Study on disturbance torques compensation in high precise servo turn table control system

Transcription

1 EL ECTR ICMACH IN ESANDCON TROL Vol113 No14 July 2009,, (, ) :, PD,, Lyapunov, ;,, : ; ; ; Lyapunov; : TP 273 : A : X (2009) Study on disturbance torques compensation in high precise servo turn table control system YANG Song, WANG Yi, SU Bao2ku (Department of Control Science and Engineering, Harbin Institute of Technology, Harbin , China) Abstract: The friction torque and motor ripp le torque are m ain factors that influence the position tracking accuracy of high p recise servo turntable control system. Against the influence of friction torque and motor ripp le torque on the system, the paper p resents an integrate disturbance torques compensation strategy. First, it p roposed a PD feedforward control method w ith the friction observer, which compensated dynam2 ic friction torque in the system, and it analyzed the system s stability depending on Lyapunov stability theory. Furthermore, combining w ith the disturbance observer based on the repetitive learning control, it p roposed an integrate disturbance torques compensation strategy. On one hand, the p roposed method may compensate the friction in the system. On the other hand, the inductive repetitive controller m ay restrain well the periodic ripp le torque and the disturbance observer is used to compensate the uncertainty that is aroused by repetitive control and friction compensation to the system. fectiveness of the p roposed method. Key words: servo turntable; position tracking accuracy; stability theory; repetitive control The simulation results p rove the ef2 disturbance torques compensation; Lyapunov : : ( HT01) : (1978),,, ; (1967),,,,; (1941),,,,

2 ,,,,,, Stibeck,LuGre,Stribeck, [ 1 ] LuGre,, LuGre,,,,, [ 2 ] ; [ 3 ], H, ; [ 4 ], [ 5 ], ; [ 6 ], ; [ 7 ], ; [ 8 ], [ 9 ],,,, PD ;, 1, [ 10 ] : a = - pk e ; b = 2 3 b = a + u - T f - T r, (1) JR pk e ; T f = 2 3 R pk e T fric ; T r = 2 R 3 pk e T rip; ; u ; J p k e R ; T fric T rip T f LuGre, dz d t = g ( z, (2) ) dz T f = 0 z + 1 dt + 2 (3) : z; 0 1 2, 3; g ( ), Stribeck 0 g ( ) = T c + ( T s - T c ) e - ( / s ) 2, (4) : T c T s ; s Stribeck,,,, T r =A r sin ( +) =A r1 cos +A r2 sin, (5) A r A r1 A r2 2 (2) ( 4)( 1),

3 4 617 = ( 1 = 1 b [ a + u - 0 z + 1 g ( ) z - ], (6) + 2 ) > 0T r, 211L ugre LuGre,T s T c K v Stribeck s 0 6 ( 1) T r, b = a + u - T f (7), dz dt = 0, (2) z = g ( ) sgn ( ) (8) (8) (3), T ss = 0 g ( ) sgn ( ) + 2 = [ T c + ( T s - T c ) e - ( / s ) 2 ] sgn ( ) +2, = 0, (7) T ss (9) (10), (9) = a + u (10) [ T c + (T s - T c ) e - ( / s ) 2 ]sgn ( ) + 2 = a + u (11) u, 2, T c, T s s, z, (3) T f (12) (12)(7), u = b + ( a) + 0 (13) (13), ( s) U ( s) = 1 + ( a) s + 0 (14) (14),, a b 2, LuGre z,,,, [ 1 ] z, LuGre z d^z dt = - g ( ) ^z - ke 1, (15) : ^zz ; k ; e 1, e 1 = d -, (16) d, d^z T^f = 0 ^z + 1 dt + 2, (17) T^f T f,, e 1 z = z - ^z, PD, u = b d - a d + T^f + K p e 1 + K d ge 1, (18) K p K d (18)(7), gt f = b e 1 + ( K d - a) ge 1 + K p e = b e 1 + K d ge 1 + K p e 1 (19) : gt f = T f - T^f; K d = K d - a( 19), E ( s) = 1 gt f ( s) (20) + K d s + K p (3) ( 17 )( 20 ),, (21) 1 s + 0 E ( s) = gz ( s) (21) + K d s + K p 1 s + 0 H ( s) =, (22) + K d s + K p E ( s) = H ( s) gz ( s) (23)

4 gx =A x +B gz e 1 = C x (24) H ( s), Kalman2Yakubovich, PQ, A T P + PA = - Q, PB = C (25) Lyapunov V = x T Px + gz2 (26) k (26), V = - x T Q x + 2xPB gz + 2 k z z = - x T Q x + 2e 1 gz + 2 k gz[ - g ( ) gz - ke 1 ] = - x T Q x - 2 k g ( gz 2 ) - x T Q x0 (27),Lyapunov ( 23), e 1 gz,la2 Salle, e 1 gz, : a = , b = 0115; d = sin t sin2 t; LuGre : 0 = 918 N m / ( rad / s), 1 = 518 N m / ( rad / s), 2 = 4 N m / ( rad / s) ; Stribeck : T c s = = 3 N m, T s = 8 N m, 01001;: K p = 100, K d = 10, K = 50 23PD PD 3,,, [ 9 ],,,, 1 1 F ig. 1Structure F igure of System w ith In tegra te Con trol 4, 1,PD 23 PD, PD A r : = 011 N m,= 75 rad,= 0105, 4 4,

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