(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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1 DOI: /CTA Control Theory & Applications Vol. 32 No. 2 Feb /,,, (, ) : (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 , 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 ) : ; : yu.hs@163.com; Tel.: ( , ), (J1lLG04). Supported by National Natural Science Foundation of China ( , ) and Science and Technology Program of Shandong Province Universities and Colleges (J1lLG04).

2 (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)

3 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 ) (τ ) τ , i q = 0.002(τ ) (τ ) τ (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 ) (τ ) τ , i q = 0.002(τ ) (τ ) τ (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

4 (System stability analysis) Lyapunov (19) (7)(15)(19) (20) V = 1 2 s ĩ2 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 = Ω, d, q L d = 5.4 mh, L q = 8.5 mh; Φ = Wb; J m = 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 = (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

5 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): [2],,,. [J]., 2013, 30(13): (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): ) [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): [4] FRIDMAN L M. Singularly perturbed analysis of chattering in relay control systems [J]. IEEE Transactions on Automatic Control, 2002, 47(12): [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: [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): [7]. [M]. :, (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): [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: [10],,. MTPA [J]., 2013, 30(7): (LI Jun, LUO Dayi, YU Jiajun. Maximum torque per ampere control based on variable-order fragmented curve-fitting [J]. Computer Simulation, 2013, 30(7): ) [11],,,. PMSM / [J]., 2006, 26(8): (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): ) : (1989 ),,,, @163.com; (1963 ),,,,,, yu.hs@163.com; (1978 ),,,, @163.com; (1970 ),,,, E- mail: qduchijieru@163.com.

u d = R s i d - ωl q i q u q = R s i q + ωl d i d + ωψ 1 u d u q d-q i d i q d q L d L q d q ψ f R s ω i 1 i 5th i th 5 θ 1 θ θ 3 5 5

u d = R s i d - ωl q i q u q = R s i q + ωl d i d + ωψ 1 u d u q d-q i d i q d q L d L q d q ψ f R s ω i 1 i 5th i th 5 θ 1 θ θ 3 5 5 3 5 018 10 Vol. 3 No. 5 JOURNAL OF HARBIN UNIVERSITY OF SCIENCE AND TECHNOLOGY Oct. 018 150080 Matlab /Simulink DOI 10. 15938 /j. jhust. 018. 05. 011 TM35 A 100-683 018 05-006- 06 Stator Harmonic Optimal