matlab控制系统仿真教程答案唐(matlab求传递函数的极点)

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简单的控制算法，没有用Simulink工具，直接写代码。主要点就是分清楚仿真环境和需要验证的算法。也就是说首先要数学建模，建立一个‘环境’，用来模拟实际环境。然后写自己的控制算法。最后把算法用到‘环境’上，就是在仿真了。

全部代码如下：

%The simulation of the stable pendulum cart

%using PID,poleplacement and LQR

clc;

clear;

%parameter

m = 0.09; % The pendulum mass: m = 0.09kg;

M = 1.52; % The mobile cart mass: M = 1.52kg;

L = 0.24; % The 1/2 length of the pendulum: L = 0.24m;

I = m*(2*L)*(2*L)/12; % The inertia of the pendulum: I = m*(2L)^2/12;

Ts = 0.015; % The sampling time;

g = 9.81; % The gravity accelation: g = 9.81 N/m;

%modeling

temp_den = (m+M)*I+m*M*L*L;

i = m*g*L*(m+M)/temp_den;

j = -m*m*L*L*g/temp_den;

A = [0 1 0 0;

i 0 0 0;

0 0 0 1;

j 0 0 0];

B = [0 -m*L/temp_den 0 (I+m*L*L)/temp_den]’;

C = [1 0 0 0;

0 0 1 0];

D =[0 0]’;

[G H]=c2d(A,B,Ts);

x0=[-0.2 0 0.2 0]’;

t=0:Ts:3;

u=zeros(size(t));

%without control

y0=dlsim(A,B,C,D,u,x0);

subplot(4,1,1);

plot(t,y0);

axis([0 3 -50 50]);

xlabel(‘t’);

ylabel(‘θ&x’);

title(‘未加控制’);

legend(‘θ’,’x’);

%poleplacement

P=[0.9277,-0.9489,0.9632,0.9704];

K=place(G,H,P);

G1=G-H*K;

y1=dlsim(G1,H,C,D,u,x0);

subplot(4,1,2);

plot(t,y1);

xlabel(‘t’);

ylabel(‘x&θ’);

title(‘极点配置’);

legend(‘x’,’θ’);

%LQR

Q=[200 0 0 0;

0 1 0 0;

0 0 200 0;

0 0 0 1];

R=0.1;

K=dlqr(G,H,Q,R)

G2=G-H*K;

y2=dlsim(G2,H,C,D,u,x0);

subplot(4,1,3);

plot(t,y2);

xlabel(‘t’);

ylabel(‘x&θ’);

title(‘LQR’);

legend(‘x’,’θ’);

%PID

y3=zeros(4,size(t,2));

sumx0=[0 0 0 0]’;

u=0;

kp1=150;

ki1=3;

kd1=1000;

kp2=80;

ki2=1;

kd2=1500;

for i=1:size(t,2)

lastx0=x0;

x0=G*x0+H*u;

Dx0=x0-lastx0;

sumx0=sumx0+x0;

u=kp1*x0(1)+ki1*sumx0(1)+kd1*Dx0(1)+kp2*x0(3)+ki2*sumx0(3)+kd2*Dx0(3);

y3(:,i)=x0;

end

y3=[y3(1,:);y3(3,:)];

subplot(4,1,4);

plot(t,y3);

xlabel(‘t’);

ylabel(‘x&θ’);

title(‘PID’);

legend(‘x’,’θ’);

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