MATLAB控制系统仿真计算

1、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。G(s)s3 4s 2s3(s2 2)(s2 1)3 2s 5H(z)2z 0.568(z 1)(z20.2z 0.99)T=0.1s s=tf(s);G=(sA3+4*s+2)/(sA3*(sA2+2)*(sA2+1)A3+2*s+5);GTransfer function:sA3 + 4 s + 2sA11 + 5 sA9 + 9 sA7 + 2 sA6 + 12 sA5 + 4 sA4 + 12 sA3 num=1 0 0.56;den=conv(1 -1,1 -0.2 0.99);H=tf(num,den,Ts,0.

2、1)Transfer function:zA2 + 0.56zA3 - 1.2 zA2 + 1.19 z - 0.992.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。G(s)8(s 1 j)(s 1 j)2 2s (s 5)(s 6)(s1)H(z)(z 13.2)(z 12.6)z 5(z 18.2)T=0.05sZ=-1-j -1+j; p=0 0 -5 -6 -j j;G=zpk(z,p,8)Zero/pole/gain:8 (sA2 + 2s + 2)sA2 (s+5) (s+6) (sA2 + 1)pzmap(G)1 f1t r9M0.8 - -

3、10.00.6Ci.4 z=0 0 0 0 0 -1/3.2 -1/2.6; p=1/8.2;H=zpk(z,p,1,Ts,0.05)pzmap (H)线性系统分析1. 请分析下面传递函数模型的稳定性。G(s)13-2s 2s s 2G(s)3s 122s (300s600s 50) 3s 1ans =FF=J num=1; den=1 2 1 2; G=tf(num,den); eig(G)-2.00000.0000 - 1.0000i0.0000 + 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

4、 3 1;G=tf(num,den); eig(G)ans =-1.9152-0.14140.0283 - 0.1073i0.0283 + 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。3z 2(z30.2z20.25z 0.05)H(z)2.12z211.76Z115.91z 57.368z 420.15z 3102.4z 280.39z 1 340) num=-3 2;den=1 -0.2 -0.25 0.05;H=tf(num,den,Ts,0.1);eig(H) abs(eig(H) ans =-0.50000.50000.50000

5、.50000.2000 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*zA-2+11.76*zA- 1+15.91)/(zA-5-7.368*zA-4-20.15*zA-3+102.4*zA-2+80.39*z-1-340);eig(H) abs(eig(H)ans =0000000000000000000000004.17244.17240.3755 + 0.1814i0.41700.3755 - 0.1814i0.4170-0.52920.5292-0.27160.27160.11930.1193Rcol勾询可

6、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G(s)18 s7514 s65982 s536380 s4 122664 s3222088 s2185760 s 40320s836 s7546 s6 4536 s522449 s4 67284 s3118124 s2 109584 s 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 122664 22088 185760 40320; den=1 36 546 4536 22449 67284 118124 109584

7、 40320; G=tf(num,den)Transfer function:18 sA7 + 514 sA6 + 5982 sA5 + 36380 sA4 + 122664 sA3 + 22088 sA2 + 185760 s + 40320sA8 + 36 sA7 + 546 sA6 + 4536 sA5 + 22449 sA4 + 67284 sA3 + 118124 sA2 + 109584 s + 40320 step(G10) impulse(G,10)单位阶跃响应:Time (&ecj单位脉冲响应: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)1s3

8、 2s2 s 2利用Simulink建模，建立系统仿真模型如下:11?o- Tjsr jf Fai1rStep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。G(s)3s34 s21 s2 (300s2600s 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，并求出其阶跃响应其中：G(s)s 3厂s 7s 3s 2利用Simulink建模，建立系统仿真模型如下:Step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(s 1)

9、(s 2.3)G(s)(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:Hs+2.釘倍加那* 2)StPJIL25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。未连入PID控制器时的系统仿真及其性能指标如下:1asil0.201015Tirnc offset 0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;de

10、n=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=1.86T=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 =2.64002.83871.5262den =1 0Kp =2.8387Ti =3.7200Td =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P

11、ID控制器调节后，系统性能明显改善。G(s)未连入PID控制器时的系统仿真及其性能指标如下:输入： num=1;Trre fstc1den=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=3.4T=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 =4.08002.40000.7059den =1 0Kp

12、 =2.4000Ti =6.8000Td =1.70000 ID 2030405080Tim色 offsM: 0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: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=1.8T=5.7IDpn 七Q.IW-020/UTime (sec)利用自定义的 Ziegler_std函数求出Kp、Ti、Td输入: K=1;L=1.8T=5

13、.7;num,den,Kp,Ti,Td=Ziegler_std (3,K,L ,T)得出：num =3.42003.80002.1111den =1 0Kp =3.8000Ti =3.6000Td =0.9000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 C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 2C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

14、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：010500转/分。控制规则：%if input is NB and errorinput is NB, then output isNB;%if input is NB and errorinput is NM, then output isNB;%if input is NB and errorinput is NS, then output isNB;%i

15、f input is NB and errorinput is ZE, then output isNM;%if input is NB and errorinput is PS, then output isNM;%if input is NB and errorinput is PM, then output isNM;%if input is NB and errorinput is PB, then output isNS;%if input is NM and errorinput is NB, then output isNB;%if input is NM and errorin

16、put is NM, then output isNM;%if input is NM and errorinput is NS, then output isNM;%if input is NM and errorinput is ZE, then output isNM;%if input is NM and errorinput is PS, then output isNM;%if input is NM and errorinput is PM, then output isNS;%if input is NM and errorinput is PB, then output is

17、NS;%if input is NS and errorinput is NB, then output isNM;%if input is NS and errorinput is NM, then output isNS;%if input is NS and errorinput is NS, then output isNS;%if input is NS and errorinput is ZE, then output isNS;%if input is NS and errorinput is PS, then output isNS;%if input is NS and er

18、rorinput is PM, then output isZE;%if input is NS and errorinput is PB, then output isZE;%if input is ZE and errorinput is NB, then output isNS;%if input is ZE and errorinput is NM, then output isZE;%if input is ZE and errorinput is NS, then output isZE;%if input is ZE and errorinput is ZE, then outp

19、ut isZE;%if input is ZE and errorinput is PS, then output isZE;%if input is ZE and errorinput is PM, then output isPS;%if input is ZE and errorinput is PB, then output isPS;%if input is PS and errorinput is NB, then output isZE;%if input is PS and errorinput is NM, then output isPS;%if input is PS a

20、nd errorinput is NS, then output isPS;%if input is PS and errorinput is ZE, then output isPS;%if input is PS and errorinput is PS, then output isPS;%if input is PS and errorinput is PM, then output isPM;%if input is PS and errorinput is PB, then output isPM;%if input is PM and errorinput is NB, then

21、 output isPS;%if input is PM and errorinput is NM, then output isPS;%if input is PM and errorinput is NS, then output isPM;%if input is PM and errorinput is ZE, then output isPM;%if input is PM and errorinput is PS, then output isPM;%if input is PM and errorinput is PM, then output isPM;%if input is

22、 PM and errorinput is PB, then output isPB;%if input is PB and errorinput is NB, then output isPS;%if input is PB and errorinput is NM, then output isPM;%if input is PB and errorinput is NS, then output isPM;%if input is PB and errorinput is ZE, then output isPM;%if input is PB and errorinput is PS,

23、 then output isPB;%if input is PB and errorinput is PM, then output isPB;%if input is PB and errorinput is PB, then output isPB;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 =

24、 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;

25、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=18if b=a(1)type=NB ;authorityvalue=y0;elseifb=a(2)type=NM ;authorityvalue=y1;elseifb=a(3)type=NS ;authorityvalue=y2;elseifb=a(4)type=ZE ;authorityvalue=y3;elseifb=a(5)type=PS ;authorityvalue=y4;els