PID FIR 1 4 u t 5-6 y t i d = 0 M d2 y + A dy = f - f dt 2 dt d dy u q = R a i q + K e 7 dt + L di q a dt 1 u q f = K f R a

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1 Electri c Machines and Control Vol. 20 No. 10 Oct FIR DOI /j. emc TM TP 273 A X Research on force ripple compensation and adaptive resonance suppression of linear servo system YANG Liang-liang 1 2 SHI Jun 1 2 XIANG Zhong 1 2 SHI Wei-min Zhejiang Provincial Key Lab of Modern Textile Machinery & Technology Zhejiang Sci-Tech University Hangzhou China 2. The Research Center of Modern Textile Machinery Technology of The Ministry of Education Zhejiang Sci-Tech University Hangzhou China Abstract According to the coexistence of the disturbance and resonance when linear servo system was running at high speed two control loops were established to compensate the disturbance and suppress the vibration respectively. Linear servo model with force ripple was established by experiments. Then model parameters identification was processed by Least squares method and force ripple was compensated by feedforward. According to the resonance existed in the mechanical structure of linear servo system one a- daptive FIR notch filter was introduced to suppress the phenomenon of resonance by identification of main resonance mode of linear servo system. The experiments were carried out at the high speed linear servo platform and the results show that the proposed two control loops were effective to deal with disturbance of force ripple and resonance and could improve position tracking performance and meet the requirements of high speed and high precision of linear servo. Keywords linear servo system force ripple compensation least squares resonance suppression adaptive control BAF06B

2 PID FIR 1 4 u t 5-6 y t i d = 0 M d2 y + A dy = f - f dt 2 dt d dy u q = R a i q + K e 7 dt + L di q a dt 1 u q f = K f R a M A f 8 f d cogging y t u q q R a

3 10 39 i q q K e L a K f f d 2 M d2 y dt 2 f = K f u q + A dy = f dt R a 2 2 s 3 3 FIR H fir s B = K f /R a G n s = Y s U q s = B Ms 2 + As Mÿ t + Ay t = Bu q t C s F s G s I C s F s r t e t y t F ripple t ω t F v y Fig. 1 1 Linear servo controller structure F ripple y y f l U F ripple y = n l = 1 C l sin 2πf l y + n l = 1 D l cos 2πf l y 4

4 H f s Fig. 2 Force ripple related to position 2πf n 2 H f s = 8 s 2 + 4πζf n s + 2πf n 7 2 ζ = 0. 7 f n = 60 Hz 3 a 6 1 mm /s PID ÿ Hf t = ay H f t + bu Hf t + c sin Hf 2πfy + PID d cos Hf 2πfy 8 1 mm /s PID ÿ Hf t = H f s ÿ t H y f t = H f s y t PID u Hf t = H f s u t 3 a sin Hf 2πfy = H f s sin 2πfy 3 b cos Hf 2πfy = H f s cos 2πfy 3 b mm θ φ T t 5 θ = a b c d T φ T t = y H f t u Hf t sin Hf 2πfy t cos Hf 2πfy t mm /s Fig. 3 Integrator output according to position u at closed loop and velocity of 1 mm /s and spectrum of integrator output 1 F ripple y = Csin 2πfy + Dcos 2πfy 5 ω t 4 a ~ 4 d a b c d ÿ t = ay t + bu t + csin 2πfy + dcos 2πfy θ 10 6 a = - A M b = B M c = C M d = D M 9 10 θ θ^ k = θ^ k K k y k - φ T k θ^ k - 1 K k = P k - 1 φ k I + φ T k P k - 1 φ k -1 P k = I - K k φ T k P k - 1 8

5 um 6 Fig. 6 adaptive resonance suppression loop Fig. 4 Fig Identified parameters according to iteration 5 - Standard deviation according to iteration 4. 1 FIR rad /s rad /s S G s = G n k s 2 + 2ρ i ω i s + ω 2 i 11 i = 1 s 2 + 2υ i ω i s + ω 2 i G n 3 k 7 ω i ρ i υ i Fig. 7 Amplitude-frequency of linear servo system ρ i > υ i 6 FIR 6 12 H BPF H BPF s H FIR

42 20 H BPF s = s 2 2πf bpf 2 + 4β bpf πf bpf s + 2πf bpf 12 2 β bpf f bpf 8 Baldor X-Y 1 H BPF s 9 13 FIR FIR e fir k = e bpf k - 2λe bpf k - 1 + e bpf k - 2 13 λ λ "1 1 DSP 4 12 H FIR z = 1-2λz -1

6 42 20 H BPF s = s 2 2πf bpf 2 + 4β bpf πf bpf s + 2πf bpf 12 2 β bpf f bpf 8 Baldor X-Y 1 H BPF s 9 13 FIR FIR e fir k = e bpf k - 2λe bpf k e bpf k λ λ "1 1 DSP 4 12 H FIR z = 1-2λz -1 + z DA z -1 T s λ = cos 2πf 0 T s H FIR e j2πf 0 T s = 2 cos 2πf 0 T s - λ 15 FIR f 0 f 0 λ FIR 4. 2 FIR FIR e fir k L J = 1 e L L fir k 2 16 k = 1 15 λ * 17 λ * Fig. 8 J λ * = min J 17 λ * "1 6 e bpf k FIR e fir k FIR λ k 13 e fir k = e bpf k - 2λ k e bpf k e bpf k λ * λ k + 1 = λ k - α 4 e fir k 2 λ k = λ k + αe fir k e bpf k α k! λ k λ * um DSP FPGA DSP FPGA 6 10K 32bit Fig. 9 8 experimental platform of linear servo system 9 Control structure of linear servo experimental platform

7 10 43 a 20 - X-Y X b - S Table 1 1 parameters of linear motor experimental platform / N /A 21 /kg 7 /V 600 /A Fig m /s + Using feedforward and feedback controller at velocity of 0. 5 m /s /khz 20 /mm 23 /Ω 0. 4 /H C s PID 150 Hz F s 15 λ 1 λ 2 2 s /2πf d πf i /s C s = K p s /2πf lwp 2 + 2β lwp s /2πf lwp + 1 F s = λ 1 s 2 + λ 2 s Table 2 2 Controller parameters 20 Fig m /s + + Using feedforward feedback and ripple compensation controller at velocity of 0. 5 m /s K p f i 3 f d 50 β lwp 0. 8 f lwp 500 λ 1 7 λ 2 3 Fig m /s + + FIR Using feedforward feedback and adaptive FIR controller at velocity of 0. 5 m /s ~ um 11 FIR 10 a 300 um 260 FIR um20 11 b 10 b 0. 5m /s um 64 um

8 Fig m /s FIR Using feedforward feedback ripple compensation and adaptive FIR controller at velocity of 0. 5 m /s 12 2 FIR J 250 um b 30 um 13 FIR 100 um CAO Yong LI Huade. Filtered-version iterative learning linear ser J um um vo system with forgetting factor J 12 FIR 34 um D BRAEMBUSSCHE P V SWEVERS J axes J. Mechatronics MU Haihua ZHOU Yunfei WEN Xin 6 1. J SHI Yangchun ZHOU Yunfei LI Hong et al. Research on iterative learning control to long stroke linear motor J. Proceedings of the CSEE SONG Yixu WANG Chunhong YIN Wensheng et al. Adaptivelearning control for permanent-magnet linear synchronous motors J. Proceedings of the CSEE JUNG I S HUR J HYUN D S. 3-D analysis of permanent magnet linear synchronous motor with magnet arrangement using equivalent magnetic circuit network method J. IEEE Transactions on Magnetics Journal of University of Science and Technology Beijing D... VANBRUSSEL H et al. Accurate tracking control of linear synchronous motor machine tool et al. Calibration and compensation of cogging effect in a permanent magnet linear motor J. Mechatronics J YANG Liangliang SHI Weimin system based on iterative learning J ROHRIG C Control Conference June FIR PENG Laihu. Research on parameter identification and compensation of force ripple in linear drive. MICROMOTORS 2011 JOCHHEIM A. Identification and compensation of force ripple in linear permanent magnet motors C / /American 2001 Arlington VA USA.

9 SINGER N C SEERING W P. Preshaping command inputs to reduce system vibration J. Transactions of the ASME high-precision electromechanical servo system C / /Proceedings. J of the 2007 American Control Conference July New SHI Weimin YANG Liangliang TAO Wei et al. Research on re- York USA duction of residual vibration for trajectory glue based on pulse reshape filter J. China Mechanical Engineering Massachusetts J YANG Liangliang SHI Weimin PENG Laihu. Research on residual vibration suppression of trajectory glue based on adaptive pulse reshape filter J. Manufacturing Automation BOERLAGET M STEINBUCHT M LAMBRECHTS P. Model- 14. based feedforward for motion systems C / /Control Application J TENG Wei ZHOU Yunfei ZHU Qingjie. Research on calibrating feedforward mass & motor constant for linear driving system J. ELECTRIC DRIVE MEULEN S TOUSAIN R BOSGRA O. Fixed structure feedforward controller tuning exploiting iterative trials applied to a 16 MATTHIJS B TOUSAID R STEINBUCHL M. Jerk derivative feedforward control for motion systems C / /Proceeding of the 2004 American Control Conference June 30-July 2 Boston 17 BOERLAGE M. MIMO jerk derivative feedforward for motion systems C / /Proceedings of the 2006 American Control Conference June Minneapolis Minnesota USA June 檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪 M J M. LI Zongyang WU Xusheng ZHANG Junhong et al. Analysis of commutation capability of DC machines with the split throw simplex 3. lap winding J. Electric Machines and Control J KONG Fanrang LIU Zhigang WANG Jianping et al. Image processing applying in DC motor commutation spark image-monitoring method J. Proceedings of the CSEE M M M. 11 Zygfryd Glowacz Witold Glowacz. Mathematical model of DC motor for analysis of commutation processes C / /Proceedings of 6. J PENG Yixu. The commutation of single phase series motor and the methods of improving J. Small & Special Electrical Machines 8. J J IEEE International Symposium on Diagnostics for Electric Machines Power Electronics and Drives

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1 22 2 2018 2 Electri c Machines and Control Vol. 22 No. 2 Feb. 2018 1 2 3 3 1. 214082 2. 214082 3. 150001 DOI 10. 15938 /j. emc. 2018. 02. 005 TM 301. 4 A 1007-449X 2018 02-0033- 08 Research of permanent