Proceedings of the 4 th International Middle East Power Systems Conference (MEPCON ), Cairo University, Egypt, December 9-2, 2, Paper ID 26. Speed Control of Permanent Magnet Transverse Flux Linear Motor using Artificial Neural Network Controller Ahmed Y. El-Ibiary, Hany M. Hasanien, M. A.L.Badr Electrical Power & Machines Department, Ain Shams University, Faculty of Engineering, Cairo, Egypt, E-mail: eng_ahmedelibiary@hotmail.com Abstract- Recently, permanent magnet transverse flux linear motor have been widely used in many industrial applications such as automatic door openers, machine tool positioning and the most important application is the maglev train. These types of motors one used in high power density applications. To improve the performance of this type of drives, advanced type of controllers should be used. This paper presents the difference between two methods of control on a Permanent Magnet Transverse Flux Linear Motor (PM-TFLM) and compare between the performances in both cases. The two methods of control in this paper are the and the Artificial Neural Network (ANN) controller. Both of the controllers are used for speed control of this type of motors. The dynamic response of Transverse Flux Linear Motor (TFLM) with the proposed controller is studied during the starting process and under different load disturbances. motor, which tends to align the mover in the minimum reluctance position with respect to the stator [6], the TFLM principles of force generation are shown in Fig..b the passive back irons are cut and developed to show the principles of force generation. The magnetic polarities N, S, N, N 2, N 3, S, S 2 and S 3 between mover and stator generate the total traction force F T in one direction. The PM-type TFLM uses the PMs as excitation so that the magnetic flux density in the air gap can be amplified, because the cross-sectional area of PM is bigger than the stator pole width in the air gap. This motor is fed by dc supply through an inverter which transfers the supply from one phase to another, thus each phase has a pulse nature parameters. The force is produced by the tendency of the rotor poles to align with the stator poles of the excited phase. Index Terms Speed control, PID & neural network controllers, permanent magnet Transverse Flux Linear motor (TFLM). I. INTRODUCTION In recent years, permanent magnet transverse flux linear motor drives have been widely used in many industrial applications such as automatic door openers, machine tool positioning and the most important application is the maglev train. The inherent advantages of these machines include high power density per volume because of the magnetic circuit is separated from electric circuit [, 3, 5], low noise, reduced operating cost, low inertia, increase the flexibility of operation because of gearless feature [2, 4]. With these benefits, it is commonly accepted that the TFLM with PM excitation offer a very high force density compared with other machine types by a factor of three to five times [6]. These aspects make the TFLM performance surpasses that of the conventional dc and other ac motors in drives especially where overall efficiency is critical, also the TFLM have major disadvantage as the analysis of TFLM sometime can be more difficult than that of rotary counterparts and the results can be inaccurate because of the end effect by limited mover length [2]. As a result, TFLM drives become competitive to other drives in modern industrial applications requiring precision. The simplest feature of TFLM is the same with the configuration of switched reluctance motor. It has salient pole on both the mover and the stator, but only one member carries excitation winding, as shown in Fig..a, where δ=air gap length, τ p is the pole pitch. The principle of operation is the same with a longitudinal flux counterpart of linear reluctance Fig..a Basic structure of TFLM Fig..b TFLM principles of force generation Fig.2 and Fig.3 show the arrangement of phases A and B of the TFLM. Phase current that was excited and total thrust force versus displacement of mover, in order to have a motion of the mover in one direction, the number of phases of motor should be over two, phase B should be shifted to phase A by τ p /2 in case of using two phases. This means that continuous thrust force should be generated in the same direction [5]. Fig.3 shows the excitation current of the both phases A and B 666
667 and the corresponding generated trust force due to each of this excitation current, it shows also the shift between the two phases and how is the summing of the two component of generated thrust force from each phase to produce the total thrust force in one direction. Fig.2 The arrangement of phases of the TFLM control techniques such as adaptive control [9], fuzzy control [], and variable structure control, have been developed to deal with motion control of the electrical drives. Unfortunately, it generally requires a reference model of the system. Neural networks have been one of the most interesting topics in the control community because they have the ability to treat many problems that cannot be handled by traditional analytic approaches []. The neural network has great potential, using neural topology does not need the mathematical model of the system to be controlled. In modeling and controlling dynamic systems, many different versions of neural network structures are used. Since the late 99s, several applications using neural networks for the compensation of the non linearity caused by the influence of disturbances, i.e. load or parameter variations were described [2] [4]. Combination of different artificial intelligent technologies in the control field found interesting and efficient applications [5, 6]. In fact, neural network have several attributes that make them an interesting new alternative to control a Transverse Flux Linear Motor. This paper introduces a comparison between two methods of speed tracking of Transverse Flux Linear Motor using the neural network controller and using. Moreover, the paper compares the thrust force of the TFLM in both cases and which of the controllers achieve higher dynamic performance and accurate speed tracking control with good steady-state characteristics. II. DYNAMIC MODEL OF TFLM Fig.3 phase current was excited and total thrust force placed on mover position The speed controller used in drive system plays an important rule to meet the other required criteria of the high performance drive. It should enable the drive to follow any reference speed taking into account the effects of load impact, saturation and parameter variation. Conventional controllers such as P, PI and s need accurate mathematical models describing the dynamics of the system under control [7]. In addition to this, types of controllers are difficult to be designed unless an accurate system model is available and if that accurate model is not available the controller requires fine tuning and can`t cope with system parameter variations. Moreover, unknown load dynamics and other factors such as noise, temperature, saturation, etc. affect their performance. Some adaptive control techniques, such as the variable structure and self-tuning don't need a model for system dynamics, the dynamic model is rather developed based on the on-line input/output response of the system. But some investigator overcame this difficulty by updating these models every several sampling intervals [7, 8]. To solve the problems of heavy nonlinearity and parameter variations, advanced The static thrust force is computed by numerical differentiation of the magnetic co-energy which in turn is computed by numerical integration of the flux-linkage current curves. The magnetic co-energy is computed by using the following formula: i Ψ (, i) di x = const W (x, i) = x () Where, W (x, i) is the magnetic co-energy, which is function of the linear displacement x and the electric current i. ψ(x, i) is the flux linkage which in turn is function of the linear displacement and current. This numerical integration is calculated at constant linear displacement. Also, the static thrust force is obtained as follows: ( x, i) W = x ( x, i) F x i = const Where, F x (x, i) is the static thrust force, which is function of both the linear displacement and current. This numerical differentiation is carried out at constant electric currents. The traction force density F xd can be derived by dividing the static thrust force by the area 2τ p 2h i. This force density can be written by the following equation: (2) 667
668 F xd B θ a = (3) 2τ p Where, the traction force density F xd is proportional to the magneto motive force θ a and the magnetic flux density in the air gap B, and is inverse proportional to pole pitch τ p. In this study, the computations are carried out at different rotor displacements between the first unaligned position ( mm) and the aligned position (2 mm), which forms half the rotor polepitch. The aforementioned characteristics data can be stored as a look-up table format. Thus there are two look-up tables for the flux-linkage and for the static force characteristics available to be used during the computation of the motor differential equations. III. SPEED CONTROL OF TFLM WITH THE PROPOSED CONTROLLERS The system under study is shown in Fig.4. The speed references of the individual phases follow a contour function. The speed deviations of the individual phase is then the error signals which is fed to the controller. The controller output is the individual phase current command; which is used as a compensation signal instead of being the current reference directly. A conventional controller is used for motor speed regulation where its output is the conventional square current reference. The compensation signal is then added to the conventional square current reference. Finally, the modified current reference is used to drive the power converter. V r e ω act Controller X on X on new Voltage Source Inverter Fig.4 Speed control of the TFLM TFLM Fig.4 shows also the block diagram for speed control of TFLM using controllers, where: V r :the reference speed. V act :the feedback speed signal. e :the error speed signal. The TFLM is fed from DC supply through an inverter. The feedback control signal is proportional to the actual speed. This actual speed is compared with the desired command reference speed to give the motor speed error (e). This motor speed error is the input of the controller, is used to update the switching turn-on displacement x on new, as X on new= X on old K c.e (4) V act Where: K c : the gain of the controller, X : the switching turn on displacement. That driver is tested under the following condition. First, the motor reaches rated steady state speed under full load torque. Then, the motor is subjected to a severe load disturbance where the load is suddenly decreased (at.2 sec.) to 5% of its initial value, followed by a removal of the disturbance after the motor reaches its steady state speed (at.4 sec. ) as shown in Fig.5. Load Force (P.U.).8.6.4.2.5..5.2.25.3.35.4.45.5 Fig.5 Load Force of the TFLM As said before the TFLM has the same configuration and principal of operation as the switched reluctance motor thus we will use a Switched reluctance motor simulink model and modify the parameters of the model to meet the aspects of the transverse flux linear motor. The data of the TFLM will be given as a lookup table. A) THE CONVENTIONAL PID CONTROLLER The (PID) controller is one of the famous controllers used in a wide range in the industrial applications. The output of the in time domain is defined by the following equation: t de( Δx( = kp e( + ki e( dt + kd (5) dt Where Δ x( is the output of the, K p is the proportional gain, K i is the integral gain, and Kd the derivative gain, and e( is the instantaneous error signal as a function in the time. The input to the PID are the speed error e(, while The output of the PID is Δ x( the compensating signal to control the firing signal of the converter to control the voltage and convert it into an equivalent voltage in order to regulate the motor speed. 668
669 B) THE ARTIFICIAL NEURAL NETWORK CONTROLLER The artificial neural network has found a widespread use in function approximation. A three layer ANN can approximate arbitrarily closely, any non-linear function, provided it`s nonsingular as the TFLM which considered as a heavy nonlinear load on a current controller due to the inductance dependant on the rotor position and magnetic saturation. The conventional controllers fail to achieve good tracking while applied to a nonlinear system. Also, the response of the conventional controllers differs when the operating point is changed. Moreover, the conventional controllers needs a well defined mathematical model and are very sensitive to model inaccuracy. This difficulties are overcome by the controllers use the artificial intelligent techniques. In this point we will use the controller in Fig.4 as an ANN controller which will have the error signal as an input and will give the triggering signal as an output. The function y = f (x, x 2,..., x n ) is the function to be approximated and x, x 2, x 3,... x n are the n variables (n inputs). Thus; the output y can be represented as; y = = mj w x + w x +... + w n w xj= j i m m 2 2 mn n (6) This equation can be represented as shown in Fig.6, where the network structure is n input node in the input layer and m node in the hidden layer. There is also a gain function in each neural, Fig.7 shows a number of possible activation function in neurons. The simplest of all is linear activation function, where the output varies linearly with the input but saturated at ± as shown with a large magnitude of the input. The most commonly used activation functions are non-linear, continuously varying type between two asymptotic values and or - and. These are respectively, the sigmoidal function is called logsigmoid and the hyperbolic tan function is called tansigmoid which is preferred to use - that function which we will use in our system-, there is also the waiting factors W Mn and λ M those will be constants which define the gains of the link between each neuron and the other. x Fig.6 Structure of the propose ANN speed controller The output of single neuron can be represented as: ai = n i{ wijxj bi} f = ( + (7) j Where ƒi is the activation function such as (log sigmoid, tan sigmoid, pure line,..) and bi is the bias. Fig. 7 logsigmiod, tansigmoid, and purelin activation function IV. PERFORMANCE EVALUATION In order to examine the performance of the proposed control scheme, a Matlab/Simulink model was developed. The ANN is tested with the same load torque variations applied to the in order to compare the results under the same conditions and the same disturbance as shown in Fig.5. The following part will concentrate on the dynamic response (speed response and the force response) of the motor during starting and under different disturbances when provided with the and. The neural network controller with 2 input neurons, 5 neurons in the hidden layer and output neuron as compared with that of the PID controller of gains K p = 5, K d =. and K i =.. Where, the proportional gain, derivative gain, integral gain, number of neurons and neurons function are chosen according to the time requirements specifications. It will be explained later in details the difference between the response in the two cases and focusing on that response in each zone. A. Dynamic response during Starting (zone one ): Fig.8.a shows the difference between the dynamic responses of the TFLM driven by the proposed controllers at the starting process. The magnitude of the maximum percentage overshoot which equals.4 in case of using PID and.75 in case of using the. The settling time when using ANN equal.55 sec. and that is much less than that of PID which is equals to.7 sec. It can be knotted that the PID has a very strong undershoot which reaches.994, the speed ripple factor in case of using the conventional is.65% and in case of it equals.45%, Where the speed ripple factor is: 669
67 K r = (V max V min )/ V max (8) Fig.8.b shows the force response there is no large difference between the ANN and PID where the force is depending only on the current. The dynamic response using the ANN controller reaches its steady stat value faster than that of using the where it reaches the steady state value in case of at.55sec. but in case of PID controller occurs at.7sec. Speed (P.U.).2.5..5 possible. On the other hand, the dynamic response of the motor when driven by a indicates the maximum percentage overshoot is equal to.3 but the maximum percentage overshoot when the motor is driven by ANN is.25, the peak time and the settling time is also smaller when using the compared with that the PID controller. Where in case of the peak time is.22 sec. and the settling time is.25 sec. but in the case of using the peak time is.23 sec. and the settling time is.28 sec. Fig.9.a shows the dynamic response of the motor during the second zone and shows the difference where the ripple factor in case of ANN is.37% which is smaller than that of PID which equals.42%. As it is mentioned before and is shown in Fig.9.b there is no large difference in the force response between the performance of the motor when driven by the and the..995.99.4.5.6.7.8.9. Fig.8.a The dynamic response of the motor when driven by the ANN as compared with at the starting process (zone one). Speed (P.U.).5.4.3.2..999 Thrust force (P.U.) 9 8 7 6 5 4 3 2.998.997.996.995.2.25.2.25.22.225.23.235.24.245.25 Fig.9.a The dynamic response of the motor when driven by the ANN as compared with at the half load duration (zone tow). -..2.3.4.5.6.7.8.9. Fig.8.b The dynamic response of the motor when driven by the ANN as compared with at the starting process (zone one). By inspection of the dynamic response, it can be realized that the dynamic response of the TFLM when provided with the neural network controller is much improved in the starting of the motor (zone one) compared with that obtained when the motor is provided with the. The response is faster with smaller overshoots, less ripples and it faster to reach the settling time. B. Dynamic response during a step down load torque disturbance (Zone two): For a good motor performance during this zone, the design requirements are minimum overshooting, the rise time, the peak time, the ripple factor and the settling time is small as Thrust force (P.U.).8.6.4.2 -.2.2.25.2.25.22.225.23.235.24.245.25 Fig.9.b The dynamic response of the motor when driven by the ANN as compared with at the half load duration (zone tow). By inspection of the dynamic response, it can be realized that the dynamic response of the TFLM in case of using the ANN has smaller oscillation magnitude and is faster response and is smaller overshoot than that of the. 67
67 C. Dynamic response during a step up load torque Disturbance (Zone three): Fig..a shows the performance of speed response during switching to full load again; these zone requirements are the same as that of zone two. Fig..a shows the dynamic response of the motor during the third zone, when provided with a neural network controller as compared with PID controller. The dynamic response in case of provided with the neural network controller has no overshoot in compared with the. The neural controller improves the system damping in comparison with that of the where undershoot in case of the PID equals.9945 and on the other hand the undershoot in case of using the equals.997. It also yields a much faster response that allows the motor to reach the steady state faster than in the PID technique where it equals to.4 in case of ANN and.45 in case of PID. The ripple factor in case of PID equals.58% and in case of using the the ripple factor equals.48%. It can be knotted that the gives better response than in the third zone. Fig..b shows the performance of force response with no difference between the two controllers. Speed (p.u.).3.2..999.998.997.996.995.994 2.45.4.45.42.425.43.435.44.445.45.455 Fig..a. The dynamic response of the motor when driven by the ANN as compared with (zone three). Thrust force (P.U.).8.6.4.2 -.2.4.4.42.43.44.45.46.47.48.49.5 Fig..b. The dynamic response of the motor when driven by the ANN as compared with (zone three). IV. CONCLUSION This paper presented a performance evaluation of the Transverse Flux Linear Motor when driven by two deferent controllers The PID and the to ensure excellent reference tracking. The Artificial Neural Network controller is found to enhance the speed regulation and force response of this type of drives over both starting and load disturbance periods. The response of is found to be better than that of a where it is less overshoot, faster peak time, faster settling time. V. REFERENCES [] Do Hyun Kang A study on the Design of Transverse Flux Linear Motor with High Power Density, IEEE International Symposium on, vol. 2, pp. 77-7, August 22. [2] Ji - Young Lee, and Jung-Pyo Hong Analysis of Permanent Magnet Type Transverse Flux Linear Motor by Coupling 2D Finite Element Method on 3D Equivalent Magnetic Circuit Network Method, Industry Applications Conference, 24, vol. 3, pp. 292-298, November 24. [3] Ji - Young Lee, Do Hyun Kang, and Jung-Hwan Jang Rapid Eddy Current Loss Calculation for Transvrse Flux Linear Motor, Industry Applications Conference, 26. vol., pp. 4-46, December 26. [4] Won-Gon Kim, Sang-Jun Cho Control of Transverse Flux Linear Motor to the Linear and curve section by using low-cost position sensors, Industrial Electronics, 27. ISIE 27. IEEE International Symposium on, pp. 322-326, November 27. [5] Tae-yun Kim, Do-Hyun, Jong-Moo Kim,and Dong-Hee Kim A study on control of drive for vibrator Using PM-Type Transverse Flux Linear Motor, Power Conversion Conference, 22. PCC Osaka 22, vol., pp. 43 47, August 22. [6] Jung-hwan Chang, Do-Hyun Kang, Ji-Young Lee, and Jungpyo Hong, Development of Transverse Flux Linear Motor with Permanent Magnet Excitation for Direct Drive Applications, Magnetics, IEEE Transactions on, vol. 4, no. 84453, pp.936-939, May 25. [7] M. A. El-Sharkawi, A. A. EL-Samahy and M.L.EL-Sayed, High Performance Drive of DC Brushless Motors Using NN, IEEE Trans. on Energy Conversion, vol. 9,no. 4738352, pp. 37-322, June 994. [8] S.Weerasooriya and, M.A.El-Sharkawi, Identification and Control of dc Motor Using Back-propagation Neural networks, IEEE Trans. on Energy Conversion, vol. 6, no. 4438, PP. 663-669, Dec.99. [9] B. Robyns, F. Berthereau, J-P. Hautier, and H. Buyse, A fuzzylogicbased multimodel field orientation in an indirect FOC of an induction motor",ieee Transactions on Industrial Electronics, vol. 47, no. 6573367, pp. 38 388, April 2. [] J-H Lee, and M-J Youn, A new improved continuous variable structure controller for accurately prescribed tracking control of BLDD servo motors, Automatic vol. 4, pp. 269-274, December 24. [] Seong-Hwan Kim; Tae-Sik Park; Ji-Yoon Yoo; Gwi-Tae" Speed sensorless vector control of an induction motor using neural network speed estimation" Park Industrial Electronics, IEEE Transactions on, vol. 48, no. 695735, pp. 69-64 Jun 2. [2] M.A. Wishart and R.G. Harley Identification and control of induction machines using artificial neural networks. IEEE Transactions on, vol. 3, no. 4948325, pp. 62-69, Jun 995. [3] Y.S. Kung, C.M. Liaw and M.S. Ouyang Adaptive speed control for induction motor drives using neural networks, IEEE Transactions on, vol. 42, no. 48876, pp. 25-32, August 22. [4] T.C. Chen and T.T. Sheu. Robust speed-controlled induction motor drive based on model reference with neural networks. Inter. Journ. Of Knowledge Based Intelligent Engineering System. Vol.3, pp. 62-7, August 26. [5] K.S. Narendra and K. Parthasarathy. "Identification and control of dynamical systems using neural networks", IEEE Transactions, vol., no. 3665549, pp. 4-27, August 22. [6] T. Sebastian, and G.R. Slemon, "Transient modeling and performance of variable-speed permanent magnet motors", IEEE Transactions Industry Applications, vol. 25, no. 3393958, pp. -6, Sep. 986. 67