The Study of recursive-based Sliding Mode Adaptive Control of the Permanent Magnet Synchronous Motor

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1 The Stuy of recursive-base Sliing Moe Aaptive Control of the Permanent Magnet Synchronous Motor ZHANG YAOU, ZHAO WANSHENG, WEI HONGYU School of Mechanical Engineering, Shanghai Jiao Tong University Shanghai, CHINA Abstract: The urgent nees in many occasions have stimulate the stuy of the permanent magnet synchronous motor (PMSM. The moel of the PMSM system has multi-variable, highly nonlinear, strong coupling character an the control performance of the PMSM rive system is also influence by the uncertainties of the plant compose of unpreictable plant parameter variations, external loa isturbances, an unmoelle nonlinear ynamics. In orer to esign a controller to meet with the esire requirement, base on Lyapunov stability theorem, the combine multiple recursive base sliing moe aaptive controller has been propose an the physical parameters learn algorithm has been erive. This combine controller integrates the virtues of these three kins of controllers, an it provies a solution to the servo position control of permanent magnet synchronous motor with the parameters of uncertainty an external loa isturbance an also a reference criterion for the controller parameters selection. Theory erivation an experiment simulation results verify the effectiveness an feasibility of the controller. This metho provies the founation of the settlement of the servo position control of the permanent magnet synchronous motor. Key wor: Permanent Magnet Synchronous Motor (PMSM; sliing moe control; recursive-base control; aaptive control; Lyapunov stability theorem; nonlinear ynamics. Introuction Permanent magnet synchronous motors (PMSM are of great interest, particularly for inustrial applications in the low-meium power range, since it has superior features such as compact size, high torque/weight ratio, an high torque/inertia ratio []. Moreover, compare with inuction motors, PMSM have the avantages of higher efficiency []. The typical construction of a PMSM consists of a three phase stator wining an a soli iron rotor with magnets attache to its surface or inserte into the rotor boy. This construction results in a magnetic fiel fixe to the rotor position. Since such machines are not capable of irectly starting from the mains, excitation by voltage source inverters (VSI controlle by fiel orientation is require. Control techniques such as vector control [] or irect torque control (DTC [] are stanar for this type of rives. Permanent magnet synchronous motor control system mainly consists of two parts, the main rive circuit an the control circuit. The main rive circuit topology structure remains basically unchange, while the stuy of the control system focuses on the control circuit an control strategies [5]. Base on the characteristics of the moel of permanent magnet synchronous motor, many moern control methos an intelligent control methos have been applie to the permanent magnet synchronous motor. The state feeback linearization of nonlinear systems control theory has been introuce into the motor control in [6], ISSN: Issue 5, Volume 9, May

2 an this metho can change the original nonlinear system into the -orer integrate ynamic inversion system, which can ecouple the system an euce the linear relationship between the control input an the output, then the linear control theory can be utilize, however the complexity of the theory of the metho has limite its extension usage. Sliing moe variable structure control [7] can ajust the structure of feeback control system, which can make its vector changes in the switching hyper-plane, an the boune state vectors of the system are sliing in the switch plane, an the ynamic quality of the system is ecie by the parameters of the switching surface system. Sliing moe controllers (SMCs have been wiely use for spee an position control since they provie a fast ynamic response. The aaptive control strategy has been use in the control of permanent magnet synchronous motor in [8], an the metho can upate the recognition parameters of system real-timely, moify the system control proceures, thus improving the system characters in time-varying operating conitions, however this algorithm nees a large amount of computing an high-spee ata processor. Besies these nonlinear control methos mentione above, the intelligent control methos, such as the artificial intelligence expert system [9], fuzzy control [], an neural networks [, ] have also been utilize in the motor rive system, an the great progress has been achieve. Brock [] use fuzzy logic controllers to ajust the gain of a controller in a sliing moe controller for spee an position control of PMSM. The control strategies in which recurrent fuzzy neural networks (FNN were use to ajust the gain of the SMC for position control of a PMSM was use by Wai []. To achieve fast four-quarant operation, smooth starting an acceleration, the fiel-oriente control metho is use in the esign of the PMSM rive. However, the control performance of the PMSM rive system is still influence by the uncertainties of the plant, which usually are compose of unpreictable plant parameter variations, external loa isturbances, an unmoelle nonlinear ynamics. In orer to solve this problem, the recursive-base sliing moe aaptive control metho has been use in controlling PMSM, which integrate the virtues of the sliing-moe control metho, the recursive control strategies, as well as the aaptive control methos to settle the PMSM with the unpreictable plant parameter variations, external loa isturbances. Base on the Lyapunove stability theorem, the controller can be esigne an can be testifie. As compare with the general PID controller, the control parameters of this metho have practical significance an can be accesse easily. Although there are parameter changes in the moel, the goo tracking results can also be reache an the experiments simulations show that the PMSM can quickly reach the esire position. This paper introuces a combine control metho for position servo control of PMSM rive with internal an external interference. The organization of this paper is as follows: First, the moel of the PM synchronous servo motor is introuce; then, the synthesis of the recursive-base sliing moe aaptive controller is escribe in etail with theoretical proof; finally, the servo position controller propose is implemente to control the rotor position of a PM synchronous motor for the tracking of sinusoial commans with plant parameter variations, external loa isturbances in simulation; the simulation experimental results are given to emonstrate the effectiveness of the propose control scheme.. Machine moel of the fiel-oriente PMSM The PMSM is compose of three phase s stator winings an permanent magnets mounte on the rotor surface (surface mounte PMSM or burie insie the rotor (interior PMSM. The electrical equations of the PM synchronous motor can be escribe in the rotor rotating reference frame, written in the (q rotor flux reference frame [5,6]. The mathematic moel of PMSM is base on the following assumptions: ( Neglecting the saturation of armature; ( Neglecting the wastages of ey an magnetic hysterics; ( There is no rotor amp resistance. ISSN: Issue 5, Volume 9, May

3 The relations of voltage, torque an flux of PMSM are escribe as follows: L ωr uq iɺ i q R q L u = i i L + ω ɺ r ωr φ R L L where ( i an iq are the an q axis stator currents, R an L are the stator phase resistance an inuctance respectively; the -axis self inuctance an the q-axis self inuctance are all equal to L ; ω r is the rotor electrical spee; u an uq are the stator voltages expresse in the q reference frame an φ is the flux establishe by rotor permanent magnets; P is the number of magnetic pole. Equation ( escribes electrical ynamics an is nonlinear since it involves the proucts of state variables. ω = Pω ( s r ω q ( q r B P φi + L L ii q TL = ωr + (5 t J J J The equation (5 shows that the electromagnetic torque is the prouct of state variables an it is nonlinear. The equations ( an (5 constitute the whole control moel of the PMSM. The state-space moel of the interior PMSM is similar to the surface mounte PMSM only that the moel of the surface mounte PMSM oes not have the prouct of the currents -axis an q-axis in the electromagnetic torque. However the control metho of these two kins of motor is similar, for simple, the surface mounte PMSM is chosen as the control object in this paper. In orer to facilitate the controller esign, the moel of the PMSM can be escribe in the form of the state space equation below with x = θ x = ω x = iq x = i Then ωs is inverter frequency [7]. The electromagnetic torque is given by Te = P φiq + ( L Lq ii q ( If i =, the electromagnetic torque proportional toi q.this escription is similar to the torque generate in a DC motor with inepenent fiel excitation. This feature can simplify the controller esign of the PMSM. The equation of the motor ynamics is T = T + Bω + Jɺ ω ( e L r r TL stans for external loa torque. B represents the amping coefficient an J is the moment of inertia of the rotor. Thus, the mechanical ynamic can be rewritten as Te is xɺ = x xɺ = x+ x Tt xɺ = x xx 5x+ 8u xɺ = 6x+ 7xx+ 8u y= x Where = B J Pφ f = J = 6 = R L = =P 7 = φ P f 5 L q (6 ISSN: Issue 5, Volume 9, May

4 = u u 8 q L = u = u q u is the system input, an y is the output of the into two parts: the first part is the composition of the first three equations of (6 in section, which is use to etermine the esire control voltage u q ; the last equation of (6 is utilize to esign the controller to etermine the esire control voltageu. system. The state variables of the system x, x, x can be measure by the angle sensor, angular rate sensor an current meter measurements respectively, moreover they are boune. Discussion: Some parameters of the permanent-magnet synchronous motor are changing with temperature an the external loas are changing over time when it is in operation. If the controller esigne is base on fixe parameters, the robustness of the controller to the external interference an internal parameters will be very weak. To enhance the robust of the control system, base on this moel, the aaptive control metho is introuce into recursive-base sliing moe control metho. The aaptive controller is esigne base on the real-time information of the system, thus it can aapt to internal an external interference an can improve the robustness of controller.. The synthesis recursive-base sliing moe aaptive controller esign of the PMSM For the permanent magnet synchronous motor position servo system, the controller can make the system meet: lim t ( y y = (7 Where y is the esire output an it is assume to be known, an its first-orer, secon-orer an thir-orer erivatives all existe. In orer to esign the controller to meet requirement of the equation (7, the moel of PMSM can be ivie. The Sliing moe control The basic iea unerlying a sliing moe controller (SMC is that the motion of the states of the system is constraine to a preetermine path in the state space. In a SMC, the preetermine path is calle a sliing surface or sliing motion to provie ieal sliing motion. Theoretically, the sliing motion is smooth if the switching frequency of a system is infinite. However, in practice, the switching frequency of a system is finite, thus chattering comes out along the sliing surface [9]. Select x of the original system (6 as the system output an the system state variables can treate as the intermeiate state variables base on the recursive control esign metho, an then the sub-system mae up of the first two equations of the original system (6 can be regare as the secon-orer system. Therefore, sliing moe control metho can be use to esign the system controller. The expecte value x of the state variables x can be erive an can be use as the esire control input of the next sub-system. Define the position tracking error of the system as: e= y y = x y (8 Select the sliing surface as follows: z ce eɺ ( c (9 = + > With erivative of (9 an the system moel (6, the equation ( can be reache: zɺ = c( xɺ yɺ + ( xɺ ɺɺ y = c( x yɺ + ( x+ x T ɺɺ y +( ɶ x + ɶ x Tɶ t t ( ISSN: Issue 5, Volume 9, May

5 Where: ɶ = - ɶ = - Tɶ t = Tt Tt, an of, an T t respectively. T t are the estimation values Accoring to the theory of state feeback linearization, the intermeiate control variable can be selecte as follows: x = [ x + T + ɺɺ y c ( x yɺ k z ] ( t Where k is constant an k >.. The recursive aaptive controller esign Aaptive control is a vali metho to overcome system uncertainties, especially uncertainties erive from uncertain parameters; hence several kins of nonlinear aaptive control schemes have been propose in hyraulic control systems such as feeback linearization aaptive control [8], sliing moe aaptive control [9], an nonlinear aaptive control base on back stepping techniques[-]. The nonlinear aaptive control laws not only solve the control problem coming from uncertain nonlinear system successfully in some conitions [-5] but also emonstrate that nonlinear control schemes can achieve better performance than conventional linear controllers [6-8]. For x is the intermeiate control variable an the expecte value of the state variable x, there exists some error in between, then efine the error as follows: z = e = x x ( Then, the erivative of the sliing surface (9 can be escribe as: zɺ = k z + z ɶ x + ɶ x Tɶ ( t Then, the ifferential of the equation ( can be expresse as: zɺ = x xx 5x+ 8uq xɺ = x x x x + u ( 5 8 ɶ x ɶ x x ɶ x + ɶ u xɺ 5 8 q Where ɶ = - ɶ = - ɶ 5= 5-5 ɶ 8= 8-8,, 5 an 8 are the estimation values of,, 5 an 8 respectively. Then xɺ can be reache from the equation (: xɺ = [ x + x + ɺ ɺ ɺ T + ɺɺɺ y q t ɺ c( xɺ ɺɺ y k zɺ ] x Moreover (5 zɺ = c( xɺ yɺ + ( xɺ ɺɺ y (6 Then xɺ = [( c k x + x + ɺ ɺ ɺ Tt + ( c+ k ɺɺ y + ɺɺɺ y kc( x yɺ ɺ x ] c k = x ɺ + ( ɶ x + ɶ x T ɶ Where x ɺ = [( c k ( x + x Tt + ɺ ɺ x + Tt + ( c+ k ɺɺ y + ɺɺɺ y k c( x yɺ ɺ x ] Here, the equation ( can be escribe as: t (7 (8 ISSN: Issue 5, Volume 9, May

6 zɺ = x x x x + u ɶ x ɶ x x ɶ x + ɶ u x ɺ c k ( ɶ x ɶ x Tɶ 5 8 q 5 8 q + t (9 From the erivation above, the ultimate control value can be selecte as: x+ xx+ 5x+ x ɺ kz uq = ( Where k is constant an k >. 8 Then, insert equation ( into the equation (9, the equation ( can be reache: zɺ = ɶ x ɶ xx ɶ 5x+ c k ɶ u ( ɶ x + 8 q ɶ x Tɶ k z t. The Error base Controller Design ( For the controller esign of the fourth moel of the system (6, efine the error as follows: e = x x ( Then, consiering the changes of the system parameters, the ifferential of the error can be escribe as follows: eɺ = 6x+ 7xx+ 8u xɺ ( ɶ x + ɶ x x + ɶ u Where ɶ 6 = 6-6 ɶ 7 = an 7 are the estimation values of 6 an 7 respectively. Then, the actual control value of the system can be selecte as: u 6x 7xx ke+ xɺ = ( 8 Thus, the ifferential of the error equation ( can be escribe as: eɺ = ɶ x + ɶ x x + ɶ u k e ( Stability conition an aaptive laws Define Lyapunov function as follows: 5 V = z + z + e + ρ i i ɶ + i= ρɶ ρ6tɶ t Whereρ i >, i=, 6,8 are aaptive gains. (6 With the erivation of (, the equation ( can be reache: Vɺ = zzɺ + zzɺ + eeɺ ρ ɶ ρ ɶ ρ ɶ ρ ɶ ρ ɶ (7 ρ ɶ ρ TT ɶ t t Insert the equation (6, (, ( an (5 into the equation (7, the equation (8 can be got: Vɺ = kz kz ke + zz ( c k xz ɶ ( zx + ρ ɺ + ( c k xz ɶ ( zx + ρ ɺ ɶ ( zx+ ex + ρ ɺ ɶ ( zxx (8 ex x+ ρɺ ɶ 5( zx+ ρɺ ( c k z Tɶ t ( z+ ρ ɺ 6Tt + ( z u + e u ρ ɺ ɶ8 q 8 8 As the parameter of is magnetic pole number of the permanent magnet synchronous motor, this parameter will not change uring the operation, thus, the change ISSN: Issue 5, Volume 9, May

7 rate of can be taken as zero. Thus the aaptive laws of the system can be obtaine as follows: ɺ ( c k xz = ( zx ρ ɺ ( c k xz = ( zx ρ ɺ = ( zx+ ex ρ ɺ 5= zx ρ5 ɺ ( c k z Tt = ( z+ ρ6 ɺ 8= ( zuq + eu ρ8 choosing Here, the equation (8 can be escribe as: Vɺ = k z k z k e + z z (9 Pφ f For = > an is boue.then if J >, moreover k, k, k >, k k then V ɺ <. An then V will be positive efinite anv ɺ will be negative efinite. Thus this system will be Lyapunov asymptotic stability. From the erivation above, with the efinition sliing surface of equation (9 an the error function of the equation (, the controller mae up of equation ( an equation ( can be esigne. With the selecte aaptive control law of equation (9, when selecting > ( k k The whole system will be asymptotic stability.. Simulation Experiments In this section, the propose approach above has been carrie out in PMSM to verify the performance of recursive-base sliing moe aaptive control scheme, using MATLAB/Simulink. The parameters of the PMSM are given in Tab. I. The simulation results are shown in Figs. -. Tab. PMSM Parameters Machine parameters value Resistance of the stator winings( Ω.875 Magnetic Pole number Combine inertia of rotor an loa J (kg.m Amplitue of the flux inuce by the permanent magnets of the rotor in the stator phasesφ (Wb q an axis inuctances Lq L Combine viscous friction of rotor an loa B(N.m.s/ra..75 = (H.85 In table, except magnetic pole number, the remaining parameters values of the PMSM are all change or unpreictable. The paper focuses on the stuy of the control system tracking features when the loa moment of inertia J an the loa torquet m change, an then proves the correctness of the controller use in simulation experiment. The sinusoial signal is selecte as the reference input in simulation. During the operation, the moment of inertia is J =.+.sin(.5 t( kg m, which is mae up of a constant value an a sinusoial isturbance. An the loa acte upon the motor is the superposition of a step signal an a unit sinusoial signalsin(π t. With the erivation in last section, it can be notice that in theory, the greater the controller parameters k,, an c are, the faster the system response is an the smaller the tracking error will be. However, if these parameters are chosen too larger, this will make the system spee, voltage an other control variables beyon ISSN: Issue 5, Volume 9, May

8 the allowable range. After a lot of simulation experiments, accoring to the physical parameters in Table an the erive control parameters scopes in section,the control parameters can be chosen as k = 57, k = 6, k = 5an c=. The simulation experiment shows that the control system has a goo tracking performance, an all the system parameters also operate normally, the simulation results as shown below from figure to figure. angle(ra st ata simu ata time (s Figure the compare of the esire angle an simulation angle I cunrrent(a angle error(ra time (s x - Figure the error of the angle tracing process simu current st current time(s Figure the compare of the esire current of -axis an the simulation current of -axis iq c u rre n t (A time(s Figure the control current of the q-axis in simulation In Figure, the soli line is the simulation angle of the motor, while the ot line means the esire angle change process provie. It can be seen that the motor can trace the esire angle very goo, only leaving small vibration error in figure. As the simulation is conucte in the situation where there exist uncertain in moment of inertia system an the unstable loa, this error is small enough to be accepte. An still with the larger control parameters, this error will become smaller. In figure, for the esire current of the -axis is zero, the simulation value of the -axis current can approximate the zero very sharply. Moreover, from Figure an Figure it can be notice that the current of the system permanent magnet synchronous motor are within the efinite scope. From the simulation results above, it can be conclue that with changing physical parameters in PMSM an the changing external loa, the combine recursive-base sliing moe aaptive controller can control the permanent magnet motor effectively. Discussion From the above simulation results it can be seen that the combine control metho ie.recursive-base sliing moe aaptive control, compare with common the vector control, has the following avantages: ( In the process of system esign, the ajuste parameters are less in combine control esign than vector control esign. For the position servo control, only nee four parameters while in the common controller using vector control nee seven parameters [5]. Therefore the control metho propose is more easily to esign an to achieve in engineering than the vector control. ISSN: Issue 5, Volume 9, May

9 ( The combine control metho propose can give reference to the parameters selection to the controller, which can be seen with equation (. ( The combine control metho propose with goo static characteristics an ynamic characteristics can track quickly the location of a given signal. ( The combine control metho propose with large robustness has the ability to inhibit a number of loa isturbances uner the outsie worl an parameters change internal. the effectiveness an correctness of the combine control strategy. ACKNOWLEDGEMENTS The authors woul like to thank The Ministry of Science an Technology of the People s Republic of China for her financial support in project: 7BAF9B an the Support by China Postoctoral Science Founation 5. Conclusions In orer to meet with the worlwie emans for energy-saving emission, in many areas permanent magnet synchronous motor is graually replacing the traitional three-phase asynchronous motor. The PMSM is a complex multi-variable, nonlinear, strong coupling of the multiple-input multiple-output system. It is ifficult to esign the controller, epecally the control performance of the PM synchronous motor rive system is still influence by the uncertainties of the plant, which usually are compose of unpreictable plant parameter variations, external loa isturbances. This paper try to settle the control problem of the permanent magnet synchronous motor position servo control in the situation where there exist unpreictable plant parameter variations an external loa isturbances. Accoring to the characteristics of permanent magnet synchronous motor, the combine control metho which consists of the sliing moe control metho, recursive control metho as well as aaptive control metho is propose, which integrates the virtues of these three kins of controller. The Lyapunov stability theory is use to testify the control theory an esign the tracking controller of PMSM, an with this theory, the learning algorithm of the unecie parameters has been erive an the reference to the control parameters has been given. The position servo controller has been teste in simulation experiment on the PMSM moel with internal interference an external loa isturbance. The theoretical an simulation experiments have valiate Reference [] Slemon, G. R. Electrical machines for variable-frequency rives. Proceeing of the IEEE [J], 99, 8(8:-9. [] Cetin E., Oguz U.A hybri controller for the spee control of a permanent magnet synchronous motor rive[j],control Engineering Practice, 8,6 (:6-7 [] L. Tang, L. Zhong, M.F. Rahman, Y. Hu, A novel irect torque control for interior permanent-magnet synchronous machine rive with low ripple in torque an flux - a spee-sensorless approach, IEEE Transaction Inustry Application,,(9: [] J. Rorguez, J. Pontt, C. Silva, etc. Preictive Current Control of a Voltage Source Inverter, IEEE Transaction Inustry Electronics,7,5:95 5 [5] Fayez F. M. El-Sousy, High-Performance Neural-Network Moel-Following Spee Controller for Vector-Controlle PMSM Drive System[C], Proceeings of IEEE International Conference on Inustrial Technology. Hammamet, Tunisia, :8- [6] Hemici, B.; Nezli, L.; Tajine, M.; Boucherit, M.S. Robust PID/backstepping control esign for permanent magnet synchronous motor rive.control an Intelligent Systems,6,(:9- [7] Paponpen, K., Konghirun, M., An improve sliing moe observer for spee sensorless vector control rive of PMSM[C].CES/IEEE 5th International Power ISSN: Issue 5, Volume 9, May

10 Electronics an Motion Control Conference, Shanghai, China,7,, [8] Lee Tzann-Shin, Lin Chih-Hong, Lin Faa-Jeng. An aaptive H controller esign for permanent magnet synchronous motor rives [J]. Control Engineering Practice, 5, (:5-9. [9] Elmas Cetin, Ustun Oguz, Sayan Hasan H. A neuro-fuzzy controller for spee control of a permanent magnet synchronous motor rive [J]. Expert Systems with Applications, 8, (: [] Cheng Kuang-Yao, Tzou Ying-Yu. Fuzzy optimization techniques applie to the esign of a igital PMSM servo rive [J].IEEE Transactions on Power Electronics,, 9(: [] Kumar, Rajesh,Gupta, R.A., Bansal, Ajay Kr. Ientification an control of PMSM using artificial neural network[c].ieee International Symposium on Inustrial Electronics, Caixanova-Vigo, Spain :7,-5 [] El-Sousy, Fayez F.M.Fuzzy aaptive neural-network moel-following spee control for PMSM rives WSEAS Transactions on Systems, 5, (:56-59 [] Brock S., Deskur, J.,Zawirski, K. Robust spee an position control of PMSM. In Proceeings of the IEEE International Symposium on Inustrial Electronics., : , Ble-Slovenija. [] Wai, R. J. Total sliing-moe controller for PM synchronous servo motor rive using recurrent fuzzy neural network. IEEE Transactions on Inustrial Electronics, 8(5, [5] Florent Morel, Xuefang Lin-Shi, Jean-Marie Retif etc. A preictive current control applie to a permanent magnet synchronous machine, comparison with a classical irect torque control [J], Electric Power Systems Research.8, 78(8:7-7 [6] Cascella, Giuseppe L.,Neri, F.,Salvatore, N.,Acciani, G., Cupertino, F., Hybri EAs for backup sensorless control of PMSM rives,wseas Transactions on Systems, 6,5(:-5 [7] Guchuan Zhu, Louis-A.Dessaint, Ouassima Akhrif,etc.Spee Tracking Control of a Permanent-Magnet Synchronous Motor with State an Loa Torque Observer[J],IEEE Transactions on Inustrial Electronics,, 7(:6-55 [8] Hung, J. Y., Gao, W., & Hung, J. C. Variable structure control: A survey. IEEE Transactions on Inustrial Electronics, 99, (,. [9] Garagic, D., Srinivasan, K. Application of nonlinear aaptive control techniques to an electrohyraulic velocity servomechanism. IEEE Transactionson Control Systems Technology, :(,. [] Guan, C., Zhu, S. Aaptive time-varying sliing moe control for hyraulic servo system. In International conference on control, automation, robotics an vision, China, : [] Alleyne, A., Liu, R. A simplifie approach to force control for electro hyraulic systems. Control Engineering Practice,, 8, [] Liu, R., Alleyne, A. Nonlinear force/pressure tracking of an electrohyraulic actuator. ASME Journal of Dynamic Systems, Measurement an Control, :, 7. [] Yao, B., Bu, F., Reey, J., Chiu, G. T. C. Aaptive robust motion control of single-ro hyraulic actuators: Theory an experiments. IEEE/ASME Transactions on Mechatronics, :5(, [] Duraiswamy, S.,Chiu, G.T.C. Nonlinear aaptive nonsmooth ynamic surface control of electro-hyraulic systems. In Proceeings of the American control conference, Denver, Colorao, :87 9. [5] Liu, S., & Yao, B.Inirect aaptive robust control of electro-hyraulic systems riven by single-ro hyraulic actuator. In Proceeings of the IEEE/ASME international conference on avance intelligent MeChalroniCS (AIM ZW,:96. [6] Shi, Z., Gu, F., Lennox, B., Ball, A. D.The evelopment of an aaptive threshol for moel-base fault etection of a nonlinear electro-hyraulic system. Control Engineering Practice, 5:(, [7] Zhu, W. H.,Pieboeuf, J. C.Aaptive output force tracking control of hyraulic cyliners with applications to robot manipulators. ASME Journal of ISSN: Issue 5, Volume 9, May

11 Dynamic Systems, Measurement an Control, 5:7, 6 7. [8] llyas Eker,Sliing moe control with PID sliing surface an experimental application to an electromechanical plant,isa Transactions,6: 5(: 9 8 [9] Li, G.,Khajepour, A. (5. Robust control of a hyraulically riven flexible arm using backstepping technique. Journal of Soun an Vibration, 5,8, Zhang Yaou (977, -, PhD& post-octoral in Shanghai Jiao Tong University, research areas: system moeling an control, nonlinear control, etc., yaou_zhang@sjtu.eu.cn;zhao Wan-sheng (957-, Shanghai Jiao Tong University, professor; Hong-Yu Wei (968-, Shanghai Jiao Tong University, lecturer. ISSN: Issue 5, Volume 9, May