NEURO-FUZZY SYNTHESIS OF FLIGHT CONTROL ELECTROHYDRAULIC SERVO

Ioan Ursu, Felicia Ursu, Lucian Iorga

“Elie Carafoli” National Institute for Aerospace ResearchBd. Iuliu Maniu 220, sector 6, Bucharest 77538, Romania

fax: 401 413 06 90; e-mail: iursu @ aero.incas.ro; phone: 401 413 25 52

Abstract. The purpose of this paper is to present a switching type neuro-fuzzy control synthesis. The controlalgorithm supposes as component part an neurocontrol designed to optimize a performance index. Whenever theneurocontrol saturates or a certain performance parameter of the system decreases, the scheme of controlswitches to a feasible and reliable fuzzy logic control. The procedure of return to the optimizing neurocontrol isessential and is also described. This methodology of control synthesis ensures antisaturating, antichattering androbustness properties of the controlling system, as is illustrated by numerical simulation in the case of a primaryflight controls electrohydraulic servo actuator.Keywords: neuro-fuzzy control, unmanned and unconventional flight, flight control, electrohydraulic servosynthesis, robust antichattering synthesis, intelligent control.

Introduction

The evolution of modern day aircraft includes thepromotion of new ideas and strategies, such as CCV(Control Configured Vehicle), Active Control,Unconventional Flight, Unmanned Aircraft. Theimplementation of these ideas and strategies – anauthentic technical challenge – is dependent on thedevelopment of intrinsically outstanding actuationsystems (Tyan and Bernstein, 1994). In other words,this means that new control strategies, particularly forelectrohydraulic servo actuating primary flightcontrols, must be developed. These new approachesshould result in intelligent, learning type systems;particularly, power control units – electrohydraulic,as a rule – should have increased dynamicperformances, from robustness, to fast speed ofresponse.

During the past few years, the neuralnetworks and fuzzy logic have attracted the attentionof many researchers in the field of control. Theassertion that “neural networks seem to be the mostpromising technique to design a robust, adaptive andintelligent control systems” (Feng et al., 1997) isworthy of noticing. With regard to fuzzy logic, thisoffers on excellent way “to combine mathematicalmodels and heuristics into controllers” (Wang andKong, 1994). The artificial intelligence basedsynthesis of control law (in other words, usingneurocontrol and fuzzy logic control) provides alsothe means to evade the mathematical model of thesystem. In fact, the salient feature of neurocontrol andfuzzy logic control, which distinguish them from thetraditional control and adaptive approaches, is thatthey provide a model-free description of the controlsystem. Thus, a lot of troubles relating to therobustness of the system can be surpassed. Bothneural networks and fuzzy logic show great potentialfor controlling systems that are difficult or impossible

to model using traditional techniques. The advantagesof neural networks are twofold: learning ability (aneural network mimics the function of the brain) andversatile mapping capabilities from input to output(certain types of neural networks are universalapproximators giving so special abilities in adaptivecontrol and system identification). In its turn, thefuzzy set theory provides a suitable tool for both thetreatment of intrinsic inexactness of the description ina dialectical context and imitation of human thinkingin the process of compromise in making a decision.Concerning these last two topics, two excellentsurveys were carried out by Vemuri (1993) and Klir(1993).

There has been much discussion aboutequivalencies, contrasts and possible combinations offuzzy logic and neural control. Such combinationshave been already considered for several years, as so-called neuro-fuzzy control (Kruse and Nauck, 1996).In this paper, an inedited such combination isintroduced: namely, that of a fuzzy supervisedneurocontrol (FSNC). More precisely, a neuralnetwork is taken as training architecture to optimizethe input tracking of an electrohydraulic servo (forsake of simplicity, an unilayered perceptron is used);but generally speaking, the controlled plant may bean arbitrary one. To counteract the control saturatingmode which neural network can not avoid, analternating fuzzy logic control is delivered wheneverthe neural control saturates or a certain performancecondition is fulfilled. Thus, the obtained FSNCadvantageously combines the optimal neurocontroland the robust – reliable and feasible – fuzzy logiccontrol.

Unilayered perceptron type neurocontrol

The simplest idea to illustrate the structure of theproposed FSNC is that of using an unilayeredperceptron architecture. For this elementary network,two weighting parameters ν ν1 2, and a linear

combiner generate the neurocontrolu y y= +ν ν1 1 2 2 . (1)

In the training, the system performance is assessed bythe cost function, a criterion supposing a trade-offbetween the first input y1 , which is usually a

tracking error (generally, a regulating error), thesecond input component y2 , which is usually a

certain performance index of the system, and thecontrol u

J n q y i y i q u i n J ii

n

i

n= + + = ∑∑

==

12

121 1

222

22

11( ( ) ( ) ( )): ( ) . (2)

The weighting vector νν = [ ]ν ν1 2T is updated

online by the gradient descent learning method(Vemuri, 1993) to reduce the cost J. Consequently,the update is given by the expression

νν νν νν

νν

νν

( ) ( ) ( )

( ): ( , ) ( )

( , )( )( )

( )( )

( )( )

( )( )

n n n

nJn

J ii

iu i

J iu i

u iii n N

n

+ = +

= − =

+

∑

= −

1

1 2

1 2

∆

∆ diag

- diag

δ δ ∂∂ν

δ δ∂∂

∂∂

∂∂

∂∂y

y

(3)

where the matrix diag( , )δ δ1 2 introduces the

learning scale vector, ∆νν( )n is the weight vectorupdate and N marks a back memory (of N time steps).The derivatives in (3) require only input-outputinformation about the system. ∂ ∂y( ) / ( )i u i is online

approximated by the relationship( ( ) ( )) / ( ( ) ( ))y yi i u i u i− − − −1 1 .

For the purposes of the learning method,proposed in this paper, the results obtained using thissimple unilayered perceptron are very satisfactory.

Fuzzy logic control and fuzzy supervisedneurocontrol

In many applications, particularly in the field ofaerospace engineering, actuator saturation is theprincipal impediment to achieving significant closed-loop performances (Tyan and Bernstein, 1994); infact, the effects of actuator saturation often constitutea greater source of performance limitation than evenmodeling uncertainty.

As matters stand in applying of theapparatus of linear control synthesis, actuatorsaturation cannot be avoided and this means to facestronger harmful secondary saturating effects:chattering, the reset windup phenomenon (Hanus etal., 1987). Thus, an antireset windup (AW) strategyof control synthesis follows to be inserted; in its turn,a such strategy is not exempted from other secondaryeffects (Ursu et al., 1998).

a)

b)Fig. 1. Triangular membership functions for: a)

scaled input variables y1, y2 and b) l2(y1)

Fig. 2. Singleton membership function for scaledfuzzy control uf

In the learning process with artificial neuralnetworks, the risk of control saturation is also real.To counteract this risk and not compromise thelearning neural network by harmful phenomena ascontrol’s chattering and making worse system’sperformance, a fuzzy supervised neurocontrol(FSNC) is here proposed as AW strategy. Thus, thecontrol will have a switching type structure, whichwill be clarified in the following.

A succinct describing of the commonly usedfuzzy logic control supposes the recalling of the threemain components: the fuzzyfier, the fuzzy reasoning,and the defuzzyfier (Ghazi Zadeh, 1997; Ursu et al.,2000). Herein, the proposed fuzzyfier componentconverts the crisp input signals

l y y y y kk jj k

k

k k2 1 12

21 2 1 2( ): , , , , , . . .= ∑ =

= −(4)

into their relevant fuzzy variables (or, equivalently,membership functions) using a set of linguistic terms:zero (ZE), positive or negative small (PS, NS),

−1 −2/3 −1/3 0 1/3 2/3 1 y1 ; y2

µ B(y1); µC (y2)

NB NM NS ZE PS PM PB 1

0 1/3 2/3 1 l2(y

1ZE PS PM PB

µA ( l2 (y1))

-1 -2/3 -1/3 0 1/3 2/3 1u

µD (uf)

NB NM NS ZE PS PM PB 1

positive or negative medium (PM, NM), positive ornegative big (PB, NB); thus, fuzzy sets and theirpertinent membership functions are produced (forsake of simplicity, triangular and singleton typemembership functions are chosen, see Fig. 1, 2). Theconsidered l2 norm computes, over a sliding windowwith a length of k samples, the maximum variation ofthe tracking error. The insertion of this crisp signal inthe fuzzyfier will result in a reduction of fuzzycontrol switches due to the effects of spurious noisesignals (Tzes and Peng, 1997). (The sum in (4) willbe, certainly, incomplete, if k < 3; a sum of L ≠ 3terms can be also defined).

The fuzzy reasoning (knowledge base, orIF..., THEN... rules, which generally derives fromhuman experience) totalizes a number of n “IF...,THEN” rules. Looking back to the fuzzyfier, n is thenumber of the elements of the Cartesian product A×B ×C, A := {ZE; PS; PM; PB}, B = C :={NB; NM;NS; ZE; PS; PM; PB}; the just defined sets areassociated with the sets of linguistic terms chosen todefine the membership functions for the fuzzyvariables l2 (y1), y1 and, respectively, y2. Thus,here n = 4×7×7 = 196 and the adopted fuzzyreasoning is the following:1) IF l2 (y1) is ZE and y2 is PB and y1 is PB, THEN uf

is PB ; 2) IF l2 (y1) is ZE and y2 is PB and y1 is PM,THEN uf is PM; … 7) IF l2 (y1) is ZE and y2 is PBand y1 is NB, THEN uf is NB; 8) IF l2 (y1) is ZE andy2 is PM and y1 is PB, THEN uf is PB; … 14) IF l2

(y1) is ZE and y2 is PM and y1 is NB, THEN uf is NB;… 49) IF l2 (y1) is ZE and y2 is NB and y1 is NB,THEN uf is NB; 50) IF l2 (y1) is PS and y2 is PB andy1 is PB, THEN uf is PB; … 98) IF l2 (y1) is PS and y2

is NB and y1 is NB, THEN uf is NB; … 99) IF l2 (y1)is PM and y2 is PB and y1 is PB, THEN uf is PB; …147) IF l2 (y1) is PM and y2 is NB and y1 is NB,THEN uf is NB; … 196) IF l2 (y1) is PB and y2 is NBand y1 is NB, THEN uf is NB.

To put it differently, in each of 196 rules,the membership functions µ B y( )1 and µ D fu( ) are

the same. This strategy of rules base constructionembodies the idea of a (direct) proportion betweenthe error signal y1 and the required control uf. To therough, such is the state of things with the justdescribed fuzzy logic control; to obtain the rigor andaccuracy of tracking or regulated process, the fuzzycontrol will switch in neurocontrol.

Let τ be the discrete sampling time.Consider the three scaled input crisp variablesl2 (y1k) , y1k and y2k , at each time step t kk = τ(k = 1, 2,...); taking into account the two ordinatescorresponding in Fig. 1 to each of the three crispvariables, a number of M combinations of threeordinates must be investigated; in this case, M = 23

and M < 23 only if the peculiar cases occurl y y y y

yk k k k

k

2 1 1 2 1

2

1 1 1 1

1

( )

.

≥ ≥ ≥ ≤ −≤ −

or or or

or (5)

(In fact, a new Cartesian product of three sets hasbeen involved in the calculus of the M combinations).Having in mind these combinations, a number of MIF..., THEN... rules will operate in the form

IF is and is and is

THEN is

y B y C l y A

u D i Mk i k i k i

fk i

1 2 2 1

1 2

( ) ,

, , , ... ,=(6)

(Ai,B, Ci, Di are linguistic terms belonging to the setsA, B, C, D and D = B = C, see Fig. 1, 2). These rulescould be written as a consequence of aforementionedavailable knowledge base. The defuzzyfier concernsjust the transforming of these rules into amathematical formula giving the output controlvariable uf. Indeed, the question is how to interpretand use the knowledge base (the matter is in dispute,see Zadeh, 1991). In terms of fuzzy logic, each ruleof (6) defines a fuzzy set Ai×Bi×Ci×Di in the input-output Cartesian product space R+×R3, whosemembership function can be defined in the manner

µ µ µ µ µu B k C k A k Di i i i iy y l y u

i M k

=

= =

min[ ( ), ( ), ( ( )), ( )],

, ... , ( , , ...)

1 2 2 1

1 1 2(7)

(other variants, e.g., product instead min, can bechosen). For simplicity, the singleton-typemembership function µD(u) of control variable hasbeen herein preferred; in this case, µ Di

u( ) will be

replaced by ui0 , the singleton abscissa. Therefore,

using 1) the singleton fuzzyfier for uf, 2) the center-average type defuzzyfier, and 3) the min inference,the M IF..., THEN… rules can be transformed, ateach time step kτ, into the following formula givingthe crisp control u f (Wang and Kong, 1994):

u uf u i ui

M

i

M

i i= ∑∑

==µ µ0

11/ . (8)

To complete the eight – in this case – weights µ ui,

supplementary zero weights will be automaticallyadded in the peculiar cases (5).

The main contribution of this work consistsof designing the specific switching scheme betweenthe two types of control described above,neurocontrol and fuzzy logic control.

The FSNC operates as fuzzy logic control inthe case when neurocontrol saturated, or so calledl2−norm of tracking error y1 increased. FSNCswitches on neurocontrol whenever readjusted un is

not saturating ( ),u un n max≤ and scaled

l y2 1( ) < l2,min. In the case of fuzzy control operating,

the fuzzy neurocontrol un is concomitantly updatedconsidering the real acting fuzzy control uf . At time ts

− when the switching from logic control toneurocontrol occurs − the readjusted weighting vectorννr will be derived by considering the scale factoruf / un:

ν ν ν ν1 2 2 1 2 2r f f n r f nu y u u y u u= − =( ) / ( ), / . (9)

FSNC synthesis for flight controlelectrohydraulic servo. Simulation studies

The electrohydraulic servo actuating primary flightcontrols can provide large processing force and havea good positioning capability. However, the dynamiccharacteristics of these systems are always complexand highly nonlinear and contain many uncertaintiessuch as the viscosity of oil, the bulk modulus, thewear and the cavitation. The loading conditions areusually rather unsteady, and the loading forceschange in a wide range during the operation. Due tothe above factors, one must employ a linearized orapproximated approach to formulate the systemmodel (Wang, 1963; Ursu, 1994; Hahn et al., 1994;Richard and Outbib, 1995; Ursu et al., 1996). It isusually complicated, time-consuming, and does notoffer the guarantee of a good, “truth” (Skelton, 1989)system modeling; consequently, the performances ofthe controlled system are affected. Indeed, toformulate the system model for a wide range ofoperating conditions is uneconomical and mightprove ineffective.

The application of the neuro-fuzzy control toan electrohydraulic servo actuating primary flightcontrol has not yet been tested, in our knowledge.This paper considers such a problem in a numericalexperiment framework by using as guide mark astrongly nonlinear model of the electrohydraulicservomechanism (Wang, 1963)mz fz kz F S p p r z

p B cw p p

p p Sz C Sz

p B cw p p

p p Sz C Sz

a

a

a

a

&& ( ), ( )

& { sgn[ ( sgn ) ]

( sgn ) / &} / ( )

& { sgn[ ( sgn ) ]

( sgn ) / &} / ( ).

+ + + = − = −

= + −

+ − − +

= − −

− − + −

1 2

1 1

1

2 2

2

1 2

1 2

1 2

1 2

ε λ

ε ε

ε ρ

ε ε

ε ρ

(10)

The following nomenclature is given: z(t)−(servo)actuator load displacement (defined from thecenter of the actuator cylinder); ε( )t − valve-spooldisplacement (defined from the valve’s neutralposition); p ti ( ) − actuator cylinder pressure (i = 1,

2); r(t) − the reference input (command)displacement; m − equivalent inertia load of primarycontrol surface reduced at the actuator’s rod;f − equivalent viscous friction force coefficient;k − equivalent aerodynamic elastic force coefficient;S − actuator piston area; F(t) − perturbation load;C − the cylinder semivolume; B − bulk modulus ofoil; c − volumetric flow coefficient of the valve-port;w − valve-port width; pa − supply pressure;

ρ − volumetric density of the oil; λ − coefficient of

the cinematic feedback.In view of performing the numerical

integration of the system (1) (by a Runge-Kuttaprocedure, for example), the reference displacementr(t) and initial conditions z(0), &( )z 0 , p1 0( ),

p2 0( ) must be given.

The following basic assumptions are madein processing numerical experiments. 1) The valve-actuator mechanism operation is restricted to thenoncavitation regime, i.e. p p ia i≥ > =0 1 2, , .

This constraint is implicitly satisfied for acceleratedmotions, but during deceleration, the rate of valve-port closure, without a monitorship, may inducecavitation. 2) The valve-spool motion isinstantaneous with respect to the control (drivercurrent); so, a proportionality

ε = k uvs (11)

is considered. 3) The physical constraint of controlsaturation is also implied: relative valve-spooldisplacement is limited, ε ε≤ m .

The aforementioned FSNC was applied insimulation studies of the system (10); the secondequation of this system was substituted by equations

u y y r k z k zp v= + = − +ν ν ν ν1 1 2 2 1 2: ( ) & (1′)

and (11).The system parameters were as follows:

m = 30Kg, f = 103Ns/m, k = 105N/m, S = 10-3 m2,pa = 21x106 N/m2, B = 6x108N/m2, ρ = 850kg/m3,c = 0.63, w = 0.85x10-3m, εm = 0.12x10-2m,C = 3x10-3m2, kp = 103/3V/m, kv = 100Vs/m,F = 200 2 2sin π × t daN, r = 1/3V, τ = 0 003. s ,kvs = 6x10-5m/mA, u mAn,max = 20 , l2 1 3, /min = ,

λ = 0.55. The scaled variables l y y2 1 1( ), and y2

were obtained by multiplying respectively with 3, 3and 1 / ( )k vv max , where v m smax = 01. / (the

maximal velocity of the servomechanism, withoutload). The back memory was N = 1. The length of(macro)integration steps for the nonlinear system (10)was 133 (with the sampling time τ = 0 003. s ); so, theoverall integration time is approximately 0.4s.

Invoking the paradigm of sampled datasystems (Dorato and Levis, 1971; Åström andWittenmark, 1984), the response of a system to stepsignals is representative, having in view theprocedure of sampling general reference signals.Nevertheless, it should be noted that very satisfyingresults have been obtained with the proposed FSNCin the presence of sinusoidal combination typereferences, but these response-graphs have beenevaded in this paper.

The best tracking performance of the non-learning servomechanism, estimated as time constant(defined in the sense of the first order system) is0.034s (see the response z0, Fig. 3) and was obtainedwith the fixed (initial) weighting vector νν = [10 1]. Inthe case of fuzzy supervised neurocontrol, startingwith the initial weighting vector νν = [35.5 5] andusing learning rate[ ] [ ]δ δ1 2

2 45 10 10= × − − and

L = 3, the best time constant is 0.011s (see theresponse znf, Fig. 3). The response of the learningwith neurocontrol servomechanism (with the sameinitial νν = [35.5 5]), but non-supervised by fuzzylogic control, is shown in Fig. 4; such a behavior

reveals the extreme significance of the supervisingfuzzy control: only the first 3 steps out of the total of133 steps were necessary for the fuzzy control to actin order that the tracking regime does not take a turnfor the worse as in Fig. 4. But the real performance ofthe tracking with FSNC system appears from thecomparison with the mechanical servo, for which thebest time constant (0.025s) has been obtained with

the value λ = 0.55. Thus, the introduced FSNCpromotes a servo at least twofold faster than theequivalent mechanical servo. The time constant of0.011s obtained with FSNC is also better than thetime constant obtained in the case of an anti-windupoptimal synthesis shown in Ursu et al. (1998).

0 0.2 0.40

0.05

0.1

0.15

0 0.2 0.4-5

0

5

10

15

0 0.2 0.4

100

110

120

0 0.2 0.4

0

10

20

0 0.2 0.40

10

20

30

40

0 0.2 0.4

1

3

5

rz0

znf

[cm]

t[s]

[cm/s]

&znf

&z0

[daN/cm2] p01, pnf1

p02, pnf2

[mA]

u0

unf

ν1ν2

Fig. 3 A comparison between the non-learning tracking performance (0-subscript)and learning with neuro-fuzzy control tracking performance (nf-subscript)

0 0.2 0.4-0.2

-0.1

0

0.1

0.2[cm]

0 0.2 0.4-100

-50

0

50

100

0 0.2 0.40

100

200

250

0 0.2 0.4-20

-10

0

10

20 un

0 0.2 0.40

500

1000

1500

0 0.2 0.4-800

-400

0

200

[cm/s] [dN/cm2] pn1, pn2

r

zn

&zn

t[s]

[mA]

ν1

ν2

Fig. 4 The case of chattering neuro-control (non-supervised by fuzzy control)

Conclusions

In this paper, a Fuzzy Supervised Neurocontrol(FSNC) synthesis has been developed. The structureof the obtained control is a switching one, between a

neurocontrol and fuzzy logic control. The proposedFSNC is categorically advantageous in comparisonwith the system presented by Ursu et al. (1998), sincein that approach the synthesis is dependent of a linearmodel of the controlled system. This new approach ofcontrol synthesis accounts for the saturationnonlinearity and provides in addition antichatteringand robustness properties to the controlling system.

Indeed, the obtained control is robust since it doesnot demand a model of the system.

The aforementioned FSNC was applied insimulation studies on the mathematical model of anelectrohydraulic servo actuating primary flightcontrols. The system controlled with FSNC is provedto be at least twofold better than the equivalentmechanical system: 0.011s time constant for thesystem with FSNC versus 0.025s time constant forthe best equivalent mechanical system (λ = 0.55).The simulation studies attest good trackingperformance in the presence of sinusoidalcombination type signals, particularly in the presenceof step signals; based on sampled data systemsparadigm, a good tracking performance of arbitraryreferences can be also stipulated. Thus, the aboveresults are very encouraging from viewpoint ofdevelopment of the intelligent control strategies.

References

Åström, K. J., B. Wittenmark (1984), Computer controlledsystems. Theory and design, Prentice-Hall, EnglewoodCliffs, NJ.

Dorato, P., A. N. Levis (1971), "Optimal linear regulators:the discrete-time case", IEEE Transactions onAutomatic Control, Vol. AC-16, pp. 613-620.

Feng, X., C-F. Lin, T-J. Yu, N. Coleman (1997),“Intelligent control design and simulation using neuralnetworks", AIAA Guidance, Navigation and ControlConference: A Collection of Technical Papers, NewOrleans, Louisiana, August 11-13, Part 1, pp. 294-299.

Ghazi Zadeh, A., A. Fahim, M. El-Gindy (1997), "Neuralnetwork and fuzzy logic applications to vehiclesystems: literature survey", International Journal ofVehicle Design, Vol. 18, pp. 132-193 .

Hahn, H., A. Piepenbrink, K.-D. Leimbach (1994), "Input-output linearization control of an electro servo-hydraulic actuator", Proceedings of 3rd IEEEConference on Control Applications, Glasgow, pp.995-1000.

Hanus, R., M. Kinnaert and J.-L. Henrotte (1987).Conditioning technique a general antiwindup andbumpless transfer method. Automatica, 23, pp.729-739.

Klir, G. J. (1993), "Developments in uncertainty-basedinformation", in Advances in Computers, M.C. Yovitsed. Academic Press, New York, Vol 36, pp. 23-332.

Kruse, R., D. Nauck (1996), “Neuro-fuzzy systems incomputational intelligence: Soft, computing and fuzzy-neuro integration with applications, Proceedings of theNATO Advanced Study Institute on Soft Compatingand Its Applications, Manavgat, Antalya, Turkey, Aug.21-31, NATO ASI Series, Series F: Computer andSystems Sciences, Vol. 162, pp. 230-259.

Richard E., R. Outbib (1995), "Feedback stabilization of anelectrohydraulic servo", Proceedings of 3rd EuropeanControl Conference, Rome, Vol. 1, pp. 330-335 .

Skelton, R. E. (1989), "Model error concepts in controldesign", International Journal of Control, Vol. 49, pp.1725-1753.

Tzes, A., P-Y. Peng (1997), ”Fuzzy Neural NetworkControl for DC-Motor Micromaneuvering",

Transactions of the ASME, Journal of DynamicSystems, Measurement and Control, Vol. 119, June,pp. 312-315.

Tyan, F., S. Bernstein (1994), "Antiwindup compensatorsynthesis for systems with saturating actuators",Proceedings of 33rd Conference on Decision andControl, Lake Buena Vista, FL, pp. 150-155.

Ursu, I., F. Popescu, M. Vladimirescu, R. Costin (1994),"On some linearization methods of the generalized flowrate characteristic of the hydraulic servomechanism",Revue Roumaine des Sciences Technique, Série deMécanique Appliquée, Vol. 39, pp. 207-217.

Ursu, I., M. Vladimirescu, F. Ursu (1996), "Aboutaeroservoelasticity criteria for electrohydraulicservomechanisms synthesis", Proceedings of ICAS’ 96,Sorrento, Italy, Vol. 2, pp. 2335 -2344.

Ursu, I., G. Tecuceanu, F. Ursu, T. Sireteanu, M.Vladimirescu (1998), "From robust control toantiwindup compensation of electrohydraulic servoactuators", Aircraft Engineering and AerospaceTechnology, Vol. 70, pp. 259-264 .

Ursu, I., F. Ursu, T. Sireteanu, C. W. Stammers (2000),"Artificial intelligence based synthesis of semiactivesuspension systems", Shock and Vibration Digest, Vol.32, pp. 3-10.

Vemuri, V. (1993), "Artificial neural networks in controlapplications". In Advances in Computers, edited by M.C. Yovits, Academic Press, Vol. 36, pp. 203-332 .

Zadeh, A. L. (1991), "The calculus of If-Then rules", FuzzyEngineering toward Human Friendly Systems-Proceedings of the International Fuzzy EngineeringSymposium 91, Vol. 1, Yokohama, Japan, pp. 11-12.

Wang, P. K. C. (1963), "Analytical design ofelectrohydraulic servomechanism with near time-optimal response", IEEE Transactions on AutomaticControl, Vol. AC-8, pp. 15-27.

Wang, L-X., H. Kong (1994), “Combining mathematicalmodel and heuristics into controllers: an adaptive fuzzycontrol approach", Proceedings of the 33rd IEEEConference on Decision and Control, Buena Vista,Florida, December 14-16, Vol. 4, pp. 4122-4127