FUZZY LOGIC CONTROL of SRM 1 KIRAN SRIVASTAVA, 2 B.K.SINGH 1 RajKumar Goel Institute of Technology, Ghaziabad 2 B.T.K.I.T., Dwarhat E-mail: 1 2001.kiran@gmail.com,, 2 bksapkec@yahoo.com ABSTRACT The fuzzy logic control (FLC) performs a like Proportional-Integral control strategy for switched reluctance motor (SRM) speed control. The performance of the drive system is evaluated through digital simulations through the toolbox SIMULINK of the MATLAB program. The simulated SRM has a structure of 3 phase 6/4 poles and 4 phase 8/6 poles. Simulation is based on equation of torque. The speed of the mentioned SR motors is determined by using the MATLAB /SIMULINK. FLC employ and generate current reference variations, based on error in speed and its change. The objective of this paper is to achieve a good performance and accuracy using FLC. Keywords: Fuzzy Logic Control (FLC), Switched Reluctance Motor (SRM), Membership Function, Fuzzy Rules 1. INTODUCTION The switched reluctance motor is a new entrant in domestic appliance applications. Many electrical machine researchers are investigating the dynamic behavior of switched reluctance motor (SRM) by monitoring the dynamic response (torque and speed), monitoring and minimizing the torque ripple. The researchers are now focusing on SR motors and drives with one or two phase windings so that applications for the technology are being created in low cost, high volume markets such as domestic appliances, heating ventilation and air conditioning and automotive auxiliaries[1-5]. The sensitivity study is performed by comparing the average torque developed for different stator as well as rotor pole-arc/pole-pitch ratios and choosing the ratio combination that produces the greatest value of average torque. The sensitivity analysis of SR motor geometry is carried out for stator and rotor pole arc/ pole-pitch ratio and radial air gap length as motor design variables researchers. Finite element method is very powerful tool for obtaining the numerical solution of a wide area of engineering problems. The original body or structure is considered as an aggregate of these elements connected at a finite number of joints called Nodal Points or Nodes. [6-9]. Fuzzy logic is a powerful problem-solving method with multiple applications in embedded control and information processing. Unlike classical logic which requires a deep understanding of a system, exact equations, and specific numeric values, fuzzy logic incorporates an another way of thinking, which allows modeling complex systems using a higher level of abstraction, originating from our knowledge and experience. Lotfi A. Zadeh in 1965 published his important work "Fuzzy Sets which described the mathematics of fuzzy set theory, and by extension fuzzy logic. This theory proposes making the membership function (values true and false) operate over the range of real numbers [0.0, 1.0] [10-15]. 2. MATLAB SIMULATION Matlab / Simulink is used to simulate the SRM and look up table of the torque τ (θ, I) is used to represent the simulation. The torque is a function of rotor position and current, which is extracted from the numerical data of the motor design by (FEM) finite elements method [16]. The look up table from Simulink is used to represent the developed torque in 3 phase, 6/4 poles base SRM and 3 phase, 6/4 poles optimized SRM. The displacement angles are considered as a row parameters (x-axis parameters), that varied between (0 to 45 ), and the mmf is considered as column parameters (y-axis parameters), which is varied between (30 to 210 AT) Figure 1.Fuzzy controller in MATLAB 3. FUZZY LOGIC CONTROLLER STRUCTURE Figure 3 shows how FLC use fuzzy logic as a method/course of mapping from a given input (crisp numerical value ω) to an output (signal control u). This process has a basic structure that involves a fuzzifier, an inference engine, a knowledge base (rule
data base), and a deffuzzifier, which convert fuzzy sets into real numbers to provide control signals. are located on the x-axis of figure 4, by dropping a y- axis on the two values the output is shown in table 2. Figure 2: FLC Structure Figure 3: Elements of a Fuzzy Logic Controller. In order to clarify the structure of an FLC controller. Table 1 shows the linguistic fuzzy sets for five values. Let E and DE be the red input labels corresponding to e signal and its variation. FLC output consists of a signal control u named U (the green label) as shown in Table 1. Let s assume that fuzzy linguistic sets are already defined and the rules are: Sample Rule: IF (E is NS AND DE is NS) THEN U is NM. First step is to take E and DE and determine the degree to which they belong to each of the appropriate fuzzy sets via membership functions Table 1: Linguistic Data Base(Variables E or DE) Figure 4: The Fuzzy Linguistic Sets. NM= Negative Medium, NS= Negative Small, ZE= Zero, PS= Positive Small, PM= Positive Medium Table 2: Calculation for Example U/E µnm(e) µns(e) µze(e) µps(e) µpm(e) E=0.2 0 0 0.8 0.2 0 E=1.4 0 0 0 0.6 0.4 The membership degree values are shown in Table 3 Table 3: Degree of Membership Values The inputs are always a crisp numerical values limited to the universes of discourse of the inputs (in this case the interval is assumed to be between -3 and 3)as shown in Figure 4.Therefore, fuzzification procedure is only a function evaluation or a lookup table operation. The degree to which each part of the antecedent has been satisfied for each rule is known once the inputs have been fuzzified,. If the antecedent of a given rule has more than one part, the fuzzy operator is enforced to obtain one number that represents the output of the antecedent for that rule. N o w t h i s n u m b e r is a p p l i e d to the output function. Suppose the next input values are: e = 0.2 and de = 1.4. Two values Figure 4 shows the fuzzy values related to output U as follows: PS activation degree is 0.6, and PM activation degree is 0.4 (max {0.4, 0.2, 0.2} = 0.4). In defuzzification calculation of u 0 will be found using middle of maximum, centroid, and largest of maximum. The largest maximum value between the membership PS and PM shown is 0.6 (PS), so the chosen output fuzzy set is PS. The middle of maximum of PS fuzzy set is u0 = 1 as shown in figure 5.
4.1 Membership Functions Figure 5: Output Fuzzy Values 4. SIMULATION RESULTS FOR FLC OF 3 PHASE, 6/4 POLES SRM. System Operating Rules According to figure 2, the value of error: eω=ω ref -ω actual (1) error-dot=d(error)/dt (2) Output: conclusion & system response: Input 1: Error = NB (Negative big), NM (Negative medium), NS (Negative small), ZE (Zero), PS (Positive small), PM (Positive medium), PB (Positive big). Input 2: Error-dot = NB (Negative big), NM (Negative medium), NS (Negative small), ZE (Zero), PS (Positive small), PM (Positive medium), PB (Positive big). Conclusion: Output = (NB, NB, NB, NB, NM, NS, ZE) = (NB, NB, NB, NM, NS, ZE, PS) = (NB, NB, NM, NS, ZE, PS, PM) = (NB, NM, NS, ZE, PS, PM, PB) = (NM, NS, ZE, PS, PM, PB, PB) = (NS, ZE, PS, PM, PB, PB, PB) = (ZE, PS, PM, PB, PB, PB, PB). Table 4 shows the rule matrix for the FLC, The antecedent s linguistic variables (eω,ceω) are depicted by the yellow highlighted zones and the consequent linguistic variables are shown by green highlighted zones. Both of them are depicted by seven triangular membership functions. Errordot = d(error)/dt, Speed error =ω ref -ω actual FLC generates current reference changes ( I ref ) based on speed error eω and its changes ceω. eω has its minimal value when the motor speed has its nominal value, 850 rad/sec, and is inverted to 850 rad/sec, so according to equation (1), then the speed error equals: eω=(-850)-(850)= -1700 rad/sec The maximum value, +1700, is obtained in the opposite situation as shown in figure 6 The changes of speed error (ceω) and according to equation (2) can be written in another form: ceω = e ω (k+1) - eω(k) (3) = e ω (k+1) -eω (k) = (ω ref ω (k)) (ω ref ω (k 1)) = - (ω (k) ω( k 1)= - ω Substituting equation (1) and (3) into torque equation (below); Δt is the interruption time, J is the moment of inertia, is the developed torque in Nm and maximum absolute value for the ΔI ref universe was obtained by trial and error. The initial limits for the universes after changes of the antecedents (eω, ceω) and consequent (ΔIref) were: eω=-850,850 rad/sec ceω=-20,20 rad/sec/sec ΔIref=-1.5, 1.5 A Figure 6 shows the membership function for the antecedent, the second input is the change in the speed error. Table 4: The Rule Matrix Figure 6: Speed Error (eω)
Figure 7: Change of Speed Error (ceω) Figure 8: Member Function for Output. Figure 8 shows the membership function for consequent linguistic variable. (ΔIref) is the output of the FLC. 4.2 DEFUZZIFICATION Figure 9 shows (ΔI ref ) generation by FLC, as soon as any antecedent s linguistic variables change or both (eω or ceω or both) during the process, then the output (ΔI ref ) changes accordingly. For example if the red line on speed error (eω) or the red line on the change of speed error (ceω) is varied, then ΔI ref will vary accordingly. Results are present at the bottom of the third columns. The simulation results for 3 phases, 6/4 poles SRM are shown in figures 9, 10, 11and 12. Figure 9: FLC Rules Viewer for SRM for 3 Phases, 6/4 Poles SRM (Simulation Results). Figure.10 shows the surface viewer for FLC for 3 phases, 6/4 poles switched reluctance motor. Two inputs (eω, ceω) are represented by the x-axis, while the output is represented by the y-axis as shown in the figure. Figure 10: Surface Viewer for SRM Fuzzy Logic Controller for Three Phases, 6/4 Poles SRM (Simulation Results). Another results figures 11 and 12 which show control performance when there is a change in load and speed reference. At 0.1 Nm load is applied to the motor and at 0.27s, load is increased to 1 Nm, demand higher torque. At 0.61 s, speed reference is
decreased to 80 rads and in consequence current decreases for des- acceleration. Figure 11: Speed versus Time for 3 Phases, 6/4 Poles SRM (Simulation Results). Figure 12: Current Reference versus Time for 3 Phases, 6/4 Poles SRM (Simulation Results). 5. CONCLUSIONS The FLC performs on PI-like (Proportional-Integral) control strategy. The performance of the drive system is evaluated through digital simulations through the toolbox SIMULINK of the MATLAB program. This choice is taken because this software has a good tool box and performance to undertake the task. The simulated SRM is three phase 6/4 poles and four phase 8/6 poles. The torque table function of angle and current τ (θ, I) is extracted from the numeric data of the SRM designs created by finite element method. The dynamic response of speed for an optimum design SRM is much improved compared to nonoptimum (base) design. Fuzzy Logic Control is employed and generated current reference variations, based on speed error and its change.the objective of the FLC to achieve a good performance and accuracy. FLC performed well for the speed control of SRM and overcoming its nonlinearities. REFERECES [1] P. French and A.H. Williams. A New Electric Propulsion Motor. Proceedings of AIAA, Third Propulsion Joint Specialist Conference. Washington, July, 1967. [2] L.E. Unnewehr and H.W. Koch. An Axial Air Gap Reluctance Motor for Variable Speed Application. IEEE Transactions on Power Apparatus and System, 1974. PAS-93, 1. [3] P.J. Lawrenson, J.M. Stephenson, P.T. Blenkinson, J. Corda and N.N. Fulton. Variable Speed Switched Reluctance Motors. IEE Proc., 1980, 127. [4] T.E.J. Miller and McGilp. Non-Linear Theory of the Switched Reluctance Motor for Rapid Computer Aided Design. IEE Proceedings, 1990, 137. [5] S.A. Nasar. DC switched reluctance motor. Proceedings of the institution of electrical engineers, 1996, 66(6): 1048-1049. [6] R. Arumugam, J.F. Lindsay and R. Krishnan. Sensitivity of Pole Arc/Pole Pitch Ratio on Switched Reluctance Motor Performance. Industry Applications Society Annual Meeting, Conference Record of the IEEE, 1988. [7] S.S. Murthy, B. Singh and V.K Sharma. Finite Element Analysis to Achieve Optimum Geometry of Switched Reluctance Motor. IEEE Region 10 International Conference on Global Connectivity in Energy, Computer, Communication and Control, 1998. [8] N.K. Sheth, and K.R. Rajagopal. Variations in Overall Developed Torque of a Switched Reluctance Motor with Air-Gap Non-Uniformity. Transactions on Magnetics, 2005, l.41. 215 [9] Andersen, O.W. Transformer leakage flux program based on the finite element method. IEEE Transactions, PAS- 92, 1973, 2. [10] Haimalla, A. Y. and Macdonald. D.C.Numerical analysis of transient field problems in electrical machines. Proc. IEE, 1976, 123: 893-898. [11] L.A. Zadeh. Fuzzy sets. Info. & Ctl., 1965, 8: 338-353. [12] L.A. Zadeh. Fuzzy algorithms. Info. & Ctl.,1968, 12: 94-102. [13] N. Sugeno. Fuzzy Measures and Fuzzy Integrals: A Survey. Fuzzy Automata and Decision Processes, New York 1977. [14] R. Yager. On a General Class of Fuzzy Connectives. Fuzzy Sets and Systems. 1980. [15] E.H. Mamdani and S. Assilian. An Experiment in Linguist Synthesis with Fuzzy Logic Controller. International Journal of Man-Machine Studies. 1975, [16]. W. Aljaism, M. Nagrial, and J. Rizk Switched Reluctance Motor Optimal Performance With Variable Stator Pole Arc/Pole Pitch Ratio Proc. The second International Conference on Modeling,
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