サイバネットニュース No.121

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1 2007 Spring No

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8 L R L R L R I x C G C G C G x 08

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10 σ () t σ () t = Sx() t Q σ=0 P y O S x= y y & T S= 1 1 x& () t = Ax() t + Bu() t + d(, t x, u) + f { (, t x) : d range( B) Bu(t) B Bd(t)Bd(t) SMC x& () t = AS x() t σ & = 0 (1)p.33-35(3)p AS A S(5) y 1 ( n ) A : = I B( SB) S A S A S A B S S x, A, SB, x A A B x=, A=, B=, S = S S x 2 A 21 A22 B2 x& A% A% x = + u σ& A% 21 A% 22 σ B% 2 A % 11, A % 12, A % 21, A % 22, B % 2 A% A A S S A% A S A% S A S A S A S A S S A% S A S A S B% S B = , 12 = = ( ) ( ) = ( ) 2, 2 = 2 2 σ & = 0 σ = 0 1 x& 1 = A% 11x1 = ( A11 A12S2 S1) x1 1 A11 A12S2 S 1 1 S2 S 1 σ() t σ & () t < 0 σ &() t = Sx& () t S ( ) σ () t SAx() t + SBu() t < σ() t SBd% (, t x, u) % Bd(t,x,u)=d(t,x,u) [ 1 2] 10

11 ut () ut () = ( SB) SAx () t ρsgn ( σ() t ) 1 ρ > 0 ρ ρ > SBd% (, t x, u) ρ L 0 L ξ L : =, L0 :, L: L b b 0 b Δ b = b 0 + b Δ x& () t = Ax() t + Bu() t + Bd(, t x, u) + f { (, t x) x A B d f ξ = 0.1 i L ω() t b J Kt J 0 x() t =, A=, B= i () t K L R L 1L a e d(, t x, u) = ξl( [ 0 Ke R] x() t + u() t ) bδ 0 f(, t x) = () t 0 0 x u Kt Ke R Ke J d(t,x,u) % Control Input ( V ) Speed ( rad/sec ) Time ( sec ) 11

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