第8讲现代控制系统分析设计(4)

例8_11

求典型二阶系统

2?n H(s)?22s?2??ns??n当??0.7，?n?6时的单位冲激响应。

解： wn=6; kos=0.7; figure(1); num=wn.^2;

den=[1,2*kos*wn,wn.^2]; figure

impulse(num,den)

title('Impulse response');

Impulse responseFrom: U(1)32.52AmplitudeTo: Y(1)1.510.50-0.500.511.5Time (sec.) 回目录

例8_12

有高阶系统

????1.6?0.900??1????0.9000??0??x?????0.40.5?0.5?2.45??x????u????002.450??1? ??y??1111?x??0?求单位阶跃响应，单位冲激响应激零输入响应（设初始状态x0??1解：

a=[2.25,-5,-1.25,-0.5;2.25,-4.25,-1.25,-0.25; 0.25,-0.5,-1.25,-1;1.25,-1.75,-0.25,-0.75]; b=[4,6;2,4;2,2;0,2]; c=[0,0,0,1;0,2,0,2]; d=zeros(2,2); figure;

subplot(2,2,1); step(a,b,c,d);

axis([0,6,-0.5,2.5]); %title('Step Response'); subplot(2,2,2); impulse(a,b,c,d);

%title('Impulse response'); subplot(2,2,3);

%axis([0,6,-0.5,2.5]); x0=[1;1;1;-1];

initial(a,b,c,d,x0);

%title('Intial response'); subplot(2,2,4); pzmap(a,b,c,d);

%title('Pole-Zero Map') ;

1?1?T）1

Step ResponseFrom: U(1)2To: Y(1)Impulse ResponseFrom: U(1)2To: Y(1)From: U(2)From: U(2)Amplitude010500481204812Amplitude10-2200To: Y(2)To: Y(2)-200481204812Time (sec.)Initial Condition Results 1To: Y(1)Time (sec.)Pole zero map10.5Imag AxisAmplitude0-120-20510150-0.5-1-1.5To: Y(2)Time (sec.)-1-0.5Real Axis0

回目录

例8_13

多输入多输出系统

??5?1.25?2.25??2.25?4.25?1.25?x?????0.25?0.5?1.25???1.25?1.75?0.25???000y???020???0.5??46??24??0.25??x???u?1??22???? ?0.75??02?1?x2??求单位阶跃响应和单位冲激响应。

解：

a=[2.25,-5,-1.25,-0.5;2.25,-4.25,-1.25,-0.25; 0.25,-0.5,-1.25,-1;1.25,-1.75,-0.25,-0.75]; b=[4,6;2,4;2,2;0,2]; c=[0,0,0,1;0,2,0,2]; d=zeros(2,2); figure(1);

step(a,b,c,d); figure(2);

impulse(a,b,c,d); Impulse ResponseFrom: U(1)2From: U(2)To: Y(1)10Amplitude-11510To: Y(2)50-50481204812Time (sec.)回目录

例8_14

连续系统

?00???1.6?0.9?1???0.9??0?000??x???u????x?0.5?0.5?2.45??0.4?1? ?????002.450???0???y??1111?x?以t=0.5s采样周期，采用双线性变换算法转换为离散系统，然后求出离散系统的单位阶跃响应、单位冲激响应及零输入响应（设初始状态x0T??111?1?）。

解：

a1=[-1.6,-0.9,0,0;0.9,0,0,0;

0.4,0.5,-5.0,-2.45;0,0,2.45,0]; b1=[1;0;1;0]; c1=[1,1,1,1]; d1=[0]; t=0.5;

[a,b,c,d]=c2dm(a1,b1,c1,d1,t,'tustin'); figure(1);

subplot(2,2,1); dstep(a,b,c,d); subplot(2,2,2); dimpulse(a,b,c,d); subplot(2,2,3); x0=[1;1;1;-1];

dinitial(a,b,c,d,x0); axis([0 6 0.5 2.5]); subplot(2,2,4);

[z,p,k]=ss2zp(a,b,c,d,1); zplane(z,p);