FUZZY LOGIC CONTROL DESIGN FOR ELECTRICAL MACHINES

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1 International Journal of Electrical Engineering & Technology (IJEET) Volume 7, Issue 3, May June, 2016, pp.14 24, Article ID: IJEET_07_03_002 Available online at ISSN Print: and ISSN Online: Journal Impact Factor (2016): (Calculated by GISI) IAEME Publication FUZZY LOGIC CONTROL DESIGN FOR ELECTRICAL MACHINES Franck Bétin, Amine Yazidi, Arnaud Sivert, Gérard-André Capolino Laboratory of Innovative Technologies IUT Aisne, 15, av. F. Mitterrand, Cuffies, France ABSTRACT The aim of this paper is to prove that fuzzy logic algorithm is a suitable control technique for fast processes such as electrical machines. This theory has been experimented on different kinds of electrical machines such as stepping motors, dc motors and induction machines (with 6 phases) and the experimental results show that the proposed fuzzy logic algorithm is the most suitable control technique for electrical machines since this algorithm is not time consuming and it is also robust between plant parameters variations. Key words: Fuzzy Logic, Electrical Drive, Implementation Cite this Article: Franck Bétin, Amine Yazidi, Arnaud Sivert, Gérard-André Capolino, Fuzzy Logic Control Design For Electrical Machines. International Journal of Electrical Engineering & Technology, 7(3), 2016, pp INTRODUCTION Due to the recent advances made in power electronics and in data processing, electrical machines are more and more used in many industrial fields substituting mechanical, pneumatic or hydraulic actuators. Therefore, the control of electrical machines is since few years an important research area since they can be considered as fast processes and they are also submitted to plant parameter changes. In this way, the first type of electrical machine that has been widely used in industry was the dc machine since it is really easy to control separately flux and torque. Nevertheless, the main drawbacks of dc machines are that they require maintenance operations and that they cannot be applied in corrosive or explosive environments. Then, with the field orientation control (FOC) theory birth, synchronous and induction machines have substituted the dc ones in the 80s first for constant speed applications, then for variable speed ones and now for positioning tasks. Indeed, FOC allows the decouplying between torque and flux components that is not natural with classical control schemes such as scalar control. However, the FOC scheme has to be associated with robust control laws for direct and quadratic inner 14 editor@iaeme.com

2 Fuzzy Logic Control Design For Electrical Machines loops to cope with plant parameters variations. Indeed, classical Proportional Integral Derivative regulators are not suitable since they cannot reject those actives disturbances. In this way, many advanced non linear control techniques have been used as for example: self tuning regulation, model reference adaptive control or optimal control. These ones are well-known for their robustness but they are very time consuming because of the numerous matrices operations and are not suitable for fast processes such as electrical machines. Therefore, we turn toward Fuzzy logic theory developed by Zadeh [1] to describe complicated systems (economics management, medicine), which are hard to analyse using traditional mathematics. Indeed, fuzzy logic control (FLC) offers the advantage of requiring only a simple mathematical model to formulate the algorithm, which can easily be implemented by a digital computer [2]. These features are appreciated for non-linear processes for which there is no reliable model but the main drawback with FLC is that there is no systematic procedure for the fuzzy structure design [3][4]. In this paper, a generalized fuzzy logic controller tuned off line by genetic algorithm is proposed for different kinds of electrical machines such as a dc machine for positioning, a synchronous stepping motor for variable speed and final positioning and a 6-phase induction machine for positioning. Indeed, the input and output scale factors of such controller are obtained by genetic algorithms in order to minimize error of control variables. Section 2 of this paper is dedicated to the fuzzy logic controller topology while section 3 is devoted to the experimental results obtained from the three different machines. 2. FUZZY LOGIC CONTROLLER DESIGN 2.1. FLC Concept The FLC algorithm is much closer in spirit to human thinking than traditional logic systems. Indeed, when controlling a process, a human operator compares the actual output with the desired output and observes the evolution of this difference. This is why most of the single input-single output (SISO) fuzzy controller inputs have to be based on the knowledge of the error and the change of error. The human operator generally does not reason in term of quantitative values but of qualitative values. In fuzzy logic controllers, this operation is called the fuzzification. Using its experience of the process and its intuition, the operator elaborates a qualitative action with specific inputs. This operation is called the decision making. Finally, he expresses this qualitative procedure into a quantitative set of operations. This last one is called defuzzification. The main problem with the FLC generation is linked to the choice of the regulator parameters since there is no systematic procedure for the design and the next part of the paper is dedicated to the topology configuration of the proposed FLC suitable for every kind of electrical machines FLC Topology To adjust the output of the drive unit, both the error signal e i between the set point Y i * and the measured point Y i and the change of error e i are used where i is the i th sampling period: 15 editor@iaeme.com

3 Franck Bétin, Amine Yazidi, Arnaud Sivert, Gérard-André Capolino e i = Y i * - Y i e i = e i e i-1 (1) The output of the fuzzy controller is not the control variable itself but its increment and the closed-loop control signal is given by adding the fuzzy logic controller output with the reference signal. In this way, the proposed method can be considered as an incremental controller as shown in Fig. 1. Then the designer has to determine the scaling factors, the number of fuzzy sets, the shape of the fuzzy sets and the decision making informations. k p FUZZY CONTROLLER Fuzzification Inference Defuzzification e i e n k X 1 d + - X q k 2 Quantitative to qualitative Qualitative to quantitative U n + U k 3 + U Optical encoder Motor+Load V converter Figure 1 Fuzzy control scheme Fuzzy sets determination Triangular and trapezoidal shapes with a zero symmetry and a 50% overlapping rate for fuzzy linguistic sets have been chosen for simplicity [5] [6]. Fig. 2 represents the fuzzy set shapes of the proposed FLC where the number of sets for the fuzzy controller has been determined using simulation for different configurations. Membership function j h LN MN SN ZE SP MP LP Universe of discourse Figure 2 Membership functions Indeed, by comparing the responses with different numbers of fuzzy sets, it has been observed that the use of more than 7 linguistic sets does not improve the accuracy but increases the computation time [5]. Therefore, 7 linguistic sets have been chosen for the error, the change of error and the output of the fuzzy logic controller. These sets are: Large Positive (LP), Medium Positive (MP), Small Positive (SP), Zero (ZE), Small Negative (SN), Medium Negative (MN) and Large Negative (LN) editor@iaeme.com

4 Fuzzy Logic Control Design For Electrical Machines Decision making The linguistic control rules matrix (table 1) has been designed considering the dynamic behaviour of the motor drive and analysing the error and its variation. These complete and symmetrical control rules are really close to Mac Vicar Whelan ones [7] and can be written as: if e is LP and e is LP then s is LP or if e is LP and e is MP then s is MP or The if part of the rules is called the premise while the then part is the consequence. The and operator is used to link the premises and the or operator to link the rules. To obtain the control decision, the Max-Min inference method is used. It is based on the minimum function to describe the and operator present in each control rule and the maximum function to describe the or operator. Table 1 Fuzzy matrix e n \ e n LN MN SN ZE SP MP LP LP ZE SP MP LP LP LP LP MP SN ZE SP MP LP LP LP SP MN SN ZE SP MP LP LP ZE LN MN SN ZE SP MP LP SN LN LN MN SN ZE SP MP MN LN LN LN LN MN SN ZE SP LN LN LN LN MN SN ZE Defuzzification To transform the qualitative action into a quantitative variable, the "center of gravity" method is used. For discrete membership functions, the output u can be expressed as: u i n ui i 1 i n i 1 ( ui) ( ui) Where n is the number of fuzzy sets of the output, u i is the center of the i th fuzzy set and (u i ) is the associate membership value. This algorithm considers all the membership values of the fuzzy output and therefore gives a more reliable decision table compared to other methods [5]. Fig. 3 depicts the normalised output U n of the proposed controller as a function of the normalised error e n and the normalised change of error e n. Looking at Fig. 3, it is clear that the characteristic of the fuzzy controller is non-linear. (2) 17 editor@iaeme.com

5 Franck Bétin, Amine Yazidi, Arnaud Sivert, Gérard-André Capolino U n Figure 3 Fuzzy controller output Scaling factors determination The input and output scale factors of the controllers (K 1, K 2 and K 3 ) are tuned using an off-line genetic algorithm (GA) system to minimize the error between the reference and the output. GA is a stochastic global search optimization technique based on the mechanisms of natural selection. It is also superior in avoiding local minima which is a common aspect of nonlinear systems. Indeed, GA is a derivative-free optimization technique which makes it more attractive for applications that involve nonsmooth or noisy signals. Generally GA consists of three main stages named selection, crossover and mutation. In the selection stage, individuals of the initial population are selected for reproduction with probability proportional to their fitness value. The purpose of this operation is to obtain a mating pool with the fittest individuals selected according to a probabilistic rule that allows these individuals to be mated into the new population. After the selection stage, the genetic crossover operation is then applied between parent pairs from the mating pool to generate new individuals or offsprings which acquire good features from their parents. Then, the application of genetic mutation introduces a change in the offspring bit string to produce new chromosomes which may represent a solution of the problem and at the same time avoid the population falling into a local optimal point. In our case, the fitness function used to evaluate the individuals of each generation has been chosen as integral with time of absolute error (ITAE). The mathematical expression of this cost function, which is the function minimized by the GA, can be written as: t t E(t) dt 0 or equally for the discrete systems : ITAE (3) ITAE kts E(k) (4) k The GA searches the optimal setting of the fuzzy controller gains which minimize the cost function. Individuals with low ITAE are considered as the fittest. Each chromosome represents a solution of the problem and hence it consists of three genes [K 1, K 2, K 3 ]. The range of each gain has to be specified editor@iaeme.com

6 Fuzzy Logic Control Design For Electrical Machines 3. EXPERIMENTAL RESULTS In this section, the experimental results obtained with the three machines are shown. The test bed (see Fig. 4), designed for small power machines, is composed of the tested machine (dc motor, stepping motor, 6-phase induction machine), an electromagnetic powder brake and a variable inertia arm. The parameters of the machines are given in appendix. Variable inertia Powder brake Tested motor (dc) (a) b) c) d) Figure 4 Test bed (a) for dc machine (b), stepping motor (c) and 6PIM (d) 3.1. Application to dc machine As written in introduction, the dc machines have been for a long time the only solution for high precision positioning. The main drawback is that, with a classical controller such as a PI one, overshoots can appear when the mechanical configuration is changing. One solution to cope with the effect of the plant parameters variations is to use a robust controller such as fuzzy controller. Fig. 5.a represents the experimental closed loop response (with fuzzy logic controller) of the dc machine with no load for a step position profile of 500 equivalent encoder step while Fig. 5.b and 5.c depict the experimental response in the same conditions respectively with the rated load torque and with two different values of inertia. It can be easily seen that, whatever the mechanical configuration, there is no oscillation, no overshoot and no steady state error when the dc machine is controlled using FLC algorithm editor@iaeme.com

7 Franck Bétin, Amine Yazidi, Arnaud Sivert, Gérard-André Capolino Position (step encoder) Position (step encoder) Position (step encoder) J = J min J = J max Time (ms) Time (ms) Time (ms) Figure 5 Step position response with dc machine a) no load, b) rated load torque, c) 2 different inertias 3.1. Application to stepping motors Stepping motors are widely employed in industrial applications since they can provide a high precision positioning of the rotor in open-loop. In this case, the stepping motor is driven by a predetermined pulse train with variable pulse rates for acceleration, constant speed and deceleration and therefore, the frequency of this train induces the rotation speed of the motor. In lots of applications, the acceleration and the deceleration are linear in order to obtain trapezoidal velocity profiles. These references are appreciated because they allow high stepping rates using a simple algorithm to compute the time interval between successive steps. The main drawback with open-loop control of stepping motors, is that, during the acceleration, steady state speed and deceleration, large magnitude oscillations appear on as shown on Fig. 6.a. To alleviate these oscillations, we propose to apply the proposed FLC algorithm [5]. Fig. 6.b depicts the experimental closed loop response with the FLC in the same condition that on Fig. 6.a. It can be seen that using this controller, the oscillations that appear in open-loop during the acceleration, steady state speed and deceleration are completely removed. Speed (step/s) (a) 20 editor@iaeme.com

8 Fuzzy Logic Control Design For Electrical Machines Speed (step/s) (b) Figure 6 Experimental open-loop response (a) and FLC response (b) for the stepping motor Application to 6PIM With the advances made in power electronics and data processing, the FOC strategy has become a standard for control of electrical machines and therefore the induction machines have substituted the dc machines for variable speed drive and for high precision positioning tasks [8]. To increase the efficiency of the induction machine and overcome the problem of breaking down when one stator phase is lost, multiphase induction machines have been built up in the eighties. Indeed, with a multiphase machine, when one, two or more phases are missing, the machine is still running since three phases are remaining. Nevertheless, the main problem with multiphase machine is that when one or more phases are lost, some oscillations appear if a classical controller such as PI regulator is used for the FOC. [9] In this way, the propose FLC has been used to a 6-phase induction machine (6PIM) for high precision positioning of the rotor [10]. Fig. 7.a represents the position, the I q and I d currents in healthy mode (first column), when one phase is missing (second column) and when two phases are missing (third column) with PI controllers in inner and outer loops for a 1 radian step positioning profile. It can be seen on these experimental responses that position overshoots appear with the PI controller. Fig. 7.b depicts the experimental responses in the same conditions when the motor is controlled using FLC theory. One can remark that there is no overshoot and no steady state error when the motor is controlled using FLC editor@iaeme.com

9 Franck Bétin, Amine Yazidi, Arnaud Sivert, Gérard-André Capolino a) b) Figure 7 Experimental responses for 6PIM with PI controllers (a) and FLC (b) CONCLUSION In this paper, FLC has been implemented to control a dc machine, a synchronous stepping motor and a 6PIM. To control these machines, a FLC topology has been designed. The input and output scaling factors of the controllers are tuned using an off-line genetic algorithm system to minimize the error between the reference and the output. From the experimental results obtained on our test bed, it is clear that the FLC algorithm is a very suitable control strategy (much more than classical proportional integral regulation) since there is no overshoot and no steady state error whatever the plant parameters variations (variations of mechanical configuration for dc or stepping motors, losses of stator phases for 6PIM). Furthermore, FLC strategy does not require many matrices operations and then is really easy to implement on a classical computational structure. REFERENCES [1] L.A. Zadeh, Fuzzy Sets, Information and Control, 8, 1965, pp [2] Y.F. Li, C.C. Lau, Development of fuzzy algorithms for servo systems, IEEE Control System Magazine, April 1989, pp [3] E.H. Mamdani, Application of fuzzy algorithms for control of a simple dynamic plant, Proc. of the IEEE, 121, 1974, pp [4] P.J. King, E.H. Mamdani, The application of fuzzy control systems to industrial processes, Automatica, 13, 1977, pp [5] F. Betin, D. Pinchon, G.A Capolino, Fuzzy logic applied to speed control of a stepping motor drive, IEEE Transactions on Industrial Electronics, 47(3), June 2000, pp editor@iaeme.com

10 Fuzzy Logic Control Design For Electrical Machines [6] C.C. Lee, Fuzzy logic in control systems: Fuzzy logic controller-part 1, IEEE Transactions on Systems, Man and Cybernetics, 20(2), April 1990, pp [7] P.J. Mac Vivar Whelan, Fuzzy sets for man-machine interaction, Int. J. Man- Machine Studies, 8, 1976, pp [8] F. Betin, A. Sivert, A. Faqir, G.A. Capolino, Position control of an induction machine using fuzzy-logic regulator, Electromotion, 11(2), April June 2004, pp [9] M.A. Fnaiech, F. Betin, B. Nahidmobarakeh, G.A. Capolino, F. Fnaiech, Fuzzy Logic and Sliding Mode Controls Applied to Six Phase Induction Machine with Open Phases, IEEE Transactions on Industrial Electronics, 57(1), Special Section on Advances in Electrical Machines, January 2010, pp [10] R S Shekhawat, Mathematical Modeling of Electrical Machines Using Circle Diagram. International Journal of Electrical Engineering & Technology, 4(7), 2013, pp [11] T.Balamurugan, Dr.S.Manoharan, P.Sheeba and M.Savithri, Design A Photovolatic Array With Boost Converter Using Fuzzy Logic Controller. International Journal of Electrical Engineering & Technology, 3(3), 2012, pp [12] Rajiv Ranjan and Dr. Pankaj Rai, Fuzzy Logic Based Mrac For A Second Order System. International Journal of Electrical Engineering & Technology, 4(2), 2013, pp [13] F. Betin, A. Yazidi, G.A. Capolino, Fuzzy logic applied to control of electrical machines, International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), 2014, Ischia, Pages: APPENDIX Permanent-magnet dc motor parameters: Maximum motor torque 0.3 N.m Maximum shaft speed 4200 rpm Armature resistance Armature inductance Maximum armature voltage Maximum armature current Torque constant Emf constant Stepping motor parameters: Rated phase current Rated phase voltage Self inductance Resistance of each phase winding Motor torque constant Detent torque constant Emf constant Number of rotor teeth Stepping motor inertia Viscous friction coefficient 6PIM parameters mh 60 V 3.6 A N.m/A V/rad/s I = 5.6 A U = 91 V L = 4.6 mh R = 0.28 K h = N.m/A K d = 0.12 Nm Ke = N.m/A Zr = 50 J = kg.m 2 F = N.m.s/rad 23 editor@iaeme.com

11 Franck Bétin, Amine Yazidi, Arnaud Sivert, Gérard-André Capolino Rated power 90 W Rated torque 0.3 N.m VSI DC source voltage 42 V No. of poles 2 Mutual inductance 30.9 mh Stator resistance 1.04 Stator leakage inductance 0.3 mh Rotor resistance 0.64 Rotor leakage inductance 0.65 mh Friction coefficient m/rd/s Inertia coefficient (J) Kg.m editor@iaeme.com