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Simulink/ModelSim Co-Simulation of Sensorless PMSM Speed Controller 1 Ying-Shieh Kung and 2Nguyen Vu Quynh 1,2 Department of Electrical Engineering Southern Taiwan University, Tainan, Taiwan 2 Lac Hong University, Vietnam 1 kung@mail.stut.edu.tw, 2vuquynh@lhu.edu.vn 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. 3 3,4 Green Energy and Environment Research Laboratories Industrial Technology Research Institute Hsinchu, Taiwan 3 CCHuang@itri.org.tw, 4liang.qiao@itri.org.tw 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. 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, Chung-Chun Huang and 4Liang-Chiao Huang 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 SMObased 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 L di d r 1   s id   e q iq  vd dt Ld Ld Ld (1) diq (2) dt   e r Ld K 1 id  s iq   e E  vq Lq Lq Lq Lq 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; K E is the permanent magnet flux linkage. SimuLink ModelSim  * r e + — ̂r 1-Z-1 DC Power Current controllers and coordinate transformation (CCCT) de FC uf + KI 1  Z 1 iq* + KP Speed controller i 0 * d Current controller PI vq d,q — PI + vd Modify Clark-1 v Park-1 ,  v ,  a,b,c vref 1 vref 2 vref 3 — iq id sin ˆe / cos ˆe i d,q i ,  Park ia ib ,  a,b,c Speed estimator A BC ib ic PMSM ic Clark Rotor flux position estimation IGBT-based Inverter ia e sin /cos of Flux angle ̂ e PWM1 PWM2 PWM3 PWM4 PWM5 PWM6 SVPWM v v i i Flux angle Transform. r r Model r External load 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, 3P (3) K E iq  K t iq 4 Considering the mechanical load, the overall dynamic equation of PMSM drive system is obtained by d (4) J m  r  B m  r  Te  T L dt Te  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 lowpass 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 vd  rs  sL  e L  id   0  (5) v          q   e L rs  sL  iq  e K E  Where L Ld  Lq . Transforming (5) of the circuit equation of PMSM on the    fixed coordinate can be derived by the following equation 0  i  v  rs  sL  sin  e  (6) v     i   e K E  cos    0 r sL e  s        where [v v ]T is voltage on fixed coordinate; [i i ]T 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   sin  e  (7) e     e K E   e  cos  e    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, i  1 v  1 e  d i  (8) i   A  i   v   e  dt      L  L  0  where A   rs / L  0  rs / L  Thirdly, a sliding mode observer is designed by iˆ  1 v  1  z  d iˆ  ˆ   A  ˆ        dt i  i  L v  L  z   (9) (10) where the [iˆ iˆ ]T 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. iˆ  i   z  (11) Z     k * sign(     ) ˆ  i  z i       where the current error is defined by T ~ ~ T ˆ ecur  i i  i  i iˆ  i . Further, if we choose the k     be large enough, the inequality in (12) can be reached T ecur ecur <0 (12) and the SMO can enter into sliding mode condition. Therefore, it generates the results of ecur  ecur  0 . Substituting the result into (8) and (10), the Z in (10) will approach to EMF in (6),  z  e   sin  e  (13)  z   e    e K E    cos  e      Fourthly, to alleviate the high frequency switching in bangbang control, a low-pass filter is applied in Fig.2,  z  ê  d ê     -0 ê   0  z  dt ê      (14) where  0  2f 0 . Finally, the rotor position ˆe can be computed by eˆ (15) ˆ  tan 1 (  ) eˆ Rotor position estimation Bang-bang controller Low-pass filter Flux angle computation ̂ e i 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 i 1 j 1   cm ,n [  A ( e )*  B u f ( e ,de )  and uf represents the output of the fuzzy controller. The  the speed command. The design procedure of the fuzzy controller is as follows: * is r m    A ( e )*  B n i m  j n m ( de )] i 1 j 1    cm ,n * d n ,m (23) n i m  j ( de ) where d n,m   A ( e )*  B ( de ) . And those cm ,n denote the value of n m the singleton fuzzier. (e) 1 A4(e)=1- A3(e) Input of e (for i=3) A0 A1 A2 A3 -4 -2 0 A2 A3 A4 A5 A6 2 4 6 A4 A5 A3(e) B1(de) -6 A1 A6 c04 c05 c06 B0 c00 c01 c02 c03 B1 c10 c11 c12 c13 c14 c15 c16 B2 c20 c21 c22 c23 c24 c25 c26 c34 c35 c36 de -6 E A 0 dE e -4 Input of de (for j=1) (de) 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  (19) e( n)   r* ( n)   r ( n) (20) de(n)  e(n)  e(n  1) n n i m  j i 1 j 1 -2 addition, from (14), the difference equation of the EMF estimation can also be expressed by eˆ ( n  1)  eˆ (n)   z (n)  eˆ (n)  (17) eˆ (n  1)  eˆ ( n)  2f 0  z (n)  eˆ (n)           Once the EEMF is estimated, the estimated rotor position ˆe can be directly computed by eˆ (n) (18) ˆe (n)  tan 1 (  ) eˆ (n) 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 ~i (n)  iˆ (n)  i (n) and ~ i ( n)  iˆ ( n)  i ( n) 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) (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: 0 and Ts is the sampling time. In IF e is Ai and e is B j THEN u f is c j,i B3 2 r  s Ts 1 (1  e L ) rs (c) Select the initial fuzzy control rules, such as, B4 4  j B5 6 s (21)  Ai 1 (e)  1   Ai (e) where ei  1   6  2 * (i  1) . Similar results can be obtained in computing the membership degree  B (de) . B6 de rs where  e  L T , ei  1  e and 2 1 B2(de)=1- B1(de) value in SMO; therefore, the difference equation of the modified sliding mode observer in (10) is iˆ (n  1)   0  iˆ (n)  v (n)  eˆ (n)  (16)   ˆ  ˆ       ˆ v ( n ) e n ( ) 0  i ( n 1 ) i ( n )                 Ai (e)  B0 In implementation, the above formulations in the continuous system have to transfer to the discrete system. Besides, we use [eˆ ê  ]T instead of [ z z  ]T as the feedback B1 Fig.2 Rotor flux position estimation based on SMO B2 — +  i    î  B3 Sliding mode observer + B4 v  v    ê  ê     z  z    — B5 i  i    one fixes f (1 )  f ( 3 )  0 and f ( 2 )  1 . (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  A (e ) can be derived, in which the B6 e (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  1   2   3 , if c30 c31 c40 c41 c42 c43 c44 c45 c46 c50 c51 c52 c54 c60 c61 c62 c63 c32 c33 c53 c55 c56 c64 c65 c66 Fuzzy Rule Table Fig. 3. The designed fuzzy controller e 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 cosimulation 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 cosimulation 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-1) (work-2) (work-3) Fig.4 The Simulink/ModelSim co-simulation architecture for sensorless speed control of PMSM drive k ts ˆe (n  1) ˆe (n) ˆ r (n) x + e( n  1) r* ( n) e(n) + - i e i 1 SD ek - + c j ,i c j ,i 1 c j 1 ,i c j 1 ,i 1 Look-up Fuzzy rule table j  Ai (e ) RS,1 j&i & e(n  1) - s0 s2 s1 Speed estimation de (k ) + e(n) s4 s3 de j 1 SD dek s5 Computation of speed error and error change - +  B j (de ) RS,1 s7 s6 s8 Look-up fuzzy table Fuzzification c j ,i di, j  Ai (e ) 1  B j (de )  B j (de )  Ai (e ) di, j x - 1 - + d i , j 1 d i 1 , j x x s11 x + s14 100 0 x s16  e + c j 1 ,i 1 s15 e 200 ui iq* (n) x 400 300 x d i 1, j  1 s13 s12 ui c j ,i 1 d i 1 , j 1 x + + Ki uf Kp d i 1, j s10 s9 c j  1 ,i d i , j 1 x +  B j (de )  Ai  1 ( e ) +  B j 1 ( de ) x 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 0.04 400 s18 s17 Defuzzification s20 s19 s21 300 PI controller and generate 200 e 0.05 (a) 0.06 0.07 0.08 0.09 0.1 time (sec) 0.05 (b) 0.06 0.07 0.08 0.09 0.1 time (sec) 0.05 (c) 0.06 0.07 0.08 0.09 0.1 time (sec) 0.05 (d) 0.06 0.07 0.08 0.09 0.1 time (sec)  e the command Fig.5 State diagram of an FSM for describing the speed estimation and FC 0  -  - + eˆ (n) s0 x + ê ( n ) v ( n ) x  î ( n ) î ( n ) s4 s5 s6 s7 s8 2f 0 x - +  ê ( n  1 )   + s9 z ( n )  k  N s10 z ( n )  k s11 atan2 Table - + x ê ( n ) s12 s13 Estimation of the EMF s15  e e 300 0.04 200 100 0 0 0.01 0.02 0.03 0.04 e 300  e 100 ê ( n  1 ) + 0 ê ( n ) s14 0.03 200 2f 0 z ( n ) 0.02 400 ˆe tan-1 0.01 400 Bang-bang control ê ( n ) ê ( n ) ê ( n ) ê ( n ) z ( n )  k Y ~ i ( n ) Computation of current errors 0  i ( n ) Estimation of the current values z ( n ) - + + ~ i ( n ) N î ( n ) s3 - z ( n )  k Y x î ( n  1 ) s2 s1  î ( n ) + + x i ( n ) î ( n  1 ) v ( n ) 100 s16 s17 s23 s24 s34 s35 Computation of the rotor position 0.02 0.03 0.04 PMSM speed running at (a)250rmp (b)500rpm (c)1000rpm (d)2000rpm 1600 Speed command 1400 Speed (rpm) 1200 Actual rotor speed 1000 800 600 400 Estimated rotor speed 200 0 -200 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 time (sec) (a) 0.8 current (A) 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 0.01 Fig. 7 Actual rotor flux angle (  e ) and estimated rotor flux angle ( ˆe ) under 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 ˆe are shown in 0 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 (b) 1.2 1.4 1.6 1.8 time (sec) Fig. 8 (a) Step speed command, actual rotor speed and estimated rotor speed response (b) current response 2 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. 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