Robust intelligent control of a speed sensorless induction motor

Robust Intelligent Control of a Speed Sensorless Induction Motor zyxwvutsrqp zyxwvuts zyxwvu zyxwvut zy zyxwv M. A. Denai, S. A. Attia Abstract This paper reports results of recent applications of intelligent control techniques to a j e l d oriented induction machine. Induction motors are characterised by complex, highly non-linear and time-varying dynamics and inaccessibility ($some states and outputs f i w measurements. The advent of vector control techniques has partially solved induction motor control problems because they are sensitive to drive parameter variations and pe$ormance may deteriorate if conventional controllers such as PID are used. Withfuzzy logic and neural networks based controllers, uncertainties in the plant parameters and non-linearities can be dealt with more efficiently than model-based techniques. However, a commonly known disadvantage of these methods is the lack of systematisation and rigorous design tools. Hybrid control architectures, combining control theory with artificial intelligent tools can solve eficientlv complex control problems. Three control approaches are developed and applied to adjust the speed of the drive system. The.first control design combines the variable structure theory with fuzz-y logic concept. In the second approach neural networks are used in an internal model control structure. Finally, afLlzzy state feedback controller is developed based on pole placement technique. A simulation study of these methods is presented. The effectiveness of these controllers is demonstrated,for different operating conditions of the drive system. 1 Introduction zyxwvuts Combining control theory with artificial intelligent tools leads to a more effective control design with improved system performance and robustness. While modern control allows different design objectives such as steady state and transient characteristics of the closed loop system to be specified, fuzzy logic and neural networks are integrated to overcome the problems with uncertainties and non-linearities in the plant encountered with classical model based design. Three control methods are introduced and applied to an induction motor. In the first design approach the basic fuzzy logic controller (FLC) is regarded as a kind of variable structure controller (VSC) for which stability and robustness are well established [8], [91. This follows the interpretation of linguistic IF THEN rule as a set of controller structures that are switched according to the process states. In the second approach, the basic idea of the proposed controller is similar to the gain scheduling technique. Controller design is based on a reduced order state space model of the motor drive from which a family of local state space models covering the operating range of the drive system are defined. We then use the state feedback design concept to get a linear state feedback controller for each local model [lo]. These local controllers are inferred in one global state feedback controller using a simple fuzzy inference technique. The third design approach is based on the well known internal model control concept [l 11. To improve the robustness of the controller neural networks, trained with a reduced order field oriented induction motor model, are introduced to form the inverse model control algorithm in replacement of the classical model based structure. zyxwvu Induction motors are characterised by complex, highly non-linear and time-varying dynamics and inaccessibility of some states and outputs for measurements and hence may be considered as a challenging engineering problem. Field orientation control (FOC) or vector control [ 11 of induction machine achieves decoupled torque and flux dynamics leading to independent control of the torque and flux as for a separately excited DC motor. This is achieved by orthogonal projection of the stator current into a torque producing component and a flux producing component. This technique can be performed by two basic methods: Direct vector control and indirect vector control. In direct field orientation, the instantaneous value of the flux is required and is obtained by direct measurement using flux sensors or flux estimators. Whereas indirect field orientation is based on the inverse flux model dynamics and there are three possible implementations based on stator, rotor or air-gap flux orientation. The rotor flux indirect vector control technique is the most widely used due to its simplicity. FOC methods are attractive but suffer from one major disadvantage. They are sensitive to parameter variations such as rotor time constant and incorrect flux measurement or estimation at low speeds [2]. Consequently, performance may deteriorate if a conventional speed controller such as PID is used. Fuzzy logic and neural networks based controllers are fast emerging alternatives to conventional controllers in situations where there is a large uncertainty or unknown variations in plant parameters and structure. Their application to electric drive control has been considered [ 3-71. Again these methods shortcoming is the lack of systematic design tools. ETEP Vol. 12. No. 2, March/April 2002 1 I7 ETEP zyxwvutsrqp zyxw zyxwvutsrq zyx zyxwvut zyxwvuts These controllers are evaluated under simulations for a variety of operating conditionsof the drive system and the results demonstrate the ability of the proposed control structures to improve the performance and robustness of the drive system. A speed observer based on neural networks is designed and included in the closed loop control structure to achieve a sensorless operation of the drive system. 2 Induction motor equations The d-q dynamic model of the squirrel-cage induction motor (SCIM) with the reference frame fixed to the stator is given by [2] -L, 1+ T , s 2lpJ iis Fig. Reduced Order Of the "IM zy zyxw zyxw Hence torque and rotor flux may be controlled separately through i,, an! ids, respectively. The adequate torque reference Te is generated from speed*error via the controller while the flux reference ar is kept constant for each operating point. For the purpose of controller design, the reduced order model of the SCIM given by Fig. 1[12] is used, where TLis the load torque. The state space representation of the reduced order model is 0 (7) RsLm -wLsLm -44 -wLsLm 9 2 KT = -&KT PJ i&, XI = W, ~2 = do dt (8) where The electromagnetic torque can be expressed as 3 Robust fuzzy variable structure control (FVSC) The design method of the fuzzy controller is based on the variable structure approach. The basic idea follows the interpretation of the following fuzzy rules Ri:IF A,AND Bi THEN Ci where (3) are the rotor flux components expressed in the stator reference frame. The field orientation principle consists of aligning the rotor flux on the d-axis to make the q-axis component equal to zero. Expressing this in the excitation reference frame gives @& = 0 and @& = constant (4) The equations ensuring field orientation are expressed as (9) as a control structure that is switched according to the system states. Hence fuzzy controllers may be viewed as a class of variable structure controllers. VSC strategy consists of switching a different control structure at each side of a given switching surface according to a predefined switching function. The interesting feature of VSC is that under certain conditions the system responds with a sliding mode on the switching surface and in this mode the system is insensitive to parameter variations and disturbances. The basic control law of variable structure systems (VSS)is given by u = -K s&S) (10) where K is a constant parameter, sgn(.) is the sign function and S is a switching function defined by s =fTx 3PL, where KT = 44 Under these conditions, the induction machine is transformed into a linear current/torque converter with 118 (1 1) When S = 0 this represents the switching surface and defines the desired dynamics. Let the desired dynamics of the drive system be specified in terms of the error trajectory as shown in Fig. 2 which indicates two operating regions corresponding to fast (- q)and slow (- m,) dynamics, respectively .The system response is dominated by (PB, ETEP Vol. 12, No. 2, MarcWApril2002 z zyxwvutsrqp zyxwvutsrqp E TEP de 4 Switching de4 zyxwv zyx zyxwvu Fig. 3. Fuzzy PI controller structure 4 Fuzzy state feedback control (FSFC) t EZ NB NM NS - L ~ I-Leo -50 mC PS PM Assumed that a family of linear state space models may be obtained for different operating points of the system. A related global fuzzy model may be formulated by the following rules PB R':IF XI is F,' AND x2 is F&.AND Leo Leo Lel p e mC THEN = Ai x y = c x Fig. 2. Desired dynamics specified in terms of mfand m, + Bi u i = 1, x, is F: ..., L (14) The nominal model may be described analytically zyxwvuts zyxwvutsrqp by PM, NM, NB} in the first region and by {PS, EZ, NS) in the second region. By specifying the desired mf and m, and assuming the range for the error signal { Le, me},the membership functions related to the error change (de)chosen here of triangular shape are adjusted by the following relationships X = 4~+ B,u (15) with i=l i=l pi being the membership factor for the i* rule based on Ldeo me mde = ms Le (, Le Ldei = mfLei - (mf - ms> i = 0,l (12) me the Sum-prod inference method. The basic idea is to develop for each rule a state feedback control law using the classical pole placement topology. The state feedback is formulated as R': IF x1 is F,' AND x2 is F; ...AND zyxwvuts The controller structure is Proportional-Integral (PI) and is illustrated by Fig. 3. The proportional and integral gains are given by Kp = K, - % ( K d ) and KI = K , 3 (K,) (13) % (.) is defined by the controller rule base which is resumed in Tab. 1, where {NB, NM, NS, EZ, PS, PM, PB ) are linguistic variables. t e + NB t de 4 NM NS EZ PS PM PB PS PM PB PB PB PB EZ PS PM PB PB PB NS EZ PS PM PB PB NM NS EZ PS PM PB NB NM NS EZ PS PM - {Xu = Ai- Kx ~+ xBi u = THEN X, is F: i = 1, ..., L (17) where Ki is the gain vector related to the ( A , Bi) state space model. These local controllers are inferred into one global fuzzy state feedback controller for the overall operating regimes of the drive system. L C pi Ki zyxwvutsr PB EZ PM NS PS NM EZ NB NS NM NB NB NB NB NM NS EZ PS NB NB NB NB NB NM NS EZ K = i=l Hence the fuzzy rules related to the motor speed are formulated as follows R': IF x1 is F' THEN [: Tab. 1. FVSC rule base The Max-min inference method has been used and the defuzzification procedure was based on the center of area method [ 131. ETEP Vol. 12, No. 2, March/April2002 Fi correspo..,s to the fuzzy set i defined by the linguistic labels (NG, NM, ...) and KT (F') is the gain value for a given interval. 119 ETEP zyxwvutsr zyxwvutsrqponmlk z zyxwvuts zy zyxwvutsrqponmlk e zyxwvutsrqpo SCIM - A I I -w 1I t II adaptation mechanism Fuzzy Fig. 4. FSFC with integral action + ondly, the controller robustness is improved by introducing a low pass filter to allow for modelling errors. Although this design technique produces a robust controller, it does require a model of the controlled process to be formulated and hence possesses the shortcomings of model based control techniques. Artificial Neural Networks (ANN) are potential candidates for approximating complex non-linear process dynamics and have been used to formulate a variety of control strategies [14]. There are two basic design approaches: - Direct design: where the neural network is itself the controller. The most fundamental method is termed “direct inverse control”. It uses a trained inverse model of the process as a controller. - Indirect design: the controller uses a neural network to predict the process output. In the following ANN are used in combination with IMC structure to give the overall closed loop control system of Fig. 6. In Fig. 6 Net 1 and Net 2 are neural networks representing the induction machine inverse and forward models, respectively. F is a first order compensating filter included to provide the desirable transient response and robustness chosen as zyx Furthermore, an integral action has been introduced in the control structure in order to cope with steady state errors. The overall control system configuration is shown in Fig. 4. With reference to Fig. 4, the fuzzy adaptation mechanism is based on the following algorithm R’: IF x1 is F’ 0 (20) THEN[i:]=[0 0 -Tr- I ] [ ~x ~ ] + [ K T : ~ ) ] ~ zyxwvutsrqpo ’ I-a F(2) = z - a where ki is the integral gain related to the ithoperating point. The state feedback with integral action is obtained as i=l O<a<l (23) With reference to Fig. I the speed transfer function is obtained as zyxwvut Discretizing eq. (24) with a sampling period T, leads to the following difference equation where pi represents the speed membership grade related to the fuzzy set i. ~ ( k=) a ( k - 1) + K i [iqs(k) + iqs(k - l)] (25) KT T, where KT = 2 The SCIM neural network model Net 2 is a multilayer perceptron (MLP), a feedforward neural network with a three neurons input layer, a ten neurons hidden layer and one neuron output layer trained using the Levenberg-Murquard?Algorithm (LMA) as illustrated by Fig. 7. The inverse model is described by the following difference equation 11 4 Internal model controller based on neural networks (NIMC) The basic architecture of a classical internal model controller (IMC) is illustrated by Fig. 5. A system model is placed in parallel with the actual system. The difference is used to adjust the command signal. An attractive feature of IMC is that it produces an offsetfree response even when the system is subjected to a constant disturbance. The controller design procedure is performed in two stages. Firstly, since the controller is the inverse of the process model, a perfect process model is assumed and the closed loop performances are specified. Sec- Inverse model 1 iqs(k) = - [a(k)- a(k - I)] KT - iqs(k - 1) (26) Net I Process Net 2 Fig. 5. IMC structure 120 Fig. 6. IMC based on neural networks models ETEP Vol. 12, No. 2, March/ApriI2002 L I z z zyxwvutsrqp z ETEP h Observer of Fig. (BI) zyxwvut zyxwvu zyx Fig. 7. Training of the forward neural model based on the SCIM reduced order model The stability of the training process is improved by using a different discretisation procedure. For T, small the difference equation is obtained as (z - 1) w(k) = 2 K k iq,(k) (27) The same training process is used for the inverse model. Finally, a first order reference model is introduced to overcome the problem associated with the future value w(k + 1). The overall bloc diagram of the closed loop control system is represented in Fig. 8. In what follows, the reference model at the input is taken as a first order with a time constant of 0.021 s. Fig. 9. Training of the neural network speed observer change starting at t = 0.4 s is applied for high and low speed conditions. The results are illustrated by Fig. 10 which demonstrates the ability of the trained neural network to track low and high speed waveforms. The neural network model has been trained only under nominal speed conditions and the fluctuations observed at low speed operation may be a result of this. Inverse model 0.4 0.6 0.8 s I t- Fig. 8. Closed-loop system structure Fig. 10. Performance of the ANN based speed observer for high and low speed conditions a) actual motor speed; b) neural network output 5 Speed observer design 6 Performance evaluation In the drive closed loop control scheme a rotational transducer is often included to produce the speed measurement feedback signal. These sensors lower the system reliability in hostile environment and increase the overall system investment. Recent research investigations have been focused on the design of sensorless drives. Several approaches have been proposed [ 151, [16]. In what follows, a speed estimator is designed based on neural networks. In Appendix B are derived the equations of a classical speed observer that is used to train the neural network model. The neural network model is an MLP with one hidden layer consisting of ten neurons and logarithmic activation functions. The neural estimator is placed in parallel with the classical observer and trained according to the process described by Fig. 9. In the training mode, a set of training data is used to adjust the weights of the neural network model. To validate the performance of the proposed speed estimator, a variable speed command including a ramp The parameters of the induction motor considered in this study are resumed in Appendix A. The performances of the proposed controllers are evaluated separately under different operating conditions of the drive system and then their robustness is compared with respect to rotor resistance variations. ETEP Vol. 12, No. 2, March/April2002 zy zyxw 6.1 FVSC Initial simulations are performed in order to establish the suitable range of the design parameters mfand m,.In Fig. 11 are shown the speed responses for different values of these parameters. A large value of mfproduces a fast response with a consequent overshoot while a smaller value leads to a slowly rising response. The value of m, controls the response settling time and should not be too large. In what follows the tuning parameters will be fixed to [mf, m,] = [lo, 51. Next, the tracking performance is tested. The drive system is subjected to a variable speed reference profile 121 zyxwvutsrqp zyxwvuts zyxwvutsrqp zyxwvutsrqpo E TEP tr2 140 rad/s w loo t 0 0 go 60 40 20 zyxwvut zyxwvutsrqp zyxwvutsrqpo zyxwvutsrqp zyxwvut 0 0 0.05 0.1 0.15 s 0.2 t - t--, Fig. 11. Step response of the SCIM for different values of mf and m,, [mf, m,]= [ 10,5] (dash), [5,51 (dash-dot), [5, 101 (dot) Fig. 13. Speed response with two load changes I I I I I I I I 0.2 0.4 I 200 t N-m Te 0 t !2 iL1 -200 0.4 0.6 0.8 s 1 0 0.6 0.8 s 1 t--, t--, Fig. 12. Drive system response under a variable speed reference Fig. 14. Speed response under two load changes with ANN based observer as illustrated in Fig. 12. As seen from the figure, the actual rotor speed overlaps the variable speed reference. The performance of the design controller is evaluated in the presence of load changes. In Fig. 13 is shown the speed response under two load variations from 0 to 80 Nm and from 80 to 40 Nm applied at t = 0.6 s and 0.8 s, respectively. This result demonstrates the ability of the controller to produce the required torque compensating component in order to maintain a stable response. Speed sensorless operation of the drive system is illustrated by Fig. 14. The rise time is shorter than that of Fig. 13. However, small fluctuations and an overshoot can be observed in the response. 1'' pole configuration: 6.2 FSFC In this simulation study five operating points are used for defining the fuzzy state space models using the reduced order model of the SCIM corresponding namely to the speeds 1500, 1900, 2250, 2600 and 3000 rpm. On the basis of these local models, local state feedback controllers stabilising the drive system around these operating points are designed using Akkeman's formula with the following desired pole configurations 122 Eigenvalue 9.51e-1 9.44e-1 + 5.4e-2i 9.44e-1- 5.4e-2i Magnitude 9.51e-1 9.46e-1 9.46e-1 Damping 1.00 7.00e-1 7.OOe-1 Frequency 5.OOe+l 8.OOe+l 8.OOe+l Damping 7.a-1 7.OOe-1 1.00 Frequency 3.OOe+l 3.00e+l 9.OOe+l Pdpole configuration: Eigenvalue Magnitude 9.79e-1 + 2.le-2i 9.79e-1 9.79e-1 - 2.le-2i 9.79e-1 9.14e- 1 9.14e-1 Then the five controller gains are directly inferred into a global state feedback controller using a simple fuzzy inference procedure. The resulting membership function of the global controller is given by Fig. 15. The step responses related to the pole configurations given above are shown in Fig. 16. The first configuration of poles produces to a better transient response and will be used in the remaining simulations. Next, the performance of FSFC with the first pole configuration is evaluated under different operating conditions of the drive system. The load torque is kept constant while the drive system is subjected to step changes and a slow ramp as shown by Fig. 17. The response to the ramp is rather slow which may be improved by selecting a different pole location. ETEP Vol. 12, No. 2, MarcWApril2002 z zyxwvutsrqpo zyxwvut ETEP NP EZ NM PB PM zyxwvutsr zyxwvu zyxwv A t -800-600 -400 -200 200 400 600 800 Speed + 0 o il ,-ZOO A., 0 zyxwvu I I 0.2 0.4 0.6 0.8 s 1 f+ Fig. 15. FSFC membership function Fig. 18. Speed response under load torque variations t kl t /- 1.4- k2 1.2: /- t k3 t- Fi 16. Speed step responses: I St configuration (dot), 2 configuration (dash-dot) ll9 Fig. 19. FSFC controller gains It is to be noted that FSFC design was based on the reduced order model of the K I M which demonstrates once again the ability of the controller to maintain good performance in the presence of unmodelled dynamics. 6.3 NIMC 0.6 0.4 0.8 s 1 t - Fig. 17. Speed response under variable reference The drive system is now tested under variable speed reference and load torque changes applied at t = 0.2 s, 0.5 s and 0.8 s, respectively. The result of Fig. 18 shows a good control with zero steady state errors. There are no fluctuations in the drive response hence load torque disturbances are rejected by the controller. By changing the speed command FSFC adjusts smoothly its feedback and integral gains accordingly to the new operating points as illustrated by Fig. 19. ETEP Vol. 12, No. 2, March/April2002 In IMC, the linear filter F(z-*) is designed to provide a desirable robustness with respect to modelling errors and improves the tracking properties to the overall closed-loop drive system. In Fig. 20 is shown the speed response for different values of the filter constant a.It appears that larger values of a slow down the response. In what follows a is fixed to 0.5. In the following simulation, the performance of the IMC structurebased on a first order reference model with a time constant of 0.02 1 s is subjected to load changes. In Fig. 21 load variations are applied from 0 to 80 Nm and from 80 to 40 Nm at 0.6 s and 0.8 s, respectively which confirm the robustness of the neural networks based IMC structure with respect to the model based one. The neural network model prediction error related to this result is given by Fig. 22. In the initial adaptation stage the neural network output exhibits some fluctuations due to the new operating conditions and this also affects the torque response. However, the controller is able to maintain a stable response. 123 zyxwvuts zyxwvutsr zyxwvutsr zyxwvuts ETEP a = 0.95 a = 0.7 t- t- zyxwvutsrq zyxwvutsr zyxwvut zyxwvut 0.3 s C4 t + zyxwvu zyxwvutsr s "0 0.05 0.1 t- 0.2 t- Fig. 20. Speed response for different values of the filter cutoff frequency a A 150 f i i :.:Lb/ " t Te 0 t Y0 iLI -200 0 0.2 0.6 0.4 0.8 s 1 t--, Fig. 21. NIMC speed control under load changes 11 t WE .su 0 B g I I I I -1 Fig. 23. Drive speed step response with FVSC (solid), FSFC (dot), and NIMC (dash) response rises slowly with a noticeable overshoot. FSFC exhibits a faster transient response initially but settles down slowly. According to Fig. 23 NIMC leads to a shorter rising and settling times. The results demonstrate comparable steady state performance. It is well known that during the normal operation of a drive, induction motor parameters undergo variations due to thermal changes, saturation and other non-linear effects. Among these the rotor resistance which in turn causes the rotor time constant to vary sometimes up to 50 %. As stated above this results in performance degradation of the FOC. In the next simulation result, the robustness of the three controllers with respect to a variation in the rotor time constant is investigated. This situation is simulated by a linear variation in the rotor resistance such that R, = 0.0764 (1 + 2.5 t ) corresponding to a variation of 50 % in the rotor time constant. Fig. 24 illustrates the results of this simulatiop,,The dotted line corresponds to a constant R, w h i l e , h solid one is related to a variable R,. At f = 0.4 s, where R, is twice its nominal value, a second step change in the speed reference is applied. From Fig. 24a it can be seen that -2 -3 a) -4 tr E ! G l 8 -5 100 -6 0 I 0.2 I I 0.4 0.6 I 0.8 I s 1 b, tr c, 3 The proposed controllers are now compared under the same operating conditions of the drive system. Fig. 23 shows the responses under a step change in the speed reference. Under FVSC control, the drive speed g i 100 Fig. 22. Neural network model prediction error 6.3 Comparative study of FVSC, FSFC and NIMC g 8 t+ 124 + rg€lFEE3 0.6 0.5 OO 0.7 s 0.8 0.4 t--, Fig. 24. Performance of a) FVSC, b) NIMC,c) FSFC under variable R,; R, = constant (dash); R, = 0.0764 (1 + 2.5 t ) (solid) ETEP Vol. 12, No. 2, MarcWApril2002 zy zyxwvutsr ETEP FVSC is slightly affected while NIMC (Fig. 24b) and FSFC (Fig. 24c) demonstrate robust performance to R, variations. 7 Conclusions vsc vss NIMC IMC ANN LMA MLP FLC FVSC FSFC NB NM NS EZ PS PM PB variable structure controller variable structure system neural internal model control internal model controller artificial neural networks Levenberg-Marquardt algorithm multilayer perceptron fuzzy logic controller fuzzy variable structure control fuzzy state feedback control negative big negative medium negative small equal zero positive small positive medium positive big zyxwv This paper presents some design approaches of hybrid control architectures combining conventional control techniques with fuzzy logic and neural networks. With fuzzy logic and neural networks issues such as uncertainty or unknown variations in plant parameters and structure can be dealt with more effectively and hence improving the robustness of the control system. Conventional controls have on their side well established theoretical backgrounds on stability and allow different design objectives for the closed loop system to be specified. The performance and robustness of the proposed controllers have been evaluated under a variety of operating conditions of the drive system and the results demonstrate the effectiveness of these control structures. A comparative study of the control strategiesin terms of performance and robustness has been conducted. NIMC and FSFC achieved slightly improved results than FSVC. Although their synthesis was based on the reduced order model of the SCIM. The control techniques studied are very suitable for real time implementationdue to their simplicity, robustness and ease of tuning. Appendix A The parameters of the motor used in the simulations are resumed below: P , = 15 kW R, = 0.1062 R R, = 0.0764 R zyxwv zyxwvutsrq zyxwvutsr 8 List of symbols and abbreviations 8.1 Symbols P" T,, TL J P 0 Lm [i:, L, = 0.01547 H Appendix B Starting from the flux equations 0," = L, i," + L, is 0;= L,,,i," + L, is the expressions of 0," and is can be obtained as zyxwvutsrqp zyxwvutsrqponmlkjihgfe zyxwvu R,, R, L,, Lr Tr nominal power electromagneticand load torques rotor inertia pairs of poles motor speed stator and rotor resistances stator and rotor inductances mutual inductance rotor time constant L, = 0.01604 H L, = 0.01604 H J = 0.01768 kg.m2 2p = 4 i$] [i& ],:i d- and q-axis stator currents u,"= &i," + s @ d- and q-axis rotor currents [U:, U&] d- and q-axis stator voltages [id@: ]::i Substitution of eq. (B2) in the drive voltage equations gives Us = R, is + (s - j w ) 0 s (B3) Hence stator current references [Olr 0:,]flux linkages in the stator reference frame R' L Fi' rule related to the ith operating point number of operating points fuzzy sets for the state variables 8.2 Abbreviations SCIM FOC PID squirrel-cage induction motor field orientation control proportional-integralderivative ETEP Vol. 12, No. 2, MarchlApril2002 (B5) 125 E TEP zyxwvutsrq zyxwv zyxwvutsrqp zyxwvuts zyxw Eqs. (B4) and (B5)represent the rotor flux observers and are termed “voltage model” and “current model”, respectively [l]. The rotor flux amplitude and phase are By differentiating eq. (B7) and substituting eq. (B5)gives [8] Hung, J.E; Gao, W ; Hung, J.C.: Variable Structure Control: A survey. IEEE Trans. on Ind. Electr. 40 ( 1993) no. I , pp. 2-2 I [9] Kawaji, S.; Matsunaga. N . : Fuzzy Control of VSS Type and Its Robustness. Fuzzy Control Systems. Kandel A. and Langholz G. (Eds) CRC Press., Boca Raton/USA: 1994, pp. 226-242 [lo] Cao, S.G.; Rees, N.W: Feng, G.: Analysis and Design of Fuzzy Control Systems Using Dynamic Fuzzy State Space Models. IEEE Trans. on Fuzzy Systems 7 ( 1999) no. 2, pp. 192-199 [ I I ] Morari, M . ; Zujriou, E.: Robust Process Control. Prentice Hall, Englewood Cliffs, NJ/U.S.A., I989 [ 121 Zhen, L.; Xu, L.: Sensorless Field Orientation Control of Induction Machines Based on a Mutual MRAS Scheme. IEEE Trans. on Ind. Electr. 45 (1998) no. 5, pp. 824-830 [I31 Lee, C.C.: Fuzzy Logic in Control Systems: Fuzzy Logic Controller - Part I and 11. IEEE Trans. on Syst., Man and Cybernetics 20 (1990) no. 2, pp. 404-435 [ 141 Hunt, K.J.; Sbarbaro, D.; Zbikowski. R.; Gawthrop, PJ.: Neural Networks for Control Systems: A Survey. Automatica 28 (l992), pp. 1083-1 I 12 [ 151 Tajima, H.: Speed Sensorless Field Orientation Control of Induction Motor. IEEE Trans. On Ind. Applic. 29 (1993) no. I , pp. 175-181 [ 161 Elloumi, M.; Al-Hamadi,A.; Ben-Brahim, L.: Survey of Speed Sensorless Controls of Induction Motor Drives. Conf. (IECON), AachedGermany 1998, Proc. pp. 10 18-1023 zyxwvutsrq zyxwvutsrq Hence the drive speed is obtained as In Fig. B1 a bloc diagram structure of this observer is given. Manuscript received on July 28, 2000 Flux observer (voltage model) I H 1 observer Speed - P Fig. B1. Bloc diagram of the speed observer References Vas, P.: Vector Control of AC Machines. LondonKJK: Oxford University Press, 1990 Trzynadlowski, A.M.: The Field Orientation Principle in Control of Induction Motors. BostonKJSA: Kluwer Academic Publishers, 1994 Narendra, K.S.; Parthasarathy, K.: Identification and Control of Dynamic Systems Using Neural Networks. IEEE Trans. on Neural Networks Vol. 1 (1990) no. 1, pp. 4-27 Hunt, K.J.; Sbarbaro, D.: Neural Networks for Non Linear Model Control. IEE Proceedings, Part D, 138 (l99l), pp. 431-438 Lin, EJ.; Wai, R.J.; Wang, S.L.: A Fuzzy Neural Network Controller for Parallel-Resonant Ultrasonic Motor Drive. IEEE Trans. on Ind. Electr. 45 ( 1 998) no. 6, pp. 928-937 Kung. ES.;Liaw, C.M.; Ouyang, M.S.: Adaptive Speed Control for Induction Motor Drives Using Neural Networks. IEEE Trans. on Ind. Electr. 42 (1995) pp. 25-32 Brdys, M.A.; Kulawski, G.J.: Dynamic Neural Controllers for Induction Motor. IEEE Trans. on Neural Networks 10 (1999) no. 2, pp. 340-355 The Authors Mouloud Azzedine Denai ( 1957) received his Bachelor in Electrical Engineering in 1982 from the university of AlgierdAlgeria and his Ph.D. in Control Engineering from the University of SheffielWK in 1988. He is currently Associate Professor at the university of Science and Technology of Oran (USTO). His main fields of interest are intelligent control design, intelligent fault detection in power systems, advanced control of power devices. (Faculty of Electrical Engineering, Laboratory of Computer Automation and Control, B.P. 1505 El-Mnaouar, Oran, Algeria, Fax: +2 13 4 1 425509, E-mail: denai@mail.univ-usto.dz) zyxwvut I26 Sid A b e d Attia (1975) received his Bachelor in Electrical Engineering from the University of Science and Technology of OradAlgeria, in 1999. He is currently a Master student in Vibration and Advanced control at the same University. His main field of interest is fuzzy and neural control. (ENSIEGI N K , Laboratoire d’Automatique de Grenoble (LAG)/France, E-mail: Ahmed.Attia@lag.ensieg.inpg.fr) ETEP Vol. 12, No. 2, MarcWApril 2002