Simulink/ModelSim Co-Simulation of Sensorless PMSM Speed Controller

Simulink/ModelSim Co-Simulation of Sensorless PMSM Speed Controller 1Ying-Shieh Kung and 2Nguyen Vu Quynh 1,2Department of Electrical Engineering Southern Taiwan University, Tainan, Taiwan 2Lac Hong University, Vietnam 1kung@mail.stut.edu.tw, 2vuquynh@lhu.edu.vn 3Chung-Chun Huang and 4Liang-Chiao Huang 3,4Green Energy and Environment Research Laboratories Industrial Technology Research Institute Hsinchu, Taiwan 3CCHuang@itri.org.tw, 4liang.qiao@itri.org.tw Abstract—Based on Simulink/Modelsim co-simulation technology, the design of a sensorless control IP (Intellectual Property) for PMSM (Permanent Magnet Synchronous Motor) drive is presented in this paper. Firstly, a mathematical model for PMSM is derived and the vector control is adopted. Secondly, a rotor flux position is estimated by using a sliding mode observer (SMO). These estimated values are feed-backed to the current loop for vector control and to the speed loop for speed control. Thirdly, the Very-High-Speed IC Hardware Description Language (VHDL) is adopted to describe the behavior of the sensorless speed control IP which includes the circuits of space vector pulse width modulation (SVPWM), coordinate transformation, SMO, fuzzy controller, etc. Fourthly, the simulation work is performed by MATLAB/Simulink and ModelSim co-simulation mode, provided by Electronic Design Automation (EDA) Simulator Link. The PMSM, inverter and speed command are performed in Simulink and the sensorless speed control IP of PMSM drive is executed in ModelSim. Finally, the co-simulation results validate the effectiveness of the sensorless PMSM speed control system. Keywords-PMSM; Simulink/Modelsim co-simulation; Sliding mode observer; Sensorless speed control; Fuzzy controller; VHDL. I. INTRODUCTION PMSM has been increasingly used in many automation control fields as actuators, due to its advantages of superior power density, high-performance motion control with fast speed and better accuracy. However, conventional motor control needs a speed sensor or an optical encoder to measure the rotor speed and feedback it to the controller for ensuring the precision speed control. Such sensor presents some disadvantages such as drive cost, machine size, reliability and noise immunity. In recent year, a sensorless control without position and speed sensors for PMSM drive become a popular research topic in literature [1-7]. Those sensorless control strategies have sliding mode observer, Kalmam filter, neural network, etc. However, the back EMF and the sliding mode observer are suitable to be implemented by the fix-pointed processor and have been implemented by a digital signal processor (DSP) in most studies [4-5]. Unfortunately, DSP suffers from a long period of development and exhausts many resources of the CPU [8]. FPGA can provide another alternative solution in this issue. Especially, FPGA with programmable hard-wired feature, fast computation ability, shorter design cycle, embedding processor, low power consumption and higher density is better for the implementation of the digital system [9-10] than DSP. Recently, a co-simulation work by Electronic Design Automation (EDA) Simulator Link has been gradually applied to verify the effectiveness of the Verilog and VHDL code in the motor drive system [11-14]. The EDA Simulator Link [15] provides a co-simulation interface between MALTAB or Simulink and HDL simulators-ModelSim [16]. Using it you can verify a VHDL, Verilog, or mixed-language implementation against your Simulink model or MATLAB algorithm [15]. Therefore, EDA Simulator Link lets you use MATLAB code and Simulink models as a test bench that generates stimulus for an HDL simulation and analyzes the simulation’s response [15]. In this paper, a co-simulation by EDA Simulator Link is applied to sensorless speed control for PMSM drive and shown in Fig.1. The PMSM, inverter and speed command are performed in Simulink and the sensorless speed controller described by VHDL code is executed in ModelSim. Finally, some simulations results validate the effectiveness of the sensorless speed control system of PMSM drive. II. SYSTEM DESCRIPTION OF PMSM DRIVE AND SENSORLESS SPEED CONTROLLER DESIGN The sensorless speed control block diagram for PMSM drive is shown in Fig. 1. The modelling of PMSM, the SMO- based flux position estimation and the fuzzy controller are introduced as follows: A. Mathematical Model of PMSM The typical mathematical model of a PMSM is described, in two-axis d-q synchronous rotating reference frame, as follows d d q d q ed d sd L i L L i L r dt di v1  (1) q qq eq q s d q d e q LL Ki L ri L L dt di v1 E   (2) where vd, vq are the d and q axis voltages; id, iq, are the d and q axis currents, rs is the phase winding resistance; Ld, Lq are the d and q axis inductance; e is the rotating speed of magnet flux; EK is the permanent magnet flux linkage. DC Power PMSM Model IGBT-based Inverter PWM1 PWM6 PWM2 PWM3 PWM4 PWM5 r Flux angle Transform. r SimuLink A B C External load SVPWM PI 0* di qi di Park Clark Park-1 Clark-1 — — + PI 1refv 3refv 2refv qv dv v v i i * qi + a,b,c ,d,q , , d,q , a,b,c Current controller ai bi ci Modify sin /cos of Flux angle ee ˆcos/ˆsin  + — rˆ * r Speed estimator Speed controller v v i i Rotor flux position estimation eˆ FC + 11  Z KI fu PK e de 1-Z-1 ModelSim ai bi ci e r Current controllers and coordinate transformation (CCCT) Fig.1 The sensorless speed control block diagram for PMSM drive The current loop control of PMSM drive in Fig.1 is based on a vector control approach. That is, if the id is controlled to 0 in Fig.1, the PMSM will be decoupled and controlling a PMSM like to control a DC motor. Therefore, after decoupling, the torque of PMSM can be written as the following equation, qtqEe iKiK PT 4 3  (3) Considering the mechanical load, the overall dynamic equation of PMSM drive system is obtained by Lermrm TTBdt dJ   (4) where Te is the motor torque, P is pole pairs, Kt is torque constant, Jm is the inertial value, Bm is damping ratio, TL is the external torque, r is rotor speed. B. Design of the rotor flux position estimation Rotor flux position estimation in Fig.1 constructed by a sliding mode observer (SMO), a bang-bang controller, a low- pass filter and a position computation is shown in Fig. 2. The detailed formulation is described as follows. Firstly, the circuit equation of PMSM on the d-q rotating coordinate in (1) is re-formulated as             Eeq d se es q d Ki i sLrL LsLr v v   0 (5) Where qd LLL  . Transforming (5) of the circuit equation of PMSM on the   fixed coordinate can be derived by the following equation             e e Ee s s K i i sLr sLr v v       cos sin 0 0 (6) where Tvv ] [  is voltage on fixed coordinate; Tii ] [  is current on fixed coordinate; L is the inductance of the d-axis or q axis, respectively; e is angular position at magnet flux; s is differential operator. In addition, in (6), let’s define the EMF as      e e EeKe e e     cos sin (7) The EMF includes the position information from the flux. Secondly, to easily observe the EMF, (6) is rewritten as the state space form by current variable,                  e e Lv v Li i A i i dt d 11 (8) where      Lr Lr A s s /0 0/ (9) Thirdly, a sliding mode observer is designed by                    z z Lv v Li i A i i dt d 11 ˆ ˆ ˆ ˆ (10) where the Tii ]ˆ ˆ[  is the estimated current on fixed coordinate and the Z is defined in (10) which is the output gain of the bang-bang controller in Fig.2. )ˆ ˆ (*              ii ii signk z z Z (11) where the current error is defined by    TTcur iiiiiie ˆˆ~~   . Further, if we choose the k be large enough, the inequality in (12) can be reached cur T curee  <0 (12) and the SMO can enter into sliding mode condition. Therefore, it generates the results of 0 curcur ee  . Substituting the result into (8) and (10), the Z in (10) will approach to EMF in (6),        e e Ee Ke e z z       cos sin (13) Fourthly, to alleviate the high frequency switching in bang- bang control, a low-pass filter is applied in Fig.2,               z z eˆ eˆ eˆ eˆ 00-dt d (14) where 00 f2  . Finally, the rotor position eˆ can be computed by ) ˆ ˆ (tanˆ 1   e e e   (15) Sliding mode observer — + — + Bang-bang controller Low-pass filter Flux angle computation     v v      i i      iˆ i       z z      eˆ eˆ eˆ Rotor position estimation Fig.2 Rotor flux position estimation based on SMO In implementation, the above formulations in the continuous system have to transfer to the discrete system. Besides, we use Te ]eˆ ˆ[  instead of Tz ]z [  as the feedback value in SMO; therefore, the difference equation of the modified sliding mode observer in (10) is                 )(ˆ )(ˆ )( )( )(ˆ )(ˆ 0 0 )1(ˆ )1(ˆ ne ne nv nv ni ni ni ni           (16) where ss TL r e  , )1(1 ss TL r s e r  and sT is the sampling time. In addition, from (14), the difference equation of the EMF estimation can also be expressed by            )(ˆ)( )(ˆ)( 2 )(ˆ )(ˆ )1(ˆ )1(ˆ 0 nenz nenz f ne ne ne ne        (17) Once the EEMF is estimated, the estimated rotor position eˆ can be directly computed by ) )(ˆ )(ˆ(tan)(ˆ 1 ne nene     (18) Finally, a summary for estimating the rotor position is shown by the following design procedures: Step1: Estimate the estimated current by SMO in (16). Step2: Calculate the current error by )()(ˆ)(~ ninini   and )()(ˆ)(~ ninini   Step3: Obtain the Z gain of the current observer in (11) Step4: Estimate the EMF in (17). Step5: Obtain the estimated rotor position in (18) C. Fuzzy controller (FC) The fuzzy controller in this study uses singleton fuzzifier, triangular membership function, product-inference rule and central average defuzzifier method. In Fig. 1, the tracking error e and the error change de are defined by )()()( * nnne rr   (19) )1()()(  nenende (20) and uf represents the output of the fuzzy controller. The *r is the speed command. The design procedure of the fuzzy controller is as follows: (a) Take e, de and uf as the input and output variable of fuzzy controller and define their linguist values E and dE in Fig.3 by {A0, A1, A2, A3, A4, A5, A6} and {B0, B1, B2, B3, B4, B5, B6}, respectively. Each linguist value of E and dE are based on the symmetrical triangular membership function. The symmetrical triangular membership function are determined uniquely by three real numbers 321   , if one fixes 0ff 31  )()(  and 1f 2 )( . (b) Compute the membership degree of e and de. Figure 3 shows that the only two linguistic values are excited and gave a non-zero membership in any input value, and the membership degree )(eAi can be derived, in which the error e is located between ei and ei+1, two linguist values of Ai and Ai+1 are excited, and the membership degree is obtained by 2 eee 1iAi  )( and )()( e1e i1i AA   (21) where )(* 1i26e 1i   . Similar results can be obtained in computing the membership degree )(deB j . (c) Select the initial fuzzy control rules, such as, ij,fji c is u THEN B is e and A is e IF  (22) where i and j = 0~6, Ai and Bj are fuzzy number, and cj,i is real number. (d) Construct the fuzzy system uf(e,de) by using the singleton fuzzifier, product-inference rule, and central average defuzzifier method. For example, if the error e is located between ei and ei+1, and the error change de is located between dej and dej+1, only four linguistic values Ai, Ai+1, Bj, Bj+1 and corresponding consequent values cj,i, cj+1,i, cj,i+1, cj+1,i+1 can be excited, and the (22) can be replaced by the following expression: m,n i in j jm n,mi in j jm BA i in j jm BAn,m f d*c )de(*)e( )]de(*)e([c )de,e(u mn mn               1 1 1 1 1 1    (23) where )de(*)e( d mn BAm,n  . And those n,mc denote the value of the singleton fuzzier. c00 dE 1 A0 A1 A2 A3 A4 A5 A6 0 6-6 e e E de de (e) (d e) 1 A3(e) A4(e)=1- A3(e)  B 1( de )  B 2( de )= 1-  B 1( de ) 0 6 -6 Fuzzy Rule Table Input of e (for i=3) In pu t o f d e (f or j= 1) A0 A1 A2 A3 A4 A5 A6 c01 c02 c03 c04 c05 c06 c10 c11 c12 c13 c14 c15 c16 c20 c21 c22 c23 c24 c25 c26 c30 c31 c32 c33 c34 c35 c36 c40 c41 c42 c43 c44 c45 c46 c50 c51 c52 c53 c54 c55 c56 c60 c61 c62 c63 c64 c65 c66 B0 B1 B2 B3 B4 B5 B6 B 0 B 1 B 2 B 3 B 4 B 5 B 6 42-4 -2 4 2 -4 -2 Fig. 3. The designed fuzzy controller III. SIMULINK/MODELSIM CO-SIMULATION OF SENSORLESS SPEED CONTROLL FOR PMSM DRIVE In Fig.1, it shows the sensorless speed control block diagram for PMSM drive and its Simulink/ModelSim co- simulation architecture is presented in Fig.4. The PMSM, IGBT-based inverter and speed command are performed in Simulink, and the sensorless speed controller described by VHDL code is executed in ModelSim with three works., The work-1 to work-3 of ModelSim in Fig.4 respectively performs the function of speed estimation and speed loop fuzzy controller, the function of current controller and coordinate transformation (CCCT) and SVPWM, and the function of SMO-based rotor flux position estimation. All works in ModelSim are described by VHDL. The sampling frequency of current and speed control is designed with 16 kHz and 2kHz, respectively. The clocks of 50MHz and 12.5MHz will supply all works of ModelSim. A finite state machine (FSM) is employed to model the work-1 and work-3 of ModelSim, and shown in Fig.5 and Fig.6, respectively. In Fig.5, the data type adopts 16-bit length with Q15 format and 2’s complement operation. The multiplier and adder apply Altera LPM (Library Parameterized Modules) standard. It manipulates 22 steps machine to carry out the overall computations. The steps s0~s1 execute the speed estimation, s2~s3 perform the computation of speed error and error change; steps s4~s7 execute the function of the fuzzification; s8 describe the look-up table and s9~s17 defuzzification; and steps s18~s21 execute the computation of PI controller and command output. The SD is the section determination of e and de and the RS,1 represents the right shift function with one bit. The operation of each step in Fig.5 is 80ns (12.5MHz) in FPGA; therefore total 22 steps only need 1.76s operation times. Further, In Fig.6, The data type adopts 12-bit length with Q11 format and 2’s complement operation. The multiplier, adder and divider apply Altera LPM standard component but the arctan function uses our developed component. It manipulates 36 steps machine to carry out the overall computations. The steps s0~s8 execute the estimation of current value; steps s9~s10 compute the current error; s11 is the bang-bang control; s12~s15 describe the computation of EMF and s16~s35 perform the computation of the rotor position. The operation of each step in Fig.6 is 80ns (12.5MHz) in FPGA; therefore total 36 steps only need 2.88s operation times. In Fig.4 the circuit design of CCCT and SVPWM in work-2 of ModelSim refers to [9]. The FPGA (Altera) resource usages of work-1 to work-3 of ModelSim in Fig.4 are 2,043 LEs (Logic Elements) and 0RAM bits, 2,085 LEs and 24,576 RAM bits; 1,151LEs and 49,152 RAM bits, respectively. IV. SIMULATION RESULTS The co-simulation architecture for sensorless PMSM speed control system is shown in Fig.4. The SimPowerSystem blockset in the Simulink executes the PMSM and the inverter. The EDA simulator link for ModelSim executes the co- simulation using Verilog HDL code running in ModelSim program. The designed PMSM parameters used in simulation of Fig.4 are that pole pairs is 4, stator phase resistance is 1.3, stator inductanc is 6.3mH, inertia is J=0.000108 kg*m2 and friction factor is F=0.0013 N*m*s. (work-2) (work-1) (work-3) Fig.4 The Simulink/ModelSim co-simulation architecture for sensorless speed control of PMSM drive +- + - s2 s3 )(ne )1( ne )1( ne s4 Computation of speed error and error change s9 x + 1 - )(e iA )(de jB jid , + - x x x s10 s11 s12 )(de jB )e( iA 1 1 )de( jB 1 j,id 1 1j,id 11  j,id )(de jB )(e iA s13 x x + x x + + x + ui x + s15 s16 s18 s19s14 s17 s20 ijc , i,jc 1 1i,jc 11  i,jc jid , jid ,1 1,1  jid 1, jid iK pK fu ui Defuzzification PI controller and generate the command + - + - & i j j&i s5 s6 s7 s8 )(kde )(e iA )(de jB ijc , 1i,jc i,jc 1 11  i,jc 1ie 1jde Look-up Fuzzy rule table RS,1 RS,1 Fuzzification SD ke SD kde )(ne)(ˆ nr s21 )( * niq Look-up fuzzy table )(* nr )(ˆ ne + - )1(ˆ ne x st k Speed estimation s0 s1 Fig.5 State diagram of an FSM for describing the speed estimation and FC + x s0 s1 s2 s3 s4 )n(v Estimation of the current values s10  s11 )(ˆ ne x  )n(iˆ + )n(iˆ 1 + x s5 s6 s7 s8 s9 )n(v )n(eˆ x)n(iˆ + )n(iˆ 1 - + )n(i -)n(iˆ )n(i ~  + )n(i - )n(iˆ    Y N k)n(z  k)n(z   Y N k)n(z  k)n(z  x s12 s13 s14 s15 s24 )n(z 02 f )n(eˆ s34 - + + )n(eˆ )n(eˆ 1  x)n(z )n(eˆ - + + )n(eˆ )n(eˆ 1 eˆ )n(i~  )n(eˆ )n(eˆ   s16 s23 - tan-1 atan2 s35 Computation of current errors Bang-bang control Estimation of the EMF Computation of the rotor position Table s17 - 02 f Fig.6 State diagram of an FSM for describing the SMO-based rotor position estimation algorithm In the simulation of the rotor flux position estimation, sensor speed control is considered and the running speeds of PMSM with 250rpm, 500rpm, 1000rpm and 2000 rpm are tested. The simulation results for the actual rotor flux position e , the estimated rotor flux position eˆ are shown in Fig. 7. It presents that the estimated rotor flux position can follows the actual rotor flux position with some delay time. The delay time is about 600s while PMSM running speed at 2000 rpm, but about 200s at 250 rpm. After confirming the effectiveness of the rotor flux position estimation in the sensor speed control, we continue the simulation work in sensorless control architecture. The estimated rotor flux position will be feed-backed to the current loop for vector control and to the speed loop for speed control. The simulation work of the step speed response is tested. The motor speeds command is designed with step varying from 0rpm500rpm1000rpm 1500rpm1000rpm, and the results for actual rotor speed, estimated rotor speed response and current response are shown in Fig.8. The rising time and steady-state value are about 210ms and near 0mm, which presents a good speed following response without overshoot occurred. However, the simulations shown in Figs. 7~8 demonstrate the effectiveness and correctness of the sensorless speed control IP for PMSM. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 100 200 300 400 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 100 200 300 400 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 100 200 300 400 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 100 200 300 400 e e  e e  time (sec)(b) time (sec)(c) e e  time (sec)(a) time (sec)(d) e e  Fig. 7 Actual rotor flux angle ( e ) and estimated rotor flux angle ( eˆ ) under PMSM speed running at (a)250rmp (b)500rpm (c)1000rpm (d)2000rpm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -200 0 200 400 600 800 1000 1200 1400 1600 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 time (sec)(b) time (sec)(a) Speed command Actual rotor speed Estimated rotor speed Sp ee d (r pm ) cu rr en t ( A) Fig. 8 (a) Step speed command, actual rotor speed and estimated rotor speed response (b) current response V. CONCLUSIONS This study has been presented a sensorless speed control IP for PMSM drive and successfully demonstrated its performance through co-simulation by using Simulink and ModelSim. After confirming the effective of VHDL code of sensorless speed control IP, we will realize this code in the experimental FPGA-based PMSM drive system for further verifying its function in the future work. ACKNOWLEDGMENT The financial support provided by Bureau of Energy is gratefully acknowledged. REFERENCE [1] V.C. Ilioudis and N.I. Margaris, “PMSM Sensorless Speed Estimation Based on Sliding Mode Observers,” in Proceedings of Power Electronics Specialists Conference (PESC), pp.2838~2843, 2008. [2] W. Lu and Y. Hu and W. Huang and J. Chu and X. Du and J. Yang, “Sensorless Control Of Permanent Magnet Synchronous Machine Based on A Novel Sliding Mode Observer,” in Proceedings of Power Electronics and Applications Conference, pp.1~4, 2009. [3] M. Ezzat and J.d. Leon and N. Gonzalez and A. 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