1 Electri c Machines and Control Vol. 20 No. 6 Jun dspace DOI /j. emc TM 352 A X Position control of the planar switched reluctance motor based on model reference adaptive regulator CAO Guang-zhong 1 HUANG Su-dan 2 WANG Ji-huan 1 DUAN Ji-an 3 QIAN Qing-quan 2 1. Shenzhen Key Laboratory of Electromagnetic Control Shenzhen University Shenzhen China 2. College of Electrical Engineering Southwest Jiaotong University Chengdu China 3. State Key Laboratory of High Performance Complex Manufactory Central South University Changsha China Abstract To improve the positioning accuracy of the planar switched reluctance motor PSRM a position control method of the PSRM based on model reference adaptive control MRAC theory was proposed. The parameters of the linear model were identified for the PSRM by using the recursive least square algorithm. Taking the force command as the control quantity the MRAC position controller was designed with the input and output on the basis of the Lyapunov stability theory. A real-time experimental platform is established based on dspace and the position control of the PSRM was carried out. Experimental results demonstrate that the position control system of the PSRM with the MRAC tracks the reference position smoothly and accurately the positioning accuracy is improved the feasibility and effectiveness of the proposed control method is verified. Keywords planar switched reluctance motor positioning accuracy model reference adaptive control Lyapunov stability theory position control JSGG
2 X Y IC X Y Fig. 1 Prototype of the PSRM 3 PD X Y a 4 5 μm 2 b PD PD 2 c X Y 1 3 Y X 6 X Y
3 Fig. 2 Structure of the stator of the PSRM Table 1 1 Parameters of the prototype /mm 3. 6 /mm 7. 2 X /kg 5. 9 Y /kg /kg /mm mm X 600 mm Y /Ω Fig. 3 3 Induced voltages of the phase windings of the mover 1. 2 YA 3 V 50 Hz 3 3 YA 0. 67% X Y 4 X Fig. 4 Position control block diagram for the X-axis of the PRSM U lk t = R lk i lk t + dψ lk s l t i lk t dt 1 X 4 l = X Y k = A B C y r u ψ lk i lk t s l t = L s l t i lk t i lk t 2 f xa f xb f xc i xa i xb i xc U lk t = R lk i lk t + L lk s l t i lk t di lk t + dt i lk t ds l t dl lk s l t i lk t dt ds l l = X Y k = A B C l U lk i lk R lk L lk ψ lk l k k 3
4 4 20 s l l l f l d 2 s l t ds l t = M l + B dt 2 l + f dt lp t l = X Y 4 M l l B l f l f lp 4 P s = k pn p s M p s = 1 /M l s 2 + B l /M l s 5 M p N p k p = 1 M l l k W lo = ψ lk di lk = i lk dψ lk 6 Fig. 5 Three-dimensional curve of the current position and force l 9 f l = C 1 dl lk i 2 k = A 2 ds lk t l 7 y k = φ T k - 1 θ^ + ζ k 11 7 φ k - 1 θ^ i lk = 2f lk dl -1 φ k = - y k y k - 2 } lk 8 槡 ds u k - 1 u k - 2 l θ^ = a 1 a 2 b 0 b 1 R ^θ 7 θ^ k = θ^ k K k y k φ k θ^ k - 1 u k y k ζ k P k - 1 φ k K k = φ T k P k - 1 φ k P k = I - K k φ T k P k A z -1 y k = B z -1 u k + ζ k A z -1 = 1 + a 1 z -1 + a 2 z -2 B z -1 = b 0 + b 1 z } Lyapunov 6 P k P k θ^ k P 0 = 10 4 I I 4 θ^ 0 = ε ε
5 6 5 W p W m k m N m s M m s = W m s = k mn m s M m s = s 2 k m + a m1 s + a m2 14 N m s = 1 M m s 6 k * 0 c * d * 0 d * 1 Fig. 6 Model reference adaptive control system of the PSRM k 0 c 1 d 0 d k * 0 c * d * 0 d * 1 2 W m L s L s W m s 22 F s = N m s L s L s L s = s + a0 < a < a m1 a 0 < a < a m1 15 F 1 F 2 Lyapunov v 1 = Λv 1 + bu } w 1 = c T v 1 W 1 s = c T Is - Λ -1 b = C s /F s v 2 = Λv 2 + bu w 2 = d T v 2 + d 0 W 2 s = d 0 + d T Is - Λ -1 b = d 0 + D s F s c T = c 1 d T = d 1 d 0 Λ = - l 1 l 1 > 0 b = 1 I 26 6 k k p k 0 L s + 0 L -1 s F s N k p s 0 M p s F s - C' s - d 0 + d 0 L -1 s F s + D' s k p N p s C' s = c 1 + c 1 L -1 s D' s = d 1 + d 1 L -1 s } k 0 = 0 c i = 0 d 0 = 0 d i = k * 0 = k m k p L -1 s F s = N m s M p s F s - c * 1 - d * 0 F s + d * 1 k p N p s = L s N p s M m s ω T = y r v T 1 y p v T 2 } ξ = L -1 s ω θ = - Γξem 25 θ = k 0 c T d 0 d T Γ e m = y p - y m θ = θ 26 k 0 c 1 = d 0 d 1 k 0 dt + k 0 0 c 1 dt + c 1 0 = d 0 dt + d 0 0 d 1 dt + d 1 0 k 0 dt + k * 0 t c 1 dt + c * 1 0 t d 0 dt + d * 0 0 d dt + d * 1 1 u = θ T ω + θ Tξ = θ T ω - Γe m ξ T ξ 27
6 dspace PC dspace 1GHz DS1005 PPC 24 5 DS DS2103 D /A AMC 25A 50A 50A20 Renishaw Tonic 100 nm 9 Fig. 9 Model parameters of the PSRM Fig. 7 7 Structure diagram of the control system Fig. 8 8 Experimental platform dspace 2kg X Y a m1 =21 k m = 100 a m2 = 100 X Y 15 mm 3 s X Y X Y X sy s X Y X Y 11 X ± 200 nm Y X ± 500 nm X Y - ± 4. 7 μm Y ± 4. 3 μm X Y 12
7 6 7 X Y Fig. 12 Detected current of the PSRM 10 Fig. 10 Position response of the PSRM 11 Fig Fig. 13 Position error of the PSRM Adjustable parameters of the model reference adaptive regulator of the PSRM
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