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- 1. PSO-Based Neural Network Controller for Speed Sensorless Control of PMSM A. M. Nazelan, M. K. Osman, N. A. Salim, A. A. A. Samat and K. A. Ahmad Faculty of Electrical, Universiti Teknologi Mara 13500 Permatang Pauh, Pulau Pinang, Malaysia E-mail: amnazelan@gmail.com Abstract— In this paper, estimation of rotor speed and position by using model reference adaptive system (MRAS) with multilayer perceptron (MLP) for PMSM sensorless control are presented. Conventional controller which is PI controller for adaptation scheme still hunger with high accuracy information of PMSM for low speed region. Based on PI controller, the MLP which is more well-known about their learning efficiency and performance. This paper proposes a method for training an MLP network using Particles Swarm Optimization (PSO) called MLP-PSO. The PSO is used to find the optimum weights and biases in the MLP network. Finally, the proposed method is evaluated by comparing with PI controller in controlling the speed and position of PMSM. Simulation results under various speed and load conditions has shown that the MLP-PSO achieved well results than the PI controller in terms of system parameter such as rise time ) ( r T , settling time ) ( s T , percent overshoot ) (%OS , and root mean square error ) (RMSE . Keywords— Permanent Magnet Synchronous Motor, Artificial Neural Network, Particles Swarm Optimization, Model Reference Adaptive Control. I. INTRODUCTION The Permanent Magnet Synchronous Motor (PMSM) has been widely used for various industries of technologies in robotics, electrical and automation. PMSM is one of famous and frequently used in many application AC machine type because of its high power density, large torque to inertia ratio, high efficiency and simple structure. Also, the PMSM is good in speed regulation [1].PMSM consists of two primary parts which is permanent magnet that rotates called rotor and static core surrounded by three equally space winding called stator. In PMSM world, there have two different back EMF which are sinusoidal and trapezoidal. In review that have been go thru, trapezoidal commutation can be categorize as simple method to control than sinusoidal commutation. But, trapezoidal commutation is not good enough to provide smooth and precise motor control of brushless dc motors, especially at low speeds region. Sinusoidal commutation solves this problem. Also, sinusoidal commutation produces much less torque ripple than trapezoidal [1][2]. High quality sensor is required as the feedback of the close loop system to complete the circuit. But, the existence of the sensor cause the cost and size of installation is increase. Therefore, sensorless method is approach. A variety technique have been develop to eliminate the existence of sensor in PMSM. In general, technique have been proposed is Lunberger or Kalman Filter observer (KMO), Sliding Mode observer (SMO), Model Reference Adaptive System (MRAS), fuzzy logic and artificial intelligent [3]. The demand of for variable speed drives in low, medium and high speed region for industries application was triggered many researcher to digging another method for sensorless control that can improve the efficiency of speed and position estimation. Because of this, control strategy was become a great role in order to fulfil the demands of each application. Usually, modelling and simulation is used to design the algorithm in order to identify the performance of proposed method with the conventional controller. Also, the virtual prototype are important to be done to reduce the cost of experiment. Generally, sensorless techniques have two different methods which is back electromagnetic force (EMF) estimation and signal injection method [4], [5]. Back EMF method offer a good performance at high speed revolution per minute (RPM) for PMSM. But, for the low speed region, the estimation accuracy will be decrease because the parameter reading is too small compare to the noise [6]. For signal injection method, their offer good performances at all state include zero speed. But, disadvantage of this method is requiring extra hardware and delay problem according digital implementation of the control algorithm and digital filters [7]. Therefore, this paper is focus on designing the MRAS algorithm in order to improve the accuracy of rotor speed and position estimation for all speed region which are low, medium and high. Model reference adaptive system (MRAS) consist of two functional block which is reference model and adjustable model [1], [8]–[10]. Main idea of this system is comparing the reference parameter (current id & iq for this case) between actual parameter. Error of this signal will be use to estimate the speed and position of the PMSM. Then, the signal is inject into the adaptation algorithm to estimate the quantity of which is use to tune the adjustable model. This simple method only required less of system computation [6]. 2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia 978-1-5386-3897-2/17/$31.00 ©2017 IEEE 366
- 2. Figure 2. The PMSM equivalent circuit In this paper, the novel method that proposed is MRAS with Multilayer Perceptron (MLP) as adaptation scheme which estimates the speed and position for PMSM sensorless vector control system. The proposed method are using the PMSM itself as the reference model and the PMSM current model as the adjustable model. Error signal which produce by using Popov Integral Inequality is injected into the MLP algorithm where objective of this project is to reduce the error approx. to zero value. The results of simulation and dynamic response is used to verify the effectiveness of proposed method that presented in this paper. II. PMSM MODEL In this section, PMSM mathematical model are describe to understand the behavior. The PMSM can be modeled in stationary reference (α, ß) and rotor reference (d, q) as shown in Fig. 1. The PMSM equivalent circuit as shown in Fig. 2 are considered in order to determine the mathematical model of the PMSM. q r Z d r Z Fig. 2 (a) and (b) is the equivalent circuit for voltage at d-axis and q-axis. From fig.2 the voltage equation can be derived as: q r d d d d dt di L i R V Z ) ( (1) d r q q q q dt di L i R V Z ) ( (2) where R is the phase resistor winding, r Z is the electrical angular velocity of the rotor and d , q is flux for d and q. Flux equation be derived as: m d d d i L ) ( (3) ) ( q q q i L (4) In the equation of flux above, m is the flux that generated by magnetic pole and stator. III. POSITION AND ESTIMATION METHOD A. Model Reference Adaptive System In 1958, Witark was proposed the first method of model reference adaptive system (MRAS) scheme in United States [11]. General view and idea MRAS is a closed loop system that contains reference model and adjustable model [1], [8]. This system compare the output of plant (PMSM) with the desired response from reference model. The parameters from the plant will update into the system and then, the system will determine the error between reference models. If the parameters have an error, adjustable model will automatically tune and counter the error to match with reference model. The reference model is independent from the rotor speed, calculation of variable from the terminal voltage and current. Meanwhile, for the adaptive model is dependent on it. The estimated rotor speed and position is generates based on difference between these state variables [12]. Generalized of this system is shown in Fig. 3. Input for reference and adjustable model is same which is voltage in stationary form (ud uq) that project from three phase (ua, ub uc). In Figure 3, the reference and adjustable model variable is known as x and x̂ , respectively. Reference model is develop in ideal condition where output of the model x will be used to compare with the measured performance of x̂ . The difference vector of v will be used as input for the adaptive mechanism to modify the parameters of the adjustable model. B. Model Reference Adaptive System on Popov Integral Inequality Mainly, MRAS sensorless control is based rotating reference frame. The model of the PMSM stator current describe as follows: Figure 3. Block diagram of MRAS control scheme Figure 1: The stationary and synchronous frame [16] + - R Iq Lq Vq (a) MSM (b) R Ld Id + - Vd Z R Ld Id + Z - Vd 2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia 367
- 3. d d q d q r d d d L V i L L i L R i dt d Z ] [ (5) d d r r q q q d d d q r q i L L V i L R i L L i dt d Z Z ] [ (6) where id, iq is dq-axis stator current, ud, uq is dq-axis stator voltage, R is stator resistance, Ld, Lq is stator inductance and ψr is rotor permanent magnet flux. By estimating dq-axis current, estimated speed can be formulate as follows [11]: ³ t q q d q q d re d i i L f i i i i k 0 1 )] ' ( ' ' [ ˆ W Z ) 0 ( ˆ )] ˆ ( ˆ ˆ [ 2 re q q d q q d i i L f i i i i k Z (7) where Ẑ is estimated rotor angular speed, d i' , q i' is dq-axis stator estimated current, k1, k2 is PI regulator coefficients. Then, Equation (7) can be rearrange as Equation (8) as follows: ) 0 ( ˆ ) ' ( ' ' * ˆ re q q t d q q d i p re i i L i i i i s K K Z Z » ¼ º « ¬ ª » ¼ º « ¬ ª (8) ³ t re 0 ˆ ˆ Z T (9) where Tˆ is rotor position estimation. C. Multilayer Perceptron Multilayer perceptron (MLP) is current dynamics method have been use in many application that perform in function fitting, reducing system error and recognition the problem by using supervised training algorithm such as levenberg marquardt (LM) and particles swarm optimization (PSO) [13][14]. Because of the effectiveness ability of learning the complex problem, artificial neural networks (ANN) frequently become an hot topic about prediction application of nonlinear system. Figure 4: Multilayer Perceptron Network Structure Multilayer perceptron (MLP) is a class feedforward ANN that consist of three layer of nodes. First layer known as input layer, second hidden layer and the third is known as output layer. Except of input layer, each node contain activation function that use for nonlinear system. Each layer is weighted with the appropriate value that have been found by performing system training. Fig. 4 shows the MLP network structure. The MLP algorithm can be formulated as: @ ¦ nh j j i ij jk k b t x w F w t y 1 1 0 1 2 ) ( . . ) ( (10) where 1 ij w and 2 jk w represent as weights between input layer to hidden layer and weight between hidden layer to output layer. F, 0 i x and 1 j b is represent activation function, thresholds in hidden nodes and input that supply to the input layer respectively. Then, equation in (8) and (10) can be combine to perform MRAS sensorless speed control with MLP as adaptation scheme. @» » ¼ º « « ¬ ª ¦ nh j j i ij jk re b t x w F w 1 1 0 1 2 ) ( . . Ẑ ) 0 ( ˆ ) ' ( ' ' . re q q t d q q d i i L i i i i Z » ¼ º « ¬ ª (11) D. Particle Swarm Optimization In 1995, Eberhart and Kennedy inspired by social behavior of bird flocking and fish schooling was develop an optimization technique known as Particles Swarm Optimization (PSO). Due to many advantage can be found by using this technique including simplicity and easy implementation, this algorithm can be used widely in many field such as classification, neural network training, machine study, and signal procession. Also, PSO is suit to be use as optimization parameter in many dimension and application. [15]. PSO concept is using a number of agent (particles) that establish a swarm moving around in the search space looking for the best solution. Each particles in search space adjust its ‘flying’ according to its own flying experience well as the flying experience of other particles and the best are called (pbest). Amongst the value of pbest, there have another categorize for the best value by the group known as gbest. Equation in (12) and (13) is used to modify the velocity and position of each agent based on objective function of the system. e ) ( * * ) ( * * 2 2 1 k i k i i i k i s gbest rand c s pbest rand c v (12) 1 1 k i k i k i v s s (13) where: k i v = current velocity of agent i at iteration k 1 k i v = new velocity of agent i at iteration k k i s = current position of agent i at iteration k 1 k i s = denotes the position of agent I at the next iteration k+1 i pbest = personal best agent i 2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia 368
- 4. i gbest = global best of the population 1 c = adjustable cognitive acceleration constant (self- confidence) 2 c = adjustable cognitive acceleration constant (swarm confidence) 2 , 1 rand = random number between 0 and 1 For this paper, PSO is use to optimize the value of weight for MLP controller that can minimum the error and overshoot of the PMSM sensorless control. There are four step for this algorithm optimize the value of weight that illustrate in Fig. 5. Step 1: Initial condition agent generation and declaration For the first stage, the data is choose randomly for each agent of input and speed for initialization. Each agent will set the current search point to pbest and at the same time, gbest also will determine the best value of pbest. Then, the best value that can produce low mean square error is stored for evaluation process. Step 2: Each agent searching point evaluation Second stage is evaluation for the stored value of agent where output of the system will produce an error and overshoot. The data will be analyze and new agent will be replace to see the output of system behavior. If the agent is better than pbest at this time, it will replace current value. Also, if the value of pbest is better than gbest, it will replace current value that stored inside gbest. Then, the best agent will stored. Step 3: Each agent modification By using the Equation (22) and (23), the value of each agent are declare and will be tested for the next step. Step 4: Each agent analysation Finally, several test are perform before the end of the process. If the system reach the desired output, the process will stopped and if otherwise, the process will repeat again from the first step until the desired output is achieved. IV. RESULTS AND DISCUSSION First result is shows the simulation using Heuristic-PI (H- PI) controller and then, Particles Swarm Optimization PI (PSO-PI) controller. Simulation is perform in the MATLAB Simulink and time is kept 0.3sec. The result is verified based on system performance response which are rise time (Tr), settling time (Ts), percent overshoot (%Os) and root mean square error (RMSE) where its verified under four (4) different conditions. 1) Constant speed and load. 2) Constant speed and varied load. 3) Varied speed and constant load. 4) Varied speed and load. For condition 1- Speed and load torque are constant [speed is 1500r/min and load torque is 2Nm] Figure 6: Reference and estimated speed for PI controller for condition 1 Figure 7: Reference and estimated speed for MLP controller for condition 1 For condition 2- Speed is constant and load torque is varied [speed is 1500r/min and load torque is 0-0.075sec (2Nm), 0.075-0.15sec (1Nm), 0.15-0.225sec (2Nm) and 0.225-0.3sec (1Nm)]. Figure 8: Reference and estimated speed for PI controller for condition 2 l d d d l Figure 5: Particle swarm optimization steps flowchart 2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia 369
- 5. Figure 9: Reference and estimated speed for MLP controller for condition 2 For condition 3- Speed is varied and load torque is constant [speed is 0-0.1sec (0-1500r/min), 0.1-0.18sec (1500r/min), 0.18-0.25sec (800r/min) and 0.25-0.3sec (1500r/min) and load torque is 2Nm]. Figure 10: Reference and estimated speed for PI controller for condition 3 Figure 11: Reference and estimated speed for MLP controller for condition 3 For condition 4- Speed and load torque are varied [speed is 0- 0.1sec (0-1500r/min), 0.1-0.18sec (1500r/min), 0.18-0.25sec (800r/min) and 0.25-0.3sec (1500r/min) and load torque is 0- 0.075sec (2Nm), 0.075-0.15sec (1Nm), 0.15-0.225sec (2Nm) and 0.225-0.3sec (1Nm)]. Figure 12: Reference and estimated speed for PI controller for condition 4 Figure 13: Reference and estimated speed for MLP controller for condition 4 Figure 14: Reference and estimated position for PI controller for condition 4 Figure 15: Reference and estimated position for MLP controller for condition 4 Table 1: Result by using PI controller for condition 1 to 4 Cond. 1 Cond. 2 Cond. 3 Cond. 4 Tr 0.025938 0.02612 0.09331 0.09281 Ts 0.037314 0.0376 0.26453 0.26227 %OS 1.5385 1.4781 1.1247 1.9414 RMSE 332.0508 332.978 78.5091 77.8655 Table 2: Result by using MLP-PSO controller for condition 1 to 4 Cond. 1 Cond. 2 Cond. 3 Cond. 4 Tr 0.038055 0.03839 0.13257 0.1274125 Ts 0.048551 0.049 0.29009 0.2932889 %OS 0.5118 0.4535 0.4259 1.8022 RMSE 325.149 326.474 59.8513 59.119 Based on the result that tabulated in Table 1 and 2 for speed estimation, it’s clearly shows that for rise time and settling time, Tr and Ts for PI controller produce much better than MLP controller. But, different with the overshoot and 2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia 370
- 6. root mean square, %Os and RMSE, the MLP produce better result for speed estimation. In the meantime, result RMSE for the position estimation that tabulated in Table 3 clearly shows that there have significant difference where the MLP produces lower value of RMSE than PI controller. Table 3: Result of root mean square (RMSE) for position error between reference and estimated for PI and MLP controller PI MLP-PSO RMSE 43.7159 7.1904 V. CONCLUSION This paper are proposing a new method that can produce better result between existing controller for the dynamic response such as rise time, settling time, maximum overshoot and root mean square error for PMSM sensorless based. Amongst this two controllers, MLP-PSO based was producing good results compared to conventional controler, PI. It clearly shows that this method was improve the dynamic performance of the PMSM controller. For further reccomendation, the hybrid multilayer perceptron (HMLP) will be tested to analyze the performance of speed and position estimation for PMSM sensorless method versus existing method. ACKNOWLEDGEMENT This paper was funded by the Fundamental Research Grant Scheme (FRGS) (FRGS/1/2015/TK04/UITM/02/12) from the Ministry of Education (MOE) Malaysia and Faculty of Electrical Engineering Universiti Teknologi MARA, Malaysia. REFERENCES [1] K. Jinsong, Z. Xiangyun, W. Ying, and H. Dabing, “Study of position sensorless control of PMSM based on MRAS,” Proc. IEEE Int. Conf. Ind. Technol., no. 3, pp. 3–6, 2009. [2] M. S. Mahammadsoaib and M. P. Sajid, “Vector controlled PMSM drive using SVPWM technique - A MATLAB / simulink implementation,” Int. Conf. Electr. Electron. Signals, Commun. Optim. EESCO 2015, no. January 2015, 2015. [3] P. Tiwari, “Analysis of Sensorless Permanent Synchronous Motor Using PI and Adaptive Control Scheme,” vol. 4, no. 4, pp. 1193– 1198, 2015. [4] E. M. Fernandes, a. C. Oliveira, M. a. Vitorino, E. C. Dos Santos, and W. R. N. Santos, “Speed sensorless PMSM motor drive system based on four-switch three-phase converter,” Proceedings, IECON 2014 - 40th Annu. Conf. IEEE Ind. Electron. Soc., pp. 902–906, 2014. [5] Z. Q. Zhu and L. M. Gong, “Investigation of effectiveness of sensorless operation in carrier-signal-injection-based sensorless- control methods,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3431–3439, 2011. [6] A. Mishra, V. Mahajan, P. Agarwal, and S. P. Srivastava, “MRAS based estimation of speed in sensorless PMSM drive,” 2012 IEEE 5th Power India Conf. PICONF 2012, 2012. [7] F. Cupertino, a. Guagnano, a. Altomare, and G. Pellegrino, “Position estimation delays in signal injection-based sensorless PMSM drives,” 3rd IEEE Int. Symp. Sensorless Control Electr. Drives, SLED 2012, pp. 1–6, 2012. [8] G. Wu and X. Xiao, “Speed controller of servo system based on MRAS Method,” Proc. IEEE Int. Conf. Ind. Technol., 2009. [9] P. Vaclavek and P. Blaha, “Synchronous Machine Drive Observability Analysis and Sensorless Control Design,” 2008 Ieee 2Nd Int. Power Energy Conf. Pecon, Vols 1-3, no. PECon 08, pp. 265–270, 2008. [10] H. M. Kojabadi and M. Ghribi, “MRAS-based adaptive speed estimator in PMSM drives,” Int. Work. Adv. Motion Control. AMC, vol. 2006, no. 1, pp. 569–572, 2006. [11] W. Gao and Z. Guo, “Speed sensorless control of PMSM using model reference adaptive system and RBFN,” J. Networks, vol. 8, no. 1, pp. 213–220, 2013. [12] M. Dursun, A. F. Boz, M. Kale, and M. Karabacak, “Sensorless Speed Control of Permanent Magnet Synchronous Motor With Hybrid Speed Controller Using Model Reference Adaptive,” vol. 3, no. 1, pp. 24–37, 2014. [13] S. Mishra, R. Prusty, and P. K. Hota, “Analysis of Levenberg- Marquardt and Scaled Conjugate gradient training algorithms for artificial neural network based LS and MMSE estimated channel equalizers,” Proc. - 2015 Int. Conf. Man Mach. Interfacing, MAMI 2015, no. Lm, 2016. [14] A. Zabidi, L. Y. Khuan, W. Mansor, I. M. Yassin, and R. Sahak, “Classification of infant cries with asphyxia using multilayer perceptron neural network,” 2010 2nd Int. Conf. Comput. Eng. Appl. ICCEA 2010, vol. 1, pp. 204–208, 2010. [15] W. F. Tarmizi, I. Elamvazuthi, N. Perumal, K. Nurhanim, M. K. A. A. Khan, S. Parasuraman, and a. V. Nandedkar, “A Particle Swarm Optimization-PID controller of a DC Servomotor for Multi- Fingered Robot Hand,” 2016 2nd IEEE Int. Symp. Robot. Manuf. Autom. ROMA 2016, pp. 1–6, 2017. [16] M. Elbuluk, “A sliding mode observer for sensorless control of permanent magnet synchronous motors,” Conf. Rec. 2001 IEEE Ind. Appl. Conf. 36th IAS Annu. Meet. (Cat. No.01CH37248), vol. 2, no. C, pp. 1273–1278, 2001. 2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia 371