系统平衡时：以fo,yo表示 △f=f-f0△y=y-o (mp+cp+k)xo(t)+(mp+cp+k)Ay(t) =f6(t)+f(t) (mp'+cp+k)Ay(t)=Af(t) (mp+cp+k)y(t)=f(t)
系统平衡时：以f0，y0表示 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ; 2 2 0 2 0 2 0 0 m p cp k y t f t m p cp k y t f t f t f t m p cp k y t m p cp k y t f f f y y y + + = + + = = + + + + + + = − = −
三非线性微分方程的线性化 y=f(x)=f(xo)》 - dx △y=f(x)-f(x)》 dx △y=Kx y=Kx
y K x y K x x dx df x x dx df y f x f x x x dx d f x x dx df y f x f x x x x x x x x x = = − = − + − + − + = = = = = = 0 0 0 0 | ( ) | ( ) ( ) | ( ) . 2! 1 | ( ) ( ) ( ) 0 0 2 2 0 2 0 0 三非线性微分方程的线性化
y=f(x1,x2)=f(x0x20） (X-X20)+. x (x-x0)+ X2=x20 0x2 X2=x20 △y=f(x1,x2)-f(x0,X20〉 Ax2 8x1 X2=X20 0x2 X2=X20 △y=K△x1-K2△x2 0x1x2=20 1=10 X2=X20 y=K1x1-K22
1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 2 1 0 2 0 2 0 2 1 0 1 1 2 1 0 2 0 2 2 0 1 1 0 2 2 0 1 1 0 2 2 0 1 1 0 2 2 0 1 1 0 2 2 0 1 1 0 2 2 0 1 1 0 | ; | | | ( , ) ( , ) | ( ) | ( ) . ( , ) ( , ) y K x K x x f K x f K y K x K x x x f x x f y f x x f x x x x x f x x x f y f x x f x x x x x x x x x x x x x x x x x x x x x x x x x x = − = = = − + = − − + − + + = = = = = = = = = = = = = =
高压油 油箱 油箱 阀芯 液压缸 负载 图：2.1.3液压伺服机构
m+C少=A△p 9=A少 gwc4层p-c,月如 qx,p)=q(x0,p0)+ 0(-x0)+ lk=0(p-p0)+ p=p0 p=pO △q=q(x,p)-q(x0,p0) 04 △x+ 6q △p 8x Ix=x0 x=x0 p=p0 op p=p0 △q=K,△x-K△p Ka 1=x0K。= Ix=x0 p=p0 p=p0
q q x p C A p C Wx p q Ay my cy A p = = d == d = + = 2 2 ( , ) 0 0 0 0 0 0 0 0 0 0 0 0 | ; | | | ( , ) ( 0, 0) ( , ) ( 0, 0) | ( 0) | ( 0) . p p c x x p p q x x q c p p x x p p x x p p x x p p x x p q K x q K q K x K p p p q x x q q q x p q x p p p p q x x x q q x p q x p = = = = = = = = = = = = = = = − + = − − + − + = +