实验七控制系统的时域分析方法

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使用软件安装版一套（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Nyquist图和

2、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。(1) Gk(s)10(1s)(1 2s)(13s)Gk(s)10s(1s)(1 10s)Gk(s)10s2(10.1s)(10.2s)(4)Gk(s)102s (10.1s)(110s)2、设单位反馈系统的开环传递函数为Gk(s)=Ks2ss( 21)WnWn，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 ）禾9用step函数求单位阶跃响

3、应（3）利用gen sig函数产生方波信号，利用lsim函数求方波响应。13、已知系统传递函数 G （ s）s2 + 0.2s+1.01（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。z - 0 7一4、 一个离散时间系统模型传递函数为H （z），采样周期为0.1s，对其重新采样,z 0.5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,Pm

4、1,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(sys1) 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(sy

5、s4) 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) 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

6、/pole/gain:1.6667(s+1) (s+0.5) (s+0.3333)Zero/pole/gain:5s (s+1) (s+0.5)Zero/pole/gain:500sA2 (s+10) (s+5)Zero/pole/gain: sA2 (s+10) (s+0.1)Warning: The closed-loop system is unstable.> In D:MATLAB6p5toolboxcontrolcontrolltimargin.m at line 89In d:MATLAB6p5workUntitled2.m at line 6 Gm1 =1.0000Pm1

7、 =0Wg1 =1Wp1 =1Warning: The closed-loop system is unstable.> In D:MATLAB6p5toolboxcontrolcontrolltimargin.m at line 89 In d:MATLAB6p5workUntitled2.m at line 7Gm2 =0.1500Pm2 =-40.4477Wg2 =0.7071Wp2 =1.5927Warning: The closed-loop system is unstable.> In D:MATLAB6p5toolboxcontrolcontrolltimargin

8、.m at line 89In d:MATLAB6p5workUntitled2.m at line 8 Gm3 =InfPm3 =-46.0756Wg3 =NaNWp3 =2.8848Warning: The closed-loop system is unstable.> In D:MATLAB6p5toolboxcontrolcontrolltimargin.m at line 89In d:MATLAB6p5workUntitled2.m at line 9 Gm4 =InfPm4 =-83.5723Wg4 =NaNWp4 =0.58162wn=90,xi=0.2den=1/w

9、n2 2*xi/w n 1 0for k=1:0.5:40num=ksys=tf(num,den) Gm,Pm,Wcg,Wcp=margin(sys) if (Wcg>=Wcp)kGmPmWcgWcpelseif (Wcg=Wcp)kGmPmWcgWcpelseif (Wcg<=Wcp)kGmPmWcgWcpendend3g1=0.5g2=tf(2,0,2,1) g3=zpk(,0,-2,1); g4=parallel(g1,-g2);sys=g3*g4 step(sys,50) gm,pm,wcg,wcp=margin(sys) Zero/pole/gain:-0.5 (s-0.

10、5) s (s+2) (s+0.5) gm =1.6667pm =30.1549 wcg =0.4082 wcp =0.2481 wcp =0.2481Real Axis;te?u：n：YFret|jercy (radfcec)u J0Real AxisFrequency (radfsec)RealAxisFrecy (radfcec)耐恥 x10()Figure Ro. 4File Edit Viw Insert Tools Vindw HelpU7/ 00?卜%开船/ I?驭两IL.勺D：P飞川仃!i.丿E:.曲八卜2佬1仙J LTI TieferJilf Hit 山伽 Hdf6S10Hi

11、m M14161B2D-.Ld3O1VCT*T/血Pnp-QUJVAu-o-£JBode tarn-EOrop) c-x-te匚Estrg1ja.u74. nA-u -u 勺p】UMflxn-io1ioJio'1LTI Viewery.wtAB'J L.H7LKB5p5. . J PifUT4 Id 1Gs=zpk(,0,-1,10) Gz1=c2d(Gs,0 01,'zoh')Gz2=c2d(Gs,1,'zoh')figure(1) subplot(2,2,1),bode(Gz1) subplot(2,2,2),nyquist(Gz1

12、) 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:0.00049834 (z

13、+0.9967)(z-1) (z-0.99)Sampling time: 0.01Zero/pole/gain:3.6788 (z+0.7183) (z-1) (z-0.3679)Sampling time: 1Zero/pole/gain:0.00049834 (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: 1 num1 =0.49670.98962.6424-0.95331.0e-003 * 0 0.4983 den1 =1.0000 -1.9905 Ts = 0.0100 num2 = 0 3.6788 den2 =1.0000 -3.2073 Ts = 1J Fwrc up'Ei IE:?&”'*04'?= DR-R助” A、w o到X