MATLAB控制系统仿真

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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) T=0.1s 3 s +4s + 2 =3 2 2 3 s (s - 2)[( s 1) 2s 5]  2 z +0.568 H (z) 厂 (z _1)( z _0.2z +0.99) >> s=tf(s); G=(sA3+4*s+2)/(sA3*(sA2+2)*((sA2+1)A3+2*s+5)); G Transfer function: sA3 + 4 s + 2 sA11 + 5 sA9 + 9 sA7 + 2 sA6 + 1

2、2 sA5 + 4 sA4 + 12 sA3 >> num=[1 0 0.56]; den=conv([1 -1],[1 -0.2 0.99]); H=tf(num,den,Ts,0.1) Transfer function: zA2 + 0.56 zA3 - 1.2 zA2 + 1.19 z - 0.99 2.请将下面的零极点模型输入到 8(s +1 + j)(s +1 — j) G(s) 2 2 s (s +5)( s +6)( s +1) matlab环境。请求出上述模型的零极点，并绘制其位置。 H (z) (z」• 3.2)( z」• 2.6) z

3、^(z」—8.2) T=0.05s >>Z=[-1-j -1+j]; p=[0 0 -5 -6 -j j]; G=zpk(z,p,8) Zero/pole/gain: 8 (sA2 + 2s + 2) Pcle-Zerq Myp i 1 1 1— 1 e k 0.8 - - 1 0.8 0.6 sA2 (s+5) (s+6) (sA2 + 1) >>pzmap(G) 2 o. 4 -O. >> z=[0 0 0 0 0 -1/3.2 -1/2.6]; P=[1/8.2]; H=zpk(z,p,1,Ts,0.05) ■D6 -0.8 -1 Po

4、le-Zero Map -1 卫田 -0 6 -0 4 JO.2 0 0.2 0.4 0.S 00 Reai Axis Zero/pole/gain: zA5 (z+0.3125) (z+0.3846) (z-0.122) Sampling time: 0.05 >>pzmap (H) 线性系统分析 1 1 1. 请分析下面

5、传递函数模型的稳定性。 1 1 1 G(S)「2s2*2 G(s) 3s 1 2 2 s (300 s 600 s 50) ■ 3s 1 1 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]; Pole-Zero Map .5 o- -D D5 o. 5 o

6、. -O >」启 SEE- den=[300 600 50 3 1]; 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。 「3z 2 W—.25Z55) H (z) 2.12z^ +11 .76 z 丄 +15 .91 z 乂 -7.368 z 、一20.15 z - 102 .4z • 80 .39 z一340 ) >> num=[-3 2]; den

7、=[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。 4 Pote-Zero Map i i i ■ i 0.3 - / ■ J - 0-6 - Z X = I / I 0.4 f ~ r 1 % J h f 1

8、 0.2 F i 1" 1 a ； V _ - -0.2 1 L ■ -0.4 ■fc •B L * f J h f ■■ -0.8 ■ % ■h. 尹* ■ ->-0.3 - 、、 : - : ”* -1 -1 ■ f 1 1 J "If M」-1 ■■尸十八 1 1 ■ -0.8 -O.e 4).4 4左 0 0.2

9、0.4 0.6 O.B 1 ft&al Axis >> 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 = 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

10、 -0.5292 0.5292 -0.2716 0.2716 1 2 Real AJ(is D- Q Q2KV AJeularaf 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 18 s7 +514 s 6 +5982 s5 +36380 s" +122664 s3 + 222088 s 2 +185760 s + 40320 G(s) = ~8 7 6 5 4 3 2 s +36 s +546 s +4536 s +

11、22449 s + 67284 s +118124 s +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 40320]; G=tf(num,den) Transfer function: 18 sA7 + 514 sA6 + 5982 sA5 + 36380 sA4 + 122664 sA3 + 22088 sA2 + 185760 s +

12、40320 sA8 + 36 sA7 + 546 sA6 + 4536 sA5 + 22449 sA4 + 67284 sA3 + 118124 sA2 + 109584 s + 40320 >> step(G,10) >> impulse(G,10) 单位阶跃响应: 1 g y B _ime i sec. Step Response 单位脉冲响应: Impure Rfr&pflnse S 6 7 S 9 1C Time is&c)

13、 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。 1 G(S) 3 T~ s +2s +s +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: 2.请分析下面离散系统的脉冲响应。 3s3 +4s2 +1 G (s) 2 厂 s (300 s +600 s +50 ) +3s +1 利用Simulink建模，建立系统仿真模型如下:

14、 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: s + 3 G（S）「7s2”2 利用Simulink建模，建立系统仿真模型如下: A 5*3 —r s3+7$2+35+2 Z.&ri>OrdeF Hold T rsnsfer Fdh H Soc-p< 单击启动仿真按钮，双击示波器得到系统的阶跃响应如下: Time offset: 0 4.设计控制器，使得下列系统

15、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: 25 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。 1 G(

16、s) L 未连入PID控制器时的系统仿真及其性能指标如下: 08 0.6 0.4 0.2 0 0 5 10 15 20 可见，未调节时的系统性能有待提高，需设计 rime off-set： 0 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

17、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 = 2.6400 2.8387 1.5262 den = 1 0 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，未调节时的系统性能有待提高，需设计 PID控制器连入。 可见，未调节时的系统性能有

18、待提高，需设计 PID控制器连入。 可见，加入PID控制器调节后，系统性能明显改善。 5 （S 1） 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。 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 1 倍1叶阳叶加■ 1 Zerc-Pale E SqC-C- 1 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 2 4 Step Response 10 Time (sec)

19、 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

20、 = 1 0 Kp = 2.4000 Ti = 6.8000 Td = 1.7000 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 2 4 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 2 4 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 2 4 可见，加入PID控制器调节后，系统性能明显改善。 -1.5s +1 G(s) - (s+1) 利用Simulink建

21、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。 2 4 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 2 4 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 2 4 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=

22、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 0 Kp = 3.8000 Ti = 3.6000 Td = 0.9000 可见，未调节时的系统性能有待提高，需设计 PID控制器连入。 0 20 40 60 Time offset 0 80 100

23、 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 ~2 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； 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

24、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 i

25、nput 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 out

26、put 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 error

27、input 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

28、 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 out

29、put 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 errori

30、nput 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 i

31、nput 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 outpu

32、t 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 errorin

33、put 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 in

34、put 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(x

35、1, [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]);

36、 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

37、= 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; e

38、lseif 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;

39、 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 = ga

40、ussmf(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

41、 ; 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 ; eauthorit

42、yvalue=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

43、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

44、 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 ou

45、t=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 o

46、utput 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;

47、% 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

48、== 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 errori

49、nput 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=authori

50、tyvalue*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;

51、 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 Z

52、E 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

53、 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 o

54、utput 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; %

55、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

56、 & 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

57、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=authorityval

58、ue*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; els

59、eif 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 a

60、nd 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