MATLAB控制系统仿真作业1

来源：爱go旅游网

一、控制系统的模型与转换

1．请将下面的传递函数模型输入到matlab环境。

s34s2z20.568 H(z)，T=0.1s G(s)32s(s2)[(s21)32s5](z1)(z20.2z0.99)>> s=tf('s');

G=(s^3+4*s+2)/(s^3*(s^2+2)*((s^2+1)^3+2*s+5)); G

Transfer function:

s^3 + 4 s + 2 ------------------------------------------------------ s^11 + 5 s^9 + 9 s^7 + 2 s^6 + 12 s^5 + 4 s^4 + 12 s^3

>> num=[1 0 0.56];

den=conv([1 -1],[1 -0.2 0.99]); H=tf(num,den,'Ts',0.1)

Transfer function: z^2 + 0.56 ----------------------------- z^3 - 1.2 z^2 + 1.19 z - 0.99

2．请将下面的零极点模型输入到matlab环境。请求出上述模型的零极点，并绘制其位置。

8(s1j)(s1j)(z13.2)(z12.6)G(s)2 H(z)，T=0.05s 251s(s5)(s6)(s1)z(z8.2)

>>z=[-1-j -1+j]; p=[0 0 -5 -6 -j j]; G=zpk(z,p,8)

Zero/pole/gain: 8 (s^2 + 2s + 2) -------------------------- s^2 (s+5) (s+6) (s^2 + 1)

>>pzmap(G)

>> z=[0 0 0 0 0 -1/3.2 -1/2.6]; p=[1/8.2];

H=zpk(z,p,1,'Ts',0.05)

Zero/pole/gain:

z^5 (z+0.3125) (z+0.3846) ------------------------- (z-0.122)

Sampling time: 0.05

>>pzmap（H）

二、线性系统分析

1. 请分析下面传递函数模型的稳定性。

G(s)

1s32s2s2 G(s)3s1

s2(300s2600s50)3s1>> num=[1];

den=[1 2 1 2]; G=tf(num,den); eig(G)' ans =

-2.0000 0.0000 - 1.0000i 0.0000 + 1.0000i

可见，系统有两个特征根在虚轴上，一个特征根在虚轴左侧，所以系统是临界稳定的。

>> num=[3 1];

den=[300 600 50 3 1];

G=tf(num,den); eig(G)' ans =

-1.9152 -0.1414

0.0283 - 0.1073i 0.0283 + 0.1073i

可见，有两个特征根在虚轴右侧，所以系统是不稳定的。

2. 请判定下面离散系统的稳定性。

H(z)3z2

(z30.2z20.25z0.05)H(z)

z52.12z211.76z115.91 43217.368z20.15z102.4z80.39z340)>> num=[-3 2];

den=[1 -0.2 -0.25 0.05]; H=tf(num,den,'Ts',0.1); [eig(H) abs(eig(H))] ans =

-0.5000 0.5000 0.5000 0.5000

0.2000 0.2000

可以看出，由于各个特征根的模均小于1，所以可以判定闭环系统是稳定的。

>> z=tf('z',0.1);

H=(2.12*z^-2+11.76*z^-1+15.91)/…;

(z^-5-7.368*z^-4-20.15*z^-3+102.4*z^-2+80.39*z-1-340);

[eig(H) abs(eig(H))] ans =

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.1724 4.1724 0.3755 + 0.1814i 0.4170 0.3755 - 0.1814i 0.4170 -0.5292 0.5292 -0.2716 0.2716

0.1193 0.1193

可以看出，由于4.1724这个特征根的模大于1，所以可以判定闭环系统是不稳定的。

3. 设描述系统的传递函数为

18s7514s65982s536380s41226s3222088s2185760s40320，假定系统

G(s)8s36s76s64536s522449s467284s3118124s2109584s40320具有零初始状态，请求出单位阶跃响应曲线和单位脉冲响应曲线。

>> num=[18 514 5982 36380 1226 22088 185760 40320]; den=[1 36 6 4536 22449 67284 118124 109584 40320]; G=tf(num,den)

Transfer function:

18 s^7 + 514 s^6 + 5982 s^5 + 36380 s^4 + 1226 s^3 + 22088 s^2 + 185760 s + 40320 -----------------------------------------------------------------------------------------

s^8 + 36 s^7 + 6 s^6 + 4536 s^5 + 22449 s^4 + 67284 s^3 + 118124 s^2 + 109584 s + 40320

>> step(G,10) >> impulse(G,10)

单位阶跃响应：

单位脉冲响应：

三、线性系统Simulink仿真应用

1. 请分析下面传递函数模型阶跃响应。

G(s)1s2ss232

利用Simulink建模，建立系统仿真模型如下：

单击启动仿真按钮，双击示波器得到系统的阶跃响应如下：

2. 请分析下面离散系统的脉冲响应。

3s34s21 G(s)2 2s(300s600s50)3s1

利用Simulink建模，建立系统仿真模型如下：

单击启动仿真按钮，双击示波器得到系统的脉冲响应如下：

3. 对离散采样系统进行分析，并求出其阶跃响应。

u(t)+零阶保持器G(s)y(t)- 其中：G(s)s3 32s7s3s2

利用Simulink建模，建立系统仿真模型如下：

单击启动仿真按钮，双击示波器得到系统的阶跃响应如下：

4. 设计控制器，使得下列系统稳定。

G(s)(s1)(s2.3)(s3)(s2)(s1.2)

利用Simulink建模，未连入控制器时，仿真模型和响应如下：

利用Simulink建模，设计控制器：

从响应输出图形可以看出，连入控制器后系统稳定，性能明显提高。

四、基于MATLAB的PID 控制器设计

设计题目：

1. 应用Ziegler — Nichols算法设计PID控制器，实现系统的闭环稳定，并比较对各个系统的控制效果。

G(s)1(s1)3

未连入PID控制器时的系统仿真及其性能指标如下：

可见，未调节时的系统性能有待提高，需设计PID控制器连入。

输入：

>> num=1;

den=conv( [1,1],conv( [1,1],[1,1] )); Step(num,den); K=dcgain (num,den)

得出：

K =1

根据图形，得出：

L=1.86 T=4.4

利用自定义的Ziegler_std函数求出Kp、Ti、Td 输入：

>> K=1; L=1.86; T=4.4;

[num,den,Kp,Ti,Td]=Ziegler_std (3,[K,L,T])

得出：

num =

2.00 2.8387 1.5262 den =

Kp =2.8387 Ti =3.7200 Td =0.9300

根据得出的Kp、Ti、Td值，设计PID控制器，并利用利用Simulink仿真建模。仿真模型及其响应如下：

可见，加入PID控制器调节后，系统性能明显改善。

G(s)1(s1)5

未连入PID控制器时的系统仿真及其性能指标如下：

可见，未调节时的系统性能有待提高，需设计PID控制器连入。

输入：

>> num=1;

den=conv([1,1],conv([1,1],…;

conv( [1,1],conv( [1,1],[1,1] )))); Step(num,den); K=dcgain (num,den)

得出：

K = 1

根据图形，得出：

L=3.4 T=6.8

利用自定义的Ziegler_std函数求出Kp、Ti、Td 输入：

>> K=1; L=3.4; T=6.8;

[num,den,Kp,Ti,Td]=Ziegler_std (3,[K,L,T])

得出:

num =

4.0800 2.4000 0.7059 den = 1 0 Kp = 2.4000 Ti = 6.8000 Td =

1.7000

根据得出的Kp、Ti、Td值，设计PID控制器，并利用利用Simulink仿真建模。仿真模型及其响应如下：

可见，加入PID控制器调节后，系统性能明显改善。

G(s)-1.5s1(s1)3

利用Simulink建模，未连入控制器时，仿真模型和响应如下：

可见，未调节时的系统性能有待提高，需设计PID控制器连入。

输入:

>>num=[-1.5 1];

den=conv( [1,1],conv( [1,1],[1,1] )); Step(num,den); K=dcgain (num,den)

得出:

K =1

根据图形，得出：

L=1.8 T=5.7

利用自定义的Ziegler_std函数求出Kp、Ti、Td 输入:

>> K=1; L=1.8 T=5.7;

[num,den,Kp,Ti,Td]=Ziegler_std (3,[K,L,T])

得出:

num =

3.4200 3.8000 2.1111 den =

1 Kp =

3.8000 Ti =

3.6000 Td =

0.9000

根据得出的Kp、Ti、Td值，设计PID控制器，并利用利用Simulink仿真建模。仿真模型及其响应如下：

可见，加入PID控制器调节后，系统性能明显改善。

五、模糊控制器设计

设计任务：试设计一个模糊控制器，实现对室内温度的控制的模拟。

参考输入：

（1）温度18-40℃范围内分为七个论域，NB NM NS ZE PS PM PB；隶属度函数满足高斯分布；

（2）温度变化率-2 ~2℃范围内分为七个论域，NB NM NS ZE PS PM PB；隶属度函数满足高斯分布；参考输出：

变频空调输出的控制信号。在一定范围内分为七个论域，NB NM NS ZE PS PM PB，隶属度函数为常数1。

模糊推理过程，output=输入隶属度函数值*输出论域的中心值。

注：本模糊程序采用PAM控制方式的压缩机，则其输出的转速范围为：0~10500转/分。控制规则：

% % if input is NB and errorinput is NB, then output is NB; % % if input is NB and errorinput is NM, then output is NB; % % if input is NB and errorinput is NS, then output is NB; % % if input is NB and errorinput is ZE, then output is NM;

% % if input is NB and errorinput is PS, then output is NM; % % if input is NB and errorinput is PM, then output is NM; % % if input is NB and errorinput is PB, then output is NS; % % if input is NM and errorinput is NB, then output is NB; % % if input is NM and errorinput is NM, then output is NM; % % if input is NM and errorinput is NS, then output is NM; % % if input is NM and errorinput is ZE, then output is NM; % % if input is NM and errorinput is PS, then output is NM; % % if input is NM and errorinput is PM, then output is NS; % % if input is NM and errorinput is PB, then output is NS; % % if input is NS and errorinput is NB, then output is NM; % % if input is NS and errorinput is NM, then output is NS; % % if input is NS and errorinput is NS, then output is NS; % % if input is NS and errorinput is ZE, then output is NS; % % if input is NS and errorinput is PS, then output is NS; % % if input is NS and errorinput is PM, then output is ZE; % % if input is NS and errorinput is PB, then output is ZE; % % if input is ZE and errorinput is NB, then output is NS; % % if input is ZE and errorinput is NM, then output is ZE; % % if input is ZE and errorinput is NS, then output is ZE; % % if input is ZE and errorinput is ZE, then output is ZE; % % if input is ZE and errorinput is PS, then output is ZE; % % if input is ZE and errorinput is PM, then output is PS; % % if input is ZE and errorinput is PB, then output is PS; % % if input is PS and errorinput is NB, then output is ZE; % % if input is PS and errorinput is NM, then output is PS; % % if input is PS and errorinput is NS, then output is PS; % % if input is PS and errorinput is ZE, then output is PS; % % if input is PS and errorinput is PS, then output is PS; % % if input is PS and errorinput is PM, then output is PM; % % if input is PS and errorinput is PB, then output is PM; % % if input is PM and errorinput is NB, then output is PS; % % if input is PM and errorinput is NM, then output is PS; % % if input is PM and errorinput is NS, then output is PM; % % if input is PM and errorinput is ZE, then output is PM; % % if input is PM and errorinput is PS, then output is PM; % % if input is PM and errorinput is PM, then output is PM; % % if input is PM and errorinput is PB, then output is PB; % % if input is PB and errorinput is NB, then output is PS; % % if input is PB and errorinput is NM, then output is PM; % % if input is PB and errorinput is NS, then output is PM; % % if input is PB and errorinput is ZE, then output is PM; % % if input is PB and errorinput is PS, then output is PB; % % if input is PB and errorinput is PM, then output is PB; % % if input is PB and errorinput is PB, then output is PB; 1.输入为：程序为：

>> x1 = (18:0.1:40)'; y0 = gaussmf(x1, [1 18]); y1 = gaussmf(x1, [1 21]); y2 = gaussmf(x1, [1 25]); y3 = gaussmf(x1, [1 29]); y4 = gaussmf(x1, [1 33]); y5 = gaussmf(x1, [1 37]); y6 = gaussmf(x1, [1 40]); plot(x1,[y0 y1 y2 y3 y4 y5 y6])

2.误差图：程序为： >> x1 = (-2:0.1:2)'; y0 = gaussmf(x1, [0.5 -2]); y1 = gaussmf(x1, [0.5 -1.3]); y2 = gaussmf(x1, [0.5 -0.7]); y3 = gaussmf(x1, [0.5 0]); y4 = gaussmf(x1, [0.5 0.7]); y5 = gaussmf(x1, [0.5 1.3]); y6 = gaussmf(x1, [0.5 2]); plot(x1,[y0 y1 y2 y3 y4 y5 y6])

3.程序为； x=35; ex=-0.8;

% define input type in fuzzy zone y0 = gaussmf(x, [1 18]); y1 = gaussmf(x, [1 21]); y2 = gaussmf(x, [1 25]); y3 = gaussmf(x, [1 29]); y4 = gaussmf(x, [1 33]); y5 = gaussmf(x, [1 37]); y6 = gaussmf(x, [1 40]);

a=[y0 y1 y2 y3 y4 y5 y6]; b=max(a);

% caculate input in fuzzy zone,get input_type and input_authorityvalue if x<=40 & x>=18 if b==a(1) type='NB'; authorityvalue=y0; elseif b==a(2) type='NM'; authorityvalue=y1; elseif b==a(3) type='NS'; authorityvalue=y2; elseif b==a(4) type='ZE'; authorityvalue=y3;

elseif b==a(5) type='PS'; authorityvalue=y4;

elseif b==a(6) type='PM'; authorityvalue=y5;

elseif b==a(7) type='PB'; authorityvalue=y6; end else if x>40 type='PB'; authorityvalue=1; elseif x<18 type='NB'; authorityvalue=1; end end type

authorityvalue %error calculate. ey0 = gaussmf(x, [0.5 -2]); ey1 = gaussmf(x, [0.5 -1.3]); ey2 = gaussmf(x, [0.5 -0.7]); ey3 = gaussmf(x, [0.5 0]); ey4 = gaussmf(x, [0.5 0.7]); ey5 = gaussmf(x, [0.5 1.3]); ey6 = gaussmf(x, [0.5 2]);

a=[ey0 ey1 ey2 ey3 ey4 ey5 ey6]; b=max(a);

% caculate input in fuzzy zone,get input_type and input_authorityvalue if x<=2 & x>=-2 if b==a(1) etype='NB'; eauthorityvalue=y0; elseif b==a(2) etype='NM'; eauthorityvalue=y1; elseif b==a(3) etype='NS';

eauthorityvalue=y2; elseif b==a(4) etype='ZE';

eauthorityvalue=y3;

elseif b==a(5) etype='PS';

eauthorityvalue=y4;

elseif b==a(6) etype='PM'; eauthorityvalue=y5; elseif b==a(7) etype='PB';

eauthorityvalue=y6; end else if x>2

etype='PB'; eauthorityvalue=1; elseif x<-2 etype='NB'; eauthorityvalue=1; end end etype eauthorityvalue % caculate output by

if type=='NB'& etype=='NB' out=authorityvalue*0.001;

% if input is NB and errorinput is NB, then output is NB; elseif type=='NB'& etype=='NM' out=authorityvalue*0.001;

% if input is NB and errorinput is NM, then output is NB; elseif type=='NB'& etype=='NS' out=authorityvalue*0.001;

% if input is NB and errorinput is NS, then output is NB; elseif type=='NB'& etype=='ZE' out=authorityvalue*1750;

% if input is NB and errorinput is ZE, then output is NM; elseif type=='NB'& etype=='PS' out=authorityvalue*1750;

% if input is NB and errorinput is PS, then output is NM; elseif type=='NB'& etype=='PM' out=authorityvalue*1750;

% if input is NB and errorinput is PM, then output is NM; elseif type=='NB'& etype=='PB' out=authorityvalue*3500;

% if input is NB and errorinput is PB, then output is NS; elseif type=='NM'& etype=='NB' out=authorityvalue*0.001;

% if input is NM and errorinput is NB, then output is NB; elseif type=='NM'& etype=='NM' out=authorityvalue*1750;

% if input is NM and errorinput is NM, then output is NM;

elseif type=='NM'& etype=='NS'

out=authorityvalue*1750;

% if input is NM and errorinput is NS, then output is NM;

elseif type=='NM'& etype=='ZE'

out=authorityvalue*1750;

% if input is NM and errorinput is ZE, then output is NM;

elseif type=='NM'& etype=='PS'

out=authorityvalue*1750;

% if input is NM and errorinput is PS, then output is NM;

elseif type=='NM'& etype=='PM'

out=authorityvalue*3500;

% if input is NM and errorinput is PM, then output is NS;

elseif type=='NM'& etype=='PB'

out=authorityvalue*3500;

% if input is NM and errorinput is PB, then output is NS;

elseif type=='NS'& etype=='NB'

out=authorityvalue*1750;

% if input is NS and errorinput is NB, then output is NM;

elseif type=='NS'& etype=='NM'

out=authorityvalue*3000;

% if input is NS and errorinput is NM, then output is NS;

elseif type=='NS'& etype=='NS'

out=authorityvalue*3000;

% if input is NS and errorinput is NS, then output is NS;

elseif type=='NS'& etype=='ZE'

out=authorityvalue*3000;

% if input is NS and errorinput is ZE, then output is NS;

elseif type=='NS'& etype=='PS'

out=authorityvalue*3000;

% if input is NS and errorinput is PS, then output is NS;

elseif type=='NS'& etype=='PM'

out=authorityvalue*5250;

% if input is NS and errorinput is PM, then output is ZE;

elseif type=='NS'& etype=='PB'

out=authorityvalue*5250;

% if input is NS and errorinput is PB, then output is ZE;

elseif type=='ZE'& etype=='NB'

out=authorityvalue*3500;

% if input is ZE and errorinput is NB, then output is NS;

elseif type=='ZE'& etype=='NM'

out=authorityvalue*5250;

% if input is ZE and errorinput is NM, then output is ZE;

elseif type=='ZE'& etype=='NS'

out=authorityvalue*5250;

% if input is ZE and errorinput is NS, then output is ZE;

elseif type=='ZE'& etype=='ZE'

out=authorityvalue*5250;

% if input is ZE and errorinput is ZE, then output is ZE;

elseif type=='ZE'& etype=='PS'

out=authorityvalue*5250;

% if input is ZE and errorinput is PS, then output is ZE;

elseif type=='ZE'& etype=='PM'

out=authorityvalue*7000;

% if input is ZE and errorinput is PM, then output is PS;

elseif type=='ZE'& etype=='PB'

out=authorityvalue*7000;

% if input is ZE and errorinput is PB, then output is PS;

elseif type=='PS'& etype=='NB'

out=authorityvalue*5250;

% if input is PS and errorinput is NB, then output is ZE;

elseif type=='PS'& etype=='NM'

out=authorityvalue*7000;

% if input is PS and errorinput is NM, then output is PS;

elseif type=='PS'& etype=='NS'

out=authorityvalue*7000;

% if input is PS and errorinput is NS, then output is PS;

elseif type=='PS'& etype=='ZE'

out=authorityvalue*7000;

% if input is PS and errorinput is ZE, then output is PS;

elseif type=='PS'& etype=='PS'

out=authorityvalue*7000;

% if input is PS and errorinput is PS, then output is PS;

elseif type=='PS'& etype=='PM'

out=authorityvalue*8750;

% if input is PS and errorinput is PM, then output is PM;

elseif type=='PS'& etype=='PB'

out=authorityvalue*8750;

% if input is PS and errorinput is PB, then output is PM;

elseif type=='PM'& etype=='NB'

out=authorityvalue*7000;

% if input is PM and errorinput is NB, then output is PS;

elseif type=='PM'& etype=='NM'

out=authorityvalue*7000;

% if input is PM and errorinput is NM, then output is PS;

elseif type=='PM'& etype=='NS'

out=authorityvalue*8750;

% if input is PM and errorinput is NS, then output is PM;

elseif type=='PM'& etype=='ZE'

out=authorityvalue*8750;

% if input is PM and errorinput is ZE, then output is PM;

elseif type=='PM'& etype=='PS'

out=authorityvalue*8750;

% if input is PM and errorinput is PS, then output is PM;

elseif type=='PM'& etype=='PM'

out=authorityvalue*8750;

% if input is PM and errorinput is PM, then output is PM;

elseif type=='PM'& etype=='PB'

out=authorityvalue*10500;

% if input is PM and errorinput is PB, then output is PB;

elseif type=='PB'& etype=='NB'

out=authorityvalue*7000;

% if input is PB and errorinput is NB, then output is PS;

elseif type=='PB'& etype=='NM'

out=authorityvalue*8750;

% if input is PB and errorinput is NM, then output is PM;

elseif type=='PB'& etype=='NS'

out=authorityvalue*8750;

% if input is PB and errorinput is NS, then output is PM;

elseif type=='PB'& etype=='ZE'

out=authorityvalue*8750;

% if input is PB and errorinput is ZE, then output is PM;

elseif type=='PB'& etype=='PS'

out=authorityvalue*10500;

% if input is PB and errorinput is PS, then output is PB;

elseif type=='PB'& etype=='PM'

out=authorityvalue*10500;

% if input is PB and errorinput is PM, then output is PB;

elseif type=='PB'& etype=='PB'

out=authorityvalue*10500;

% if input is PB and errorinput is PB, then output is PB;

end out 运行结果： type = PS

authorityvalue = 0.1353 etype = PB

eauthorityvalue = 1 out =

1.1842e+003 >>

控制系统仿真设计电气与控制工程学院测控技术与仪器0701 Xx xx

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