the gyro-mirror LOSstabilization platform is a multivariable and highlycoupled nonlinear system that is widely used for sta-bilizing and tracking purposes. The word “gyroscope”refers to a variety of mechanisms each having in com-mon a rotating mass that provides an angular momen-tum. The gyroscope functions a stabilizer for trackingpointer in both yaw and pitch axes based on the princi-ple of gyroscopic, which has two important attributesnamely, precession and directional stability [14,19]:

(i) Precession. This physical phenomenon happenswhen a rotating mass is disturbed by a force. Thereaction of the system looks quite deceiving sincethe reaction force’s dimension is not con<ned by thedimension of the action force. Fig. 2 shows a massrotating about the z-axis. If two forces F parallel tothe y-axis on the yz-plane are applied to the system, itwould generate a coupling force M about the x-axis.However, this is only true if the mass is not rotating.

Fig. 2. Characteristics of the attribute of precession.

Fig. 3. A two-degree-of-freedom gyroscope system.

Instead, the system will actually react by rotating onthe xz-plane about the y-axis through an angle of �.(ii) Directional stability. A Gywheel spinning at

high-speed possesses good ability to stay in its ori-entation in inertia space despite the presence of largeexternal force. This is due to the large momentumgenerated by spinning the Gywheel. Fig. 3 shows aGywheel mounted in gimbal rings and spinning at ahigh speed. The orientation of the inner gimbals willbe <xed in space for any external disturbance in axes1 and 2 due to the constant momentum incurred. Ifthe magnitude of the momentum is constant, the direc-tional orientation is maintained. This directional sta-bility characteristic is usually employed in inertia andstabilization systems.

The method of passive stabilization [16] is em-ployed here to produce a stabilized platform for thenonlinear gyroscope control system. This methodessentially depends on the stability of the axis of ahigh-speed gyroscope and the extremely slow rate atwhich it deviates from its original orientation if theapplied torque is small. It utilizes the large angular


momentum of the Gywheel to directly stabilize theplatform, that is, the gyro itself provides the musclesfor the stabilization. The free gyro stabilized mirroris a system that uses passive stabilization to achievedirectional stability, which is adopted in this paper.

2.2. Nonlinear model of the gyroscope

As shown in Fig. 1, the gyro-mirror LOS stabi-lization platform has two coordinate axes (yaw axisand pitch axis), one tracking pointer (mirror) anda Gywheel. By de<ning the coordinate frames forvehicle=system, rotor, the inner gimbal, the outergimbal and the mirror, and applying the Lagrange’sequations of motion, a dynamic nonlinear model ofthe LOS stabilization platform can be derived and isgiven as follows:

M1() O1 + F1(; ) + G1(; ) = �1; (1)

M2() O2 + F2(; ) + G2(; ) = �2; (2)

where = [1; 2]T, with 1 and 2 being the an-gles of rotation about outer and inner gimbal axes;= [1; 2]T is the velocity vector corresponding tothe vector; �1 and �2 are the actuator torques, and3 is the velocity of the spin wheel. The functions inEqs. (1) and (2) are de<ned as follows:

M1 = (A+ D) + (B− D + H) cos2 2

+12(E + G) +

12(G − E) sin 2;

F1 =−(B− D + H)12 sin 22

+12(G − E)12 cos 2 + J 12 sin 2 cos 2;

G1 = J 23 cos 2;

M2 = C +F4+ H;

F2 =12(B− D + H)

21 sin 22

− 14(G − E)

21 cos 2 − J

21 sin 2 cos 2;

G2 = −J 13 cos 2;

Table 1Parameters of the nonlinear gyroscope model

Parameter Value Parameter Value

A 0:004 kg m2 F 0:0025 kg m2

B 0:00128 kg m2 G 0:00125 kg m2

C 0:00098 kg m2 H 0:0032 kg m2

D 0:02 kg m2 J 0:0025 kg m2

E 0:0049 kg m2 3 3000 rpm

where A denotes the moment of inertia of the outergimbal about g1 = v1; B; C and D represent the mo-ments of inertia about r1; r2 and r3 respectively; E; Fand G denotes the moments of inertia of the mirrorabout m1; m2, and m3 respectively; and H and J arethe moments of inertia of the rotor of Gywheel about r1and r3, respectively. Here, v; g; r and m stand for thecoordinate axes for the frames of the vehicle=system,outer gimbal, inner gimbal (rotor) and mirror, re-spectively. Since the system is naturally open-loopunstable, the method of time domain closed-loop iden-ti<cation was applied to identify the various param-eters of the nonlinear gyroscope model as listed inTable 1 [11]:

3. Development of fuzzy gyroscope control system

3.1. Full-matrix fuzzy control con6guration

The gyro-mirror LOS stabilization platform is anonlinear multivariable system with two inputs i.e.,torques for the yaw axis and pitch axis as well astwo outputs i.e., the yaw coordinate and pitch coordi-nate. It can be seen from the dynamic equations thatthe nonlinear gyro-mirror system exhibits strong in-teractions between its two channels as a result of therotation of the Gywheel. Further, there is a hard con-straint limit of 1 Nm for the two torque inputs of theplant. The overall control objectives are to achievegood transient and tracking performances with respectto step input commands despite the coupling e;ects,and to exhibit good disturbance rejection capability. Inthis paper, a full-matrix FLCs con<guration as shownin Fig. 4 is adopted in order to achieve good closed-loop performance and minimize the coupling e;ect inthe multivariable system. Here C11 and C22 are the


Fig. 4. The full-matrix fuzzy gyroscope control con<guration.

Fig. 5. The structure of a fuzzy logic controller.

two fuzzy controllers that provide good transient andtracking performances, while C12 and C21 are the de-couplers used to reduce the coupling e;ect betweenthe two channels. The mathematical equation of thefull-matrix FLCs con<guration can be written as,

[�1�2

]=

[C11 C12C21 C22

][1 − R12 − R2

]; (3)

where �1 and �2 are the controllers’ output; 1 and 2are the two outputs of the system.The basic structure of the fuzzy logic controller is

shown in Fig. 5, which has a fuzzy knowledge basethat contains two main types of information: (a) adata-base de<ning the fuzzy sets used by the inputand output variables, and (b) a rule-base which mapsfuzzy values of the inputs to fuzzy values of the out-puts. Here, a PD-like FLC is adopted, which is by farthe most popular FLC in the industry and is perfectlysuitable for servo systems [16]. Each of the FLCs hastwo input variables Error (e) and Derror (e). Erroris de<ned as the di;erence between the values of in-put reference and the channel’s output, whereas Der-ror is de<ned as the rate of change in e with respectto the time. Each of the input variables has <ve fuzzysets: Negative Big (NB), Negative Small (NS), Zero(ZE), Positive Small (PS) and Positive Big (PB). Tri-

Fig. 6. The fuzzy membership functions with Sugeno fuzzy in-ference.

angular membership functions are used in this paper,where each fuzzy set may be expressed in the formof (a1; a2; a3) representing the width and the centerof a triangle. This, however, results 104 parametersfor the 8 input variables in order to express a givensolution. A simpli<ed approach in de<ning the fuzzymembership function as shown in Fig. 6(a) is thusadopted, where each membership function is de<nedby just two parameters. Sugeno’s fuzzy inference [15]that is well suited for nonlinear dynamic systems isemployed here, which has a typical rule of the FLCsin the form of:

IF Error IS NB AND Derror IS NB THEN U = PB;

where the control command U is a Sugeno type offuzzy variable as shown in Fig. 6(b).

3.2. Automatic design of fuzzy control via geneticalgorithms

As addressed in Section 1, the selection of anoptimal parameter set of fuzzy rule bases and mem-bership functions that represents the human expert’sinterpretation of linguistic variables in FLC is essen-tial to guarantee an excellent closed-loop control per-formance. Di;erent membership functions determine


di;erent extent to which the rules a;ect the controlsignal and hence the closed-loop responses. Also, itis practically di9cult to transfer experts’ knowledgeto a fuzzy knowledge structure such as designingthe decouplers in a multivariable system. Since theprocedure of ‘trial-and-error’ selecting these fuzzyparameters is very tedious and time-consuming [16],a systematic approach based on a hybrid genetic al-gorithm is thus applied in this section to automatingthe design of the FLCs.Genetic algorithm is a polynomial algorithm that

improves tractability and robustness in global opti-mization by slightly trading o; precision in a nonde-terministic manner [3]. As illustrated in Fig. 7, suchan algorithm can “intelligently” explore, without theneed of a di;erentiable or well-behaved performanceindex, a noisy and poorly understood space at multi-ple points by a population of candidate solutions lead-ing to several globally optimized answers. For fasterconvergence and better accuracy, individuals in eachgeneration of the GA are further <ne-tuned by go-ing through a multiple-point local hill-climbing pro-cess. This hybrid approach results in a broader localexploration and overcomes the well-known weaknessof GA in <nding the exact optima at each generation[16]. Steady-state GA with tournament selection and

decimal coding is employed in this paper for rapid re-production and preservation of the diversity. Readersmay refer to Li et al. [9] for details of the algorithm.The information that is coded in the GA chromo-

somes for designing a complete FLC is the fuzzydata-base and fuzzy rule-base. The data-base includesall the information about the fuzzy sets’ parameters,whereas the rule-base represents the fuzzy rules usedin the fuzzy reasoning mechanism. The symmetricaltriangle membership function as shown in Fig. 6 isused to describe the fuzzy sets of the two input vari-ables, Error and Derror. This function only requirestwo parameters, �1 and �2 for each of the input fuzzyvariable. The same format is also applied to de<ne theoutput variable U by �1 and �2. The complete fuzzyrule-base thus consists of 25 fuzzy rules, and each ruleis coded by <ve possible integer values between 0 and4 to represent a speci<c fuzzy set of the output variableU . Here, the fuzzy rules accommodate 5× 5 possiblecontrol actions corresponding to the <ve fuzzy setsof Error and Derror. Therefore, the total number ofvariables for the full-matrix FLCs is 124. All these pa-rameters are coded into chromosome using the integer-based representation [16], where every individual is astring of integers instead of a string of binary num-bers that makes the GA easier to manipulate. The

Fig. 7. Genetic algorithm automating fuzzy control system design.


Fig. 8. A coded GA chromosome and its partition of the FLC.

Fig. 9. Convergence trace of <tness in FLC design optimization.

chromosome is divided into four parts correspond-ing to the fuzzy logic controllers of C11; C21; C22and C21, respectively. As illustrated in Fig. 8, eachpart contains a few subsections holding the necessaryinformation required in realizing the correspondingFLCs.The input patterns that are made of several steps as

similar to Tan et al. [16] are used in the FLC design.

The length of the simulation is set at 20 s and the stepinputs for 1 and 2 are injected at di;erent time in-stance as to reveal the presence of the coupling e;ectin the system. To evaluate performance of each GAdesigned FLC, a simple and e9cient <tness functionthat also includes the information of absolute deriva-tive of the error is used, which avoids the possibil-ity of oscillation and accelerates the rise time of the


system:

f=1

1 +∑n

i=0 (|e1(i)|+ |e2(i)|+ |e1(i)|+ |e2(i)|)i ;(4)

where n is the duration of the simulation in evalu-ating the design; i is the time index in simulation;e1(i) and e2(i) is the error on yaw axis and pitchaxis, respectively, between the measured signal andthe desired signal at simulation step i; e1(i) and e2(i)are the change-of-error on yaw axis and pitch axis,respectively. Note that the <tness for each channel ofthe gyroscope are summed up to reGect the overallperformance of the pitch and yaw axis outputs.Due to the large number of parameters to be de-

termined, the algorithm was run for 500 generationswith a population size of 250. The convergence traceof the <tness is shown in Fig. 9 and the <nal parame-ters for the GA designed FLCs are shown in Table 2and Fig. 10.As shown in Fig. 11, excellent transient and track-

ing performances are attained in both the pitch andyaw outputs, and very acceptable decoupling perfor-mance against cross-axis interactions is also achieved.Subject to the hard voltage limit of 1Nm, responses ofthe FLCs outputs are also shown in Fig. 11. As can beseen, the design o;ers a smooth control signal withoutoscillation or chattering except the minor disturbanceat the time when the coupling e;ects are taking place.For comparison, the GA designed FLCs for the samecon<guration but without the two decouplers are alsoincluded and shown by the dashed-line in Fig. 11. Asexpected, the full-matrix FLCs had performed betterand signi<cantly reduced the coupling e;ects of themultivariable system.

3.3. Automatic design of PID control via geneticalgorithms

Besides the fuzzy controllers, proportional-integral-derivative (PID) controller which is the most popularcontroller used in industry is also included in the studyfor performance comparisons. The PID controllers canbe described by

u(t) = K[e(t) +

1Ti

∫e(t) dt + Td

de(t)dt

]; (5)

Table 2Parameters of the <nal GA designed membership functions

FLC Error Derror U

C11 �1 = 1:0075 �1 = 2:2975 �1 = 2:4925�2 = 1:6950 �2 = 0:4425 �2 = 0:7925

C12 �1 = 1:7925 �1 = 2:1300 �1 = 2:2775�2 = 2:0005 �2 = 0:3175 �2 = 0:1975

C21 �1 = 2:3375 �1 = 2:2400 �1 = 2:2600�2 = 0:5050 �2 = 0:3400 �2 = 1:4325

C22 �1 = 0:4300 �1 = 2:4925 �1 = 2:2250�2 = 1:9550 �2 = 0:1200 �2 = 0:6675

Fig. 10. The <nal GA designed fuzzy rule bases.

where u(t) is the controller output and e(t) is the errorsignal.Similar to the fuzzy controllers, GA is used to de-

sign a PID controller for the gyro-mirror line-of-sightstabilization system, i.e., to determine the parametersof K , Ti and Td in Eq. (5). Since the gyro-mirror sys-tem is multivariable, a MIMO con<guration of full-matrix PID controllers with a total number of 12 pa-rameters, is used in the design. The same <tness func-tion of Eq. (4) and similar genetic parameter settingsused in Section 3.2 are applied to the design automa-tion of the full-matrix PID controllers. The closed-loop response of the GA recommended PID controlis shown in Fig. 12. It can be seen that the transientperformance is as excellent as that of the full-matrixFLCs, in terms of the rise time, steady-state error as


Fig. 11. Closed-loop and actuator output responses of the fuzzy gyroscope control system.


Fig. 12. The response of genetic-based PID control.

Fig. 13. The control command of genetic-based PID control.

well as the coupling e;ect between the two channels.As shown in Fig. 13, however, the required upper andlower bound of the PID controllers’ outputs are muchgreater (±1 Nm) than that of FLCs (±0:6 Nm). This

indicates that, in order to acquire an similar controlperformance for gyro-mirror line-of-sight stabilizationplatform, FLCs require less control e;ort as comparedto PID controllers.


4. Real-time implementation results

The GA-based designed FLCs were implementedon a laboratory scale gyro-mirror LOS stabilizationplatform to demonstrate the e;ectiveness of the fuzzylogic control system. The hardware setup of the gy-roscope platform is shown in Fig. 14. The inputs ofthe plant are the two torques for yaw and pitch axis.These two torques are provided by two motors whichare connected to a controller board that provides highcurrent supply with good precision. The output of theplant are two angle sensors that provide informationabout the yaw and pitch axis. Since these sensors arenoisy, a second-order low-pass <lter was used to re-duce the sensor noise [11].A Pentium II-based computer was used as a central

controller in the setup to provide su9cient computa-tional power for performing several tasks simultane-ously in real-time such as transferring data in highspeed, calculating controller’s outputs and display-ing measurements on the monitor. To provide input–output facility for the CPU, the National InstrumentsData Acquisition (NIDAQ) card [12] was installed inthe computer. This card is capable of accepting eightdi;erential inputs and produce two grounded outputs,with a sampling data at 250 ns=sample and 12-bitaccuracy. It has internal and external timers althoughonly the internal timer is needed for the data samplingin this implementation.The software of LabVIEW 5.0 and the toolkit of

Fuzzy Logic for G Toolkit [13] were used in the im-plementation, which is a powerful instrumentation andanalysis programming language for the PC. Insteadof using the traditional sequential or block-structuredprogramming structure, LabVIEW has its own pro-gramming language known as the G language. It is agraphical programming language where most of thetime, a programmer can use drag and drop method tocreate a program. Fig. 15 shows one of the LabVIEWsubprograms, the full-matrix FLCs in the G language,for real-time implementation of the fuzzy gyroscopecontrol system. The I=O characteristics of the FLCsare shown in Fig. 16, which is very useful as a testfacility before running the FLC within any designatedsystem environment.Results of the real-time experiments obtained by ap-

plication of the full-matrix FLCs to the physical gyro-mirror stabilization platform are shown in Fig. 17. The

Fig. 14. The hardware set-up of the fuzzy gyroscope control sys-tem.

Fig. 15. The full-matrix FLCs subprogram in the G language.

upper graph shows response of the yaw output andthe bottom graph indicates the pitch response. As canbe seen, the closed-loop responses of the actual fuzzycontrol system are comparable with the simulation re-sult, which o;ers an excellent transient and trackingperformances in the presence of practical imperfec-tions. In addition, the coupling e;ect for both the pitchand yaw outputs are kept as minimal against the cross-axis interactions in the multivariable system.


Fig. 16. The I=O characteristics of the FLCs.

Fig. 17. The real-time full-matrix fuzzy gyroscope control exper-imentation results.

5. Conclusion

In this paper, a multivariable gyro-mirror LOSstabilization platform as well as its control di9cul-ties in the presence of nonlinearity and unmodeleddynamics has been studied. Concerning these, ane;ective full-matrix fuzzy logic controller has beendesigned and implemented for a practical gyroscopesystem. For optimal control performances, the fuzzysets and rule bases of the FLCs are automaticallydetermined via a genetic algorithm. It has showncompetitive control performance comparing to othercontrol techniques. Both the simulation and real-time

implementation results of the closed-loop responsesare consistent, which o;er an excellent transient andtracking performance in the presence of practicalimperfections. Overcoming drawbacks in traditionalcontrol con<guration without decouplers, a signi<-cantly reduction in the coupling e;ect between the twooutput channels is also achieved in the proposed fuzzygyroscope control system. Further work includes theapplication of multi-objective GA to specify a set ofperformance criteria as well as the development ofon-line identi<cation and adaptation of the FLCs toachieve an autonomous gyroscope system.

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