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1、实验七 控制系统频域分析方法1.实验目的 （1）熟练掌握Nyquist图和Bode图的绘制。（2）熟练掌握利用Nyquist图和Bode图分析系统的性能。2.实验仪器 （1）Matlab6.5应用软件安装版 一套 （3）PC机 一台3. 实验原理 依据MATLAB的建模指令，利用MATLAB对系统仿真，分析系统的频率特性。4. 实验步骤 （1）建立系统的MATLAB模型，绘制系统Nyquist图和Bode图，分析系统稳定性（2）求系统的幅值穿越频率和相位穿越频率，分析系统的稳定性。（3）依据系统框图建立系统模型，利用LTI Viewer分析系统的稳定性。（4）绘制离散系统开环传递函数的Nyqu
2、ist图和Bode图，绘制系统单位阶跃响应图。5. 实验报告内容1、绘制下列各单位反馈系统开环传递函数的Bode图和Nyquist图，并根据其稳定裕度判断系统的稳定性。2、设单位反馈系统的开环传递函数为，其中无阻尼固有频率Wn=90rad/s，阻尼比=0.2，试确定是系统稳定的K的范围。（1）利用MATLAB模型链接函数求出系统闭环传递函数。（2）利用step函数求单位阶跃响应（3）利用gensig函数产生方波信号，利用lsim函数求方波响应。3、已知系统传递函数：（1）绘制系统阶跃响应曲线（2）绘出离散化系统阶跃响应曲线，采样周期Ts=0.3s。4、一个离散时间系统模型传递函数为，采样周期为
3、0.1s，对其重新采样，采样周期为0.05s，求重新采样后的系统模型。1sys1=zpk(,-1,-1/2,-1/3,10/6)sys2=zpk(,0,-1,-1/2,5)sys3=zpk(,0,0,-10,-5,500)sys4=zpk(,0,0,-10,-0.1,2)Gm1,Pm1,Wg1,Wp1=margin(sys1)Gm2,Pm2,Wg2,Wp2=margin(sys2)Gm3,Pm3,Wg3,Wp3=margin(sys3)Gm4,Pm4,Wg4,Wp4=margin(sys4)(1)subplot(2,4,1),bode(sys1)subplot(2,4,2),nyquist(s
4、ys1)subplot(2,4,3),bode(sys2)subplot(2,4,4),nyquist(sys2)subplot(2,4,5),bode(sys3)subplot(2,4,6),nyquist(sys3)subplot(2,4,7),bode(sys4)subplot(2,4,8),nyquist(sys4) (2)figure(1)subplot(1,2,1),bode(sys1)subplot(1,2,2),nyquist(sys1)figure(2)subplot(1,2,1),bode(sys2)subplot(1,2,2),nyquist(sys2)figure(3)
5、subplot(1,2,1),bode(sys3)subplot(1,2,2),nyquist(sys3)figure(4)subplot(1,2,1),bode(sys4)subplot(1,2,2),nyquist(sys4)Zero/pole/gain: 1.6667-(s+1) (s+0.5) (s+0.3333) Zero/pole/gain: 5-s (s+1) (s+0.5) Zero/pole/gain: 500-s2 (s+10) (s+5) Zero/pole/gain: 2-s2 (s+10) (s+0.1) Warning: The closed-loop system
6、 is unstable. In D:MATLAB6p5toolboxcontrolcontrolltimargin.m at line 89 In d:MATLAB6p5workUntitled2.m at line 6Gm1 = 1.0000Pm1 = 0Wg1 = 1Wp1 = 1Warning: The closed-loop system is unstable. In D:MATLAB6p5toolboxcontrolcontrolltimargin.m at line 89 In d:MATLAB6p5workUntitled2.m at line 7Gm2 = 0.1500Pm
7、2 = -40.4477Wg2 = 0.7071Wp2 = 1.5927Warning: The closed-loop system is unstable. In D:MATLAB6p5toolboxcontrolcontrolltimargin.m at line 89 In d:MATLAB6p5workUntitled2.m at line 8Gm3 = InfPm3 = -46.0756Wg3 = NaNWp3 = 2.8848Warning: The closed-loop system is unstable. In D:MATLAB6p5toolboxcontrolcontr
8、olltimargin.m at line 89 In d:MATLAB6p5workUntitled2.m at line 9Gm4 = InfPm4 = -83.5723Wg4 = NaNWp4 = 0.58162wn=90,xi=0.2den=1/wn2 2*xi/wn 1 0for k=1:0.5:40num=ksys=tf(num,den)Gm,Pm,Wcg,Wcp=margin(sys)if (Wcg=Wcp) k Gm Pm Wcg Wcpelseif (Wcg=Wcp) k Gm Pm Wcg Wcpelseif (Wcg=Wcp) k Gm Pm Wcg Wcp endend
9、3g1=0.5g2=tf(2,0,2,1)g3=zpk(,0,-2,1);g4=parallel(g1,-g2);sys=g3*g4step(sys,50)gm,pm,wcg,wcp=margin(sys)Zero/pole/gain: -0.5 (s-0.5)-s (s+2) (s+0.5) gm = 1.6667pm = 30.1549wcg = 0.4082wcp = 0.2481wcp =0.2481Gs=zpk(,0,-1,10)Gz1=c2d(Gs,0.01,zoh)Gz2=c2d(Gs,1,zoh)figure(1)subplot(2,2,1),bode(Gz1)subplot(
10、2,2,2),nyquist(Gz1)subplot(2,2,3),bode(Gz2)subplot(2,2,4),nyquist(Gz2)Gb1=feedback(Gz1,1,1)Gb2=feedback(Gz2,1,2)num1,den1,Ts=tfdata(Gb1,v)num2,den2,Ts=tfdata(Gb2,v)figure(2)subplot(1,2,1),dstep(num1,den1)subplot(1,2,2),dstep(num2,den2)Zero/pole/gain: 10-s (s+1) Zero/pole/gain:0. (z+0.9967)- (z-1) (z
11、-0.99) Sampling time: 0.01 Zero/pole/gain:3.6788 (z+0.7183)-(z-1) (z-0.3679) Sampling time: 1 Zero/pole/gain:0. (z+0.9967)-(z-1.027) (z-0.9634) Sampling time: 0.01 Zero/pole/gain: 3.6788 (z+0.7183)-(z+0.2739) (z-3.481) Sampling time: 1num1 = 1.0e-003 * 0 0.4983 0.4967den1 =1.0000 -1.9905 0.9896Ts = 0.0100num2 = 0 3.6788 2.6424den2 =1.0000 -3.2073 -0.9533Ts = 1