基于模糊变结构的机械臂控制

1 2 1

1 2 1

[1]

n

M(q)¨q+h(q,q˙)=u(t)+ω.

q(t) n×1 M(q) n×n

h(q,q˙) n×1

u(t) n×1 ω

M(q) h(q,q˙) M0(q) h0(q,q˙)

M(q)=M0(q)+ M(q), h(q,q˙)=h0(q,q˙)+ h(q,q˙).

M(q) h(q,q˙)

M0(q)¨q+h0(q,q˙)=u(t)+ρ(t).

ρ(t)= M(q)¨q h(q,q˙)+ω

M0(q)¨q+h0(q,q˙)=u1.

ρ(t) <b0+b1 q(t) +b2 q˙(t) 2.

b0 b1 b2

[6]

qr

e(t)=q qr.

X˙=AX+Bv.

T

X=

eIe˙T,A=00

0,B=0I

,v=M0(q) 1(u1 h0(q,q˙)) q¨r.

u1=h0(q,q˙)+M0(q)(KX+q¨r).

K=[ K1, K2] K1,K2∈Rn×n A1

A1=A+BK.

K

u(t)=u1+u0.

u1 u0

X

˙=A1X+BM0(q) 1u0+BM0(q) 1ρ(t).

S=CX.

C=[C1,C2] C1,C2∈Rn×n

Reλ( C 1

2C1)<0

[7] u1 u0

(ST

C2M0(q) 1)T

u STC 2

w, S =0,

0= 2M0(q) 1 0, S =0,

w= STCA1e S C2M0(q) 1 ·(b0+b1 q +b2 q˙ 2)).

u0 u0 w w w w w

s(t) u u1, s(t) u u1+u0.

s(t) u1 s(t) u1+u0

u=

µZ0u1(s)+µNZ(s)(u1+u0)

µ. Z0(s)+µNZ(s)

µZ0(s) µNZ(s)

µZ0(s)+µNZ(s)=1

u=u1+µNZ(s)u0,

µNZ(s)=1 u(t)=u1+u0 µNZ=1 µNZ(s)

s u ,

s u , s u .

α11(q2)α12(q2)q¨1

α21(q2)α22q¨=2

β12(q2)q˙2

1+2β12(q2)q˙1q˙2γ1(q1,q2)gu1

β12(q2)q˙2

+2γq+u.2(1,q2)g2

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