二阶系统matlab仿真

simulink仿真

-1<ξ<0

>> step(tf(4^2,[1,2*(-0.5)*4,4^2]))

ξ<-1

>> step(tf(4^2,[1,2*(-1.5)*4,4^2]))

ξ＝0

>> step(tf(4^2,[1,2*0*4,4^2]))

0<ξ<1

>> figure

>> step(tf(4^2,[1,2*0.1*4,4^2]))

>> step(tf(4^2,[1,2*0.2*4,4^2]))

>> step(tf(4^2,[1,2*0.3*4,4^2]))

>> step(tf(4^2,[1,2*0.4*4,4^2]))

>> step(tf(4^2,[1,2*0.5*4,4^2]))

>> step(tf(4^2,[1,2*0.6*4,4^2]))

>> step(tf(4^2,[1,2*0.7*4,4^2]))

>> step(tf(4^2,[1,2*0.8*4,4^2]))

>> step(tf(4^2,[1,2*0.9*4,4^2]))

ωn不变，ζ减小

ξ=1

>> figure

>> step(tf(4^2,[1,2*1*4,4^2]))

ξ>1

>> hold on

>> step(tf(4^2,[1,2*2.0*4,4^2]))

>> step(tf(4^2,[1,2*4.0*4,4^2]))

>> step(tf(4^2,[1,2*8.0*4,4^2]))

ωn不变，ζ减小

ξ＝0.5，改变ωn时的情况：

>> figure

>> step(tf(1^2,[1,2*0.5*1,1^2])) （ωn＝1）

>> hold on

>> step(tf(2^2,[1,2*0.5*2,2^2])) （ωn＝2）>> step(tf(4^2,[1,2*0.5*4,4^2])) （ωn＝4）>> step(tf(8^2,[1,2*0.5*8,8^2])) （ωn＝8）

ζ不变，ωn增大

曲线拟合程序

>> figure

>> x=[0,0.2,0.4,0.6,0.8,1.0,1.2];

>> y=[1.135,1.135,1.216,1.351,1.534,1.737,2.0,]; >> plot(x,y,'.')

>> hold on

>> x1=[0:0.1:1.2];

>> y1=1+0.6*x1+0.2*x1.^2;

>> plot(x1,y1)

>> y1=1+0.7*x1;

>> plot(x1,y1)