(L d L q ). i d = 0,, [8].,,,,, / (maximum torque per ampere, MTPA) [9],. MTPA [9] [10],,,. MTPA, MTPA.,,,. MTPA,,,.,. 2 (Model of PMSM) d-q, :

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32 2 2015 2 DOI: 10.7641/CTA.2015.40361 Control Theory & Applications Vol. 32 No. 2 Feb. 2015 /,,, (, 266071) : (PMSM), / (MTPA). MTPA,.., MTPA.. : ; ; ; / : TP273 : A Adaptive sliding mode maximum torque per ampere control of permanent magnet synchronous motor servo system LU Tao, YU Hai-sheng, SHAN Bing-qiang, CHI Jie-ru (College of Automation, Qingdao University, Qingdao Shandong 266071, China) Abstract: In order to enhance the disturbance attenuation of the permanent magnet synchronous motor (PMSM) servo system, an adaptive sliding mode controller based on maximum torque per ampere (MTPA) control is designed in the paper. The MTPA control is used to obtain the d, q-axes currents, and the sliding mode control is used to enhance the disturbance attenuation of the system, but the chattering is also brought to the system. In addition, an improved adaptive sliding mode reaching law is designed for the position control to attenuate the chattering. Furthermore, the polynomial curve fitting method is adopted in the MTPA control which strengthens the practicability of the controller. The simulation results show that the proposed controller not only enhances system dynamic static performances and robustness, but also attenuates the chattering caused by sliding mode control. Key words: permanent magnet synchronous motor; sliding mode control; adaptive control; maximum torque per ampere control 1 (Introduction) ( permanent magnet synchronous motor, PMSM). PMSM (proportion-integral-derivative, PID),,, [1].,,, [2 3].,,, [4]. [5],,. [6],,,,., [7],,. (L d = L q ) : 2014 04 24; : 2014 07 10.. E-mail: yu.hs@163.com; Tel.: +86 13953207531. (61174131, 61104076), (J1lLG04). Supported by National Natural Science Foundation of China (61174131, 61104076) and Science and Technology Program of Shandong Province Universities and Colleges (J1lLG04).

252 32 (L d L q ). i d = 0,, [8].,,,,, / (maximum torque per ampere, MTPA) [9],. MTPA [9] [10],,,. MTPA, MTPA.,,,. MTPA,,,.,. 2 (Model of PMSM) d-q, : L d i d = R s i d + n p ωl q i q + u d, L q i q = R s i q n p ωl d i d n p ωφ + u q, (1) J m ω = τ τ L, θ = ωr, τ = n p [(L d L q )i d i q + Φi q ], (2) : i d, i q d, q ; u d, u q d, q ; L d, L q d, q ; R s ; n p > 0 ; J m > 0 ; τ ; τ L ; Φ > 0 ; ω ; θ. (1) θ = ω = τ J m τ L J m. (3) 3 (The controller design) 3.1 (The sliding mode surface design).,,.. θ r, e = θ θ r, (4) s = ce + ė. (5) 3.2 (The sliding mode controller design),., [7] ṡ = αsgn s βs, (6) : αsgn s, α. α, ; α,,.,, β, α. ( s 0 ), αsgn s, α,,., ṡ = h 1 s m sgn s h 2 s n sgn s βs, (7) : m > 1, 0 < n < 1, h 1, h 2 > 0, h 1, h 2,.,,,.,, sgn s 0,., s > 1, m,, m, ; s < 1, n,, n. m, n,, (6). τ, (3) (5) ṡ = cė + θ θ r = cė + τ τ L J m J θ r. (8) m (4)(7) (8) τ = ( cė ë + θ h 1 s m sgn s h 2 s n sgn s βs) + τ L. (9) 3.3 / (The maximum torque per ampere control) / (MTPA), / τ i d i q [11]. (2), (L d = L q = L) τ i q,, i d = 0 MTPA. (L d L q ), [11] τ i d, i q Φ i d (i d ) 3 τ = [ L q L d n P (L q L d ) ]2, (10) Φ i d = 2(L q L d ) Φ 2 4(L q L d ) + 2 i2 q. (11)

2 : / 253 [11] i d i q, MTPA. (10) (11) MATLAB/ Simulink, i q 0 A 100 A, τ i d, i q, MATLAB i d = 0.004(τ ) 3 0.0186(τ ) 2 0.2393τ + 0.5726, i q = 0.002(τ ) 3 0.0193(τ ) 2 + 1.5458τ 0.1672. (12) 1 i d, i q, τ,, (9) (12) i d i q. ĩ d = i d i d, ĩ q = i q i q, (1) ĩ d = i d i d = u d R s i d + n p ωl q i q i L d, (13) d ĩ q = i q i q = u q R s i q n p ωl d i d n p ωφ i L q. (14) q, { ĩ d = k 1 ĩ d, ĩ q = k 2 ĩ q. (13) (15), u d, u q (15) u d = L d i d+r s i d n p ωl q i q k 1 L d ĩ d, (16) u q = L q i q+r s i q + n p ωl d i d + n p Φωk 2 L q ĩ q, (17) k 1 k 2. (12)(16) (17) u d = (R s k 1 L d )i d n p ωl q i q + k 1 L d i d + L d i d, u q = (R s k 2 L q )i q + n p ωl d i d + n p Φω + k 2 L q i q + L q i q, i d = 0.004(τ ) 3 0.0186(τ ) 2 0.2393τ + 0.5726, i q = 0.002(τ ) 3 0.0193(τ ) 2 + 1.5458τ 0.1672. 2. (18) (a) i d τ 1 i d, i q (b) i q τ Fig. 1 The real and fitted curves of i d and i q 2 Fig. 2 The structure of servo system

254 32 4 (System stability analysis) Lyapunov (19) (7)(15)(19) (20) V = 1 2 s2 + 1 2ĩ2 d + 1 2ĩ2 q, (19) V = sṡ + ĩ d ĩ d + ĩ q ĩ q. (20) V = sṡ k 1 ĩ 2 d k 2ĩ2 q = 3, MTPA,, i d = 0. 4 MTPA i d = 0, MTPA i d = 0, ;,. 5 MTPA i d = 0. ( h 1 s m sgn s h 2 s n sgn s βs)s k 1 ĩ 2 d k 2ĩ2 q = h 1 s m+1 sgn s h 2 s n+1 sgn s βs 2 k 1 ĩ 2 d k 2ĩ2 q 0. (21) s = i d = i q = 0, V = 0, V. V, V, Lyapunov (18),. 5 (Simulation research) 5.1 (Simulation parameters) : R s = 2.875 Ω, d, q L d = 5.4 mh, L q = 8.5 mh; Φ = 0.175 Wb; J m = 0.0008 kg m 2 ; P n = 4; 1800 r/min; 1.1 kw; 220 V; c = 250; h 1 = h 2 = 10, m = 2, n = 0.01, β = 1000; k 1 = k 2 = 1000. 5.2 (Simulation experiment and analysis) 2 MATLAB/Simulink. t = 0, 30 rad, τ L = 0; t = 0.5 s 3 N m, 0.1 s. 3 MTPA i d = 0. 4 MTPA i d = 0 Fig. 4 The electromagnetic torque of MTPA and i d = 0 control (a) MTPA 3 MTPA i d = 0 Fig. 3 The position response curves of MTPA and i d = 0 control (b) i d = 0 5 MTPA i d = 0 Fig. 5 i q curves of MTPA and i d = 0 control

2 : / 255 5, MTPA i d = 0, MTPA,. 6(a), 6(b), 6,,. (a) (b) 6 Fig. 6 The velocity curves of the traditional and adaptive reaching law 6 (Conclusions), MTPA.,. MTPA,.,.,.,. (References): [1] WAHYU K W. Genetic algorithm tuned PI controller on PMSM simplified vector control [J]. Journal of Central South University, 2013, 20(11): 3042 3048. [2],,,. [J]., 2013, 30(13): 1414 1421. (QIAN Rongrong, LUO Minzhou, ZHAO Jianghai, et al. Novel adaptive sliding mode control for permanent magnet synchronous motor [J]. Control Theory & Applications, 2013, 30(13): 1414 1421.) [3] THIAGO B, VINICIUS F M, HILTON A G, et al. Discrete-time sliding mode observer for sensorless vector control of permanent magnet synchronous machine [J]. IEEE Transactions on Industrial Electronics, 2014, 61(4): 1679 1691. [4] FRIDMAN L M. Singularly perturbed analysis of chattering in relay control systems [J]. IEEE Transactions on Automatic Control, 2002, 47(12): 2079 2084. [5] NABIPOUR M, ZARCHI H A, MADANI S M. Variable-structure position control-a class of fast and robust controllers for synchronous reluctance motor drives [C] //The 20th Iranian Conference on Electrical Engineering. Tehran: IEEE, 2012, 5: 410 415. [6] ZHANG X G, SUN L Z, ZHAO K, et al. Nonlinear speed control for PMSM system using sliding-mode control and disturbance compensation techniques [J]. IEEE Transactions on Power Electronics, 2013, 28(3): 1358 1365. [7]. [M]. :, 1996. (GAO Weibing. Variable Structure Control Theory and Design Method [M]. Beijing: Science Press, 1996.) [8] WANG A M, JIA X W, DONG S H. A new exponential reaching law of sliding mode control to improve performance of permanent magnet synchronous motor [J]. IEEE Transactions on Magnetics, 2013, 49(5): 2409 2412. [9] YU H S, LIU X D, YU J P. Position tracking control of PMSM based on state error PCH and MTPA principle [C] //IEEE Conference on Robotics, Automation and Mechatronics, RAM Proceedings. Qingdao: IEEE, 2011, 9: 113 118. [10],,. MTPA [J]., 2013, 30(7): 226 230. (LI Jun, LUO Dayi, YU Jiajun. Maximum torque per ampere control based on variable-order fragmented curve-fitting [J]. Computer Simulation, 2013, 30(7): 226 230.) [11],,,. PMSM / [J]., 2006, 26(8): 82 87. (YU Haisheng, ZHAO Keyou, GUO Lei, et al. Maximum torque per ampere control of PMSM based on port-controlled hamiltonian theory [J]. Proceedings of the CSEE, 2006, 26(8): 82 87.) : (1989 ),,,, E-mail: 15063035810@163.com; (1963 ),,,,,, E-mail: yu.hs@163.com; (1978 ),,,, E-mail: 13697681913@163.com; (1970 ),,,, E- mail: qduchijieru@163.com.

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