Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2132-2138 2132 www.etasr.com Masoumi Kazraji et al.: Fuzzy Predictive Force Control (FPFC) for Speed Sensorless Control … Fuzzy Predictive Force Control (FPFC) for Speed Sensorless Control of Single-side Linear Induction Motor S. Masoumi Kazraji Dept. of Electrical and Computer Engineering University of Tabriz Tabriz, Iran M. R. Feyzi Dept. of Electrical and Computer Engineering University of Tabriz Tabriz, Iran M. B. Bannae Sharifian Dept. of Electrical and Computer Engineering University of Tabriz Tabriz, Iran S. Tohidi Dept. of Electrical and Computer Engineering University of Tabriz Tabriz, Iran Abstract—In this paper a model fuzzy predictive force control (FPFC) for the speed sensorless control of a single-side linear induction motor (SLIM) is proposed. The main purpose of of predictive control is minimizing the difference between the future output and reference values. This control method has a lower force ripple and a higher convergence speed in comparison to conventional predictive force control (CPFC). In this paper, CPFC and FPFC are applied to a linear induction motor and their results are compared. The results show that this control method has better performance in comparison to the conventional predictive control method. Keywords-linear induction motor(LIM); predictive force control (PFC); fuzzy logic; estimation; speed control I. INTRODUCTION Linear induction motors (LIMs) have several advantages such as the lack of need of interface mechanical tools, low mechanical losses, high starting force, and simple and strong structure. These motors are widely used in automation systems and industrial applications such as transportation systems, conveyor drives, electromagnetic launchers, and the transfer of containers in container terminals. Among the different linear induction motors, the single-side linear induction motor receives more attention due to its simpler structure and higher endurance [1, 2]. Linear induction motors receive a lot of attention in transportation systems since they produce direct force without transforming the rotation energy to transition energy. The main characteristics of linear induction motors with electromagnetic excitation in transportation systems include: thrust force, speed, vertical force, efficiency, power factor, and airgap flux density.The appropriate control of characteristics such as force, ripple, and speed convergence of is necessary to obtain a satisfactory operation in transportation systems [3, 4]. Several LIM modeling methods have been proposed. An LIM model based on electrical design with the consideration of the end, the edge, and the skin effects has been investigated in [5]. Usual design parameters can be found in [6] Dynamic LIM models have been investigated in [7-10]. In [7] and [8], a dynamic model based on the structural elements (width and the depth of slots), secondary thickness, and the number of turns is presented. Among the different control methods, Model Predictive Force Control (MPFC) has received increased attention as an effective method [11, 12]. PFC directly predicts the considered variables such as force and stator flux. With the calculation of the effect of each possible voltage vector, a force error and minimum flux is selected as the best voltage vector. Therefore, it is clear that the MPFC selected vector is more precise and more effective in comparison with DFC. In addition, the flexibility of MPFC allows the control to include non-linear factors and to apply the limitations of the control variables. In MPFC, a cost function is usually defined based on the errors of torque amplitude and flux, but in order to have a satisfactory operation, there is a need for an appropriate weight function. However, tuning the weight function is not easy due to the lack of a theoretical design method. In [13], an empirical method for achieving appropriate weight coefficients has been investigated. In [14], a precise discrete time state-space model for induction motors has been discussed and a current restriction in the cost function has been placed for the prevention of over current. According to [15] and [16], although MPTC acts more precisely and more effectively in selecting the voltage vector (in comparison with DTC), applying the selected voltage vector without the tuning coefficient is not optimum. In DTC, the placement of the zero voltage vector along with the active voltage vector in the control period can help in regulating the voltage appropriately and precisely [17]. In [18], minimizing principles of the torque ripple for the calculation of the optimum weight coefficient have been introduced, but the equation of the optimum weight coefficient is complicated and the parameters depend on each other. II. MATHEMATICAL MODEL OF LIM In order to obtain the LIM model in a d-q reference frame, first the stator voltage equation should be introduced [2, 10]:    dsdrdsrdssds dt d iiQfRiRu  (1) Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2132-2138 2133 www.etasr.com Masoumi Kazraji et al.: Fuzzy Predictive Force Control (FPFC) for Speed Sensorless Control … qsqssqs dt d iRu  (2) The equations of the secondary voltage in the direction of dq are as follows:    dr r dr r qr r ds dr dr d u R i R f Q i i dt           (3) qrdrrqrrqr dt d iRu     (4)   Q e Qf Q  1 (5) rrm rp RLL vL Q /)( /   (6) where, Rs and Rr, Ls and Lr, Lp and vr, p and τ are primary and secondary resistance, primary and secondary inductances, primary long and linear speed, pole number and pole pitch respectively, and Lm is the magnetic inductance. f(Q) has been used to take the end effect of LIM into account in (5). Moreover, f(Q) has been used to provide the end effect on the magnetic factor of LIM in the simulation model. The vectors of the stator flux and the secondary sheet flux are calculated from the current and the measured inductance in (7)-(10). The equations of the linkage flux are as follows:    1ds s ds m ds drL i L f Q i i     (7)  qrqsmqssqs iiLiL  (8)    1dr r dr m ds drL i L f Q i i     (9)  qrqsmqrrqr iiLiL  (10) The electromagnetic force of the LIM is estimated by (11) and then (12) is calculated. The thrust force is calculated as follows:  dsqsqsdse iiPF    22 3 (11)                        qsds r r qsdr mr m e ii Qf Qf L L i QfLL QfLP F 1 1 22 3 2    (12) The above equations have been used to simulate LIM. III. FUZZY MODEL PREDICTIVE FORCE CONTROL The general control diagram for the proposed FPFC is shown in Figure 1. It can be seen that the reference of the force has been produced by an external speed control loop and the reference of the stator flux amplitude has been kept stable since the operation of the flux weakening has not been considered in this paper. The information and the details about this control diagram are provided below. A. Estimation of the Flux and Force The precise estimation of flux and force is essential for the satisfactory operation of the FPFC. In this paper, a full-order observer has been applied at low speed range due to high precision. The precision of the estimation and the robustness of the observer are increased against the changes of the motor parameters with the introduction of stator current error feedback. The mathematical model of the observer based on the LIM model in (1) is:  ss iiGBuxA dt xd ˆˆ ˆ  (13) In the above equation,  Tssix ̂ˆˆ  are the variables of the estimation state. PI 2-Level Voltage Source Inverter LIM FPFC Cost Function Mininmazation Pulse gen. uopt , t optFe ref Fe k+2 is k Ѱs k+2 Ѱs ref ωr k us k Vr ref Vr Fig. 1. Control diagram of the FPFC.        rLb b G / 2 (14) In the above equation 2 1 ( )s r mL L L    and b is the negative stable gain. This method of displacing the poles increases the convergence and the stability of the observer especially at low speeds and it is easy to be applied. B. Fuzzy Logic Control Fuzzy logic controller is suitable especially for complex or nonlinear systems. Figure 2 shows the structure of the fuzzy controller used in this paper. Asshown, the inputs of the fuzzy controller are the error signal and its derivative and the output is the reference value which is applied to the system.The input and output membership functions are normalized values. Thus, determining correct values for K1, K2 and K3 is essential. Figure 3 shows a three dimension inputs-output diagram. In this paper, the triangular membership function is used due to its simplicity and efficiency [19]. Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2132-2138 2134 www.etasr.com Masoumi Kazraji et al.: Fuzzy Predictive Force Control (FPFC) for Speed Sensorless Control … Fig. 2. The structure of the fuzzy controller. -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -0.5 0 0.5 ece O Fig. 3. Three dimension inputs-output diagram C. The Selection of the Vector In the conventional MPFCs [20], the stator flux and the electromagnetic force have been predicted as the primary states by the predictive model with is(k) and ψs(k) variables at the moment of k+1. The aim is to make the stator flux and the force follow their references. In other words, the error between the estimated flux and force with their reference values has to be minimized. This takes the form of a cost function which is provided as follows:      4,3,2,1 1ˆ1ˆ   i kkkFFJ is ref sie ref e  (15) In the proposed FPFC, in order to determine the sign of the force and the stator flux, a weight coefficient of the stator flux, kψ is selected as follows: n sn F k   (16) In the above equation, Fn is the nominal force, and ψsn is the stator flux amplitude. It should be noted that the kψ weight coefficient in (16) is only used as a starting point for tuning and the final practical amount of kψ is larger than (16), which was shown in [21]. The current of the stator is not directly used in the conventional MPFC cost function. The prediction of stator current is eliminated in order to decrease the complexity. To predict the force at the k+1th moment without the prediction of the stator current , the following equations are employed: 3 ( 1) ( 1) ( ) 2 2 e s s p F k k i k        (17)     ( ) 1 ( ) ( ) s r s sc r sc s r sc r r r sc s i k R L F j F i k R F L j L F k             (18) In the above equations, isλ(k) has been calculated based on the variables of the kth moment. IV. SIMULATION AND EXPERIMENTAL RESULTS A. Simulation Results The simulation was conducted in MATLAB/Simulink. The results of [22] have been used for comparison. The flowchart of the algorithm is shown in Figure 4. The parameters are provided in Table I. The reference of the stator flux is 0.9 Wb, which is lower than the nominal amount in order to prevent saturation. The kψ weight coefficient in the weight function is only used to regulate the parameters of FPFC. The tuning has been carried for the selection of the most appropriate kψ. However, the selection of a weight coefficient is still a new issue and is usually determined intuitively [22]. The final amount of the kψ weight coefficient is 50 in this paper, which has been applied based on a comprehensive simulation. Full oreder observer & Time delay compensation Duty ratio calculation Force and flux prediction Cost function Gi (Fe, Ѱs) Gi