Analysis on various optimization techniques for selecting gain parameters in FOC of an E-drive

Transcription

1 Analysis on various optimization techniques for selecting gain parameters in FOC of an E-drive Presented by: RAJA SEKHAR KAMMALA(RBEI/EHV2) SATHISH LAKSHMANAN(RBEI/EHV2) MEHER ANUSHA VANAPALLI (NITC, Intern at RBEI) 1

2 1. Introduction 2. Problem Statement 3. Various Optimization techniques considered 1. Pattern Search 2. Genetic Algorithm 3. Simulated Annealing 4. Error Criteria and Objective function 5. Results 1. Comparison of optimization techniques 2. Graphs and data generated. 6. Conclusion 2

3 1. Introduction Field Oriented Control (FOC) is commonly used for controlling the electrical machines like PMSM and Induction machines etc., which are majorly used in Electric and Hybrid Vehicles For optimal performance of the algorithm (FOC) or any PID based controller it is required that the controller is tuned to its best parameters over the entire operating range of the electrical machine. Several conventional methods (Ziegler-Nichols) to optimize the current control parameters in FOC, (or tuning any PID controller) were highly unsatisfactory in terms of large overshoot and steady state error, because of manual involvement in selecting the initial points and tuning them. The paper compares different optimization techniques like Pattern Search, Genetic Algorithm and Simulated Annealing algorithms and the best possible results are presented. 3

4 Torque[Nm] Optimization Techniques 2. Problem Statement P.U Speed-Torque characteristics of 83kW PMSM machine used in FIAT500e are shown below. In FOC control of above Permanent Magnet Synchronous Motor (PMSM), finding tuned Controller Gain parameters are required to achieve high performance. Each working point(in Speed torque characteristics of E-Machine) shown below, will have unique Kp and Ki values. 1P.U Base speed 1P.U Speed[rpm] P.U N-T characteristics of PMSM 4

5 Torque[Nm] Optimization Techniques 2. Problem Statement (Contd..) To find optimized values (which gives minimum overshoot and steady state error) of gain parameters as a function of speed and torque, pattern search algorithm with error criteria has been used. Pattern search failed to provide tuned Kp and Ki at working points above base speed and in few cases even at below base speed. To overcome above problem, investigations on different optimization techniques has been done. Base speed Speed[rpm] P.U N-T characteristics of PMSM 5

6 MATLAB Implementation: FOC of PMSM Implemented in MATLAB using Simulink modelling, Interpreted MATLAB Functions and Optimization tool box Implemented in MATLAB using SimElectronic toolbox Fig.1 FOC of PMSM Implemented in MATLAB using Simscape.ssc scripting 6

7 3. Various Optimization Techniques considered 1. Pattern Search 2. Genetic Algorithm 3. Simulated Annealing 7

8 4. Error Criteria and Objective function: The performance indices taken for optimization are: ISE (Integral Square Error) ITSE (Integral time Square Error) Overshoot C(t) tolerance Overshoot Steady_State Tolerance band 0.01s 0.2s 0.3s ISE ITSE The above performance indices are used to minimize error between desired and actual id, iq and torque values. The summation of above performance indices results to an objective function. Objective function = Minimum ( ISE_Id + ISE_Iq + ISE_Torque + ITSE_Id + ITSE_Iq + ITSE_Torque ) 8

9 4. Error Criteria and Objective function: ISE (Integral Square Error): where, e corresponds to error. It penalizes both positive and negative values of the error Gives more weight to larger deviations Suitable for control circuits of which one calls weak overshoot Here only error is considered and therefore no weight is given to time span of error. ITSE( Integral time squared error): For time-weighted quality criteria, the duration of the standard deviation is taken into account. By multiplying with the time, Minor variations which occur relatively later can be recognized This will be responsible for Less settling time and faster reduction in oscillations. Tolerance band: ISE e 0 If actual response lies in between this tolerance band, that solution can be accepted. 2 t dt ITSE te 0 2 t dt 9

10 4. Error Criteria and Objective function: Overshoot Function: Overshoot is the maximum peak value of the response curve measured from the desired response of the system. Cpeak C( ) % Mp 100 C( ) Here Cpeak = first peak value of the response C( ) = Steady state response of the system Steady State Function: It defines the allowable ripple in the system with respect to desired during steadystate 10

11 Torque[Nm] Optimization Techniques 5. Results : Comparison of Pattern Search, Genetic Algorithm and simulated Annealing Kp Ki Peak Overshoot (%) Ripple(%) Settling time (Secs) Working Point a : Speed 0.19P.U and Torque 0.9P.U (Below Base Speed) Convergence time (Secs) PS e+03 GA e+04 SA e+05 For comparing results of above specified optimization techniques, three working points are considered(below base speed, base speed and above base speed ). Working Point b : Speed 0.38P.U and Torque 0.9P.U (Base Speed) PS Not converged Not converged GA e+04 SA e+05 Working Point c : Speed 0.5P.U and Torque 0.578P.U (Above Base Speed) PS Not converged Not converged GA e+04 SA e+05 Below Base Base speed speed Above Base speed Speed[rpm] Fig.10 Speed torque char. Of PMSM 11

12 5. Results at above base speed with PS, GA and SA: Objective function output and Kp,Ki values are shown below for all the three techniques at above base speed. Pattern Search Genetic Algorithm Simulated Annealing (a) Pattern search failed to converge as limitation in tolfun reached. Objective function value = 1e6. (b) Objective function output reaches to 6.3e- 6. Thus the output obtained are optimized. Kp= 0.4P.U and Ki = 0.36P.U (c) Objective function output reaches to 6.3e- 6. Thus the output obtained are optimized. Kp= 0.44P.U and Ki = 0.29P.U 12 Fig.11 Results for (a)pattern search (b)genetic Algorithm (c)simulated Annealing

13 5. Results: Torque waveform in transient and steady state region: Torque( Nm) As pattern search outputs are not converging, an overshoot is observed. t(seconds) Fig.12 Torque waveform at speed:0.5p.u and torque:0.578p.u 13

14 6. Conclusion Initial point selection plays a vital role in pattern search output convergence. If a better initial point is chosen, Pattern Search converges fast. At working point greater than base speed, GA and SA are giving good results compared to PS, where SA takes more time to give a converged result. The performance of SA can be improved with hybrid function. Goal Achieved: GA and SA algorithms of optimization tool box can be used to find out optimized values of current control parameters in FOC control of 83kW PMSM for FIAT 500e machine for speeds above base speed. These values can be used in calibration stage directly. This methodology decreases lot of time in finding the tuned parameters. 14

15 References Vikrant Vishal, Vineet Kumar, K.P.S. Rana, Puneet Mishra Comparative Study of Some Optimization Techniques Applied to DC Motor Control IEEE International Advance Computing Conference (IACC) P.Tripura, Y.S.Kishore Babu, Y.R.Tagore Space Vector Pulse Width Modulation Schemes for Two-Level Voltage Source Inverter ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October Bin Wu, High-Power Converters and AC Drives. IEEE Press, Tomy Sebastian,Gordon R. Slemon and M.A. rcahman Modelling of Permanent Magnet Synchronous Motors IEEE Transactions on Magnetics, vol. mag-22, no. 5, September 1986 Simscape language Guide and Global optimization tool box guide(matlab) Bosch internal material. 15

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