线性系统的频域分析MATLAB实验

1、.工程大学实验报告专业班号组别指导教师艳菲同组者实验名称线性系统的频域分析实验日期第次实验一、实验目的二、实验容三、实验结果及分析四、实验心得与体会一、实验目的1熟练掌握用 MATLAB语句绘制频域曲线。2掌握控制系统频域围的分析校正方法。3掌握用频率特性法进行串联校正设计的思路和步骤。二，实验容。1某单位负反馈控制系统的开环传递函数4为，试设计一超前校正装置，G (s)1)s( sK v20s 1500使 校正后系统的静态速度误差系数，相位裕量，增益裕量20 lg K g10dB绘制伯德图程序，以及计算穿越频率，相位裕量ans =相位Inf9.0406频率Inf3.1425> e=5;

2、 r=50; r0=9;gm1,pm1,wcg1,wcp1=margin(num0,den0);>> phic=(r-r0+e)*pi/180;gm1,pm1,wcg1,wcp1=margin(num0,den0);>> alpha=(1+sin(phic)/(1-sin(phic)gm1,pm1,wcg1,wcp1=margin(num0,den0); alpha =6.1261 gm1,pm1,wcg1,wcp1=margin(num0,den0);gm1,pm1,wcg1,wcp1 num0=20; den0=2,1,0; w=0.1:1000;margin(nu

3、m0,den0) grid;专业技术资料.原系统的伯德图：80)60Bd(40edutin20gaM0-20-90)ged(e -135s a hP-180-210Bode DiagramGm = Inf dB (at Inf rad/sec) , Pm = 9.04 deg (at 3.14 rad/sec)System: untitled1Frequency (rad/sec): 2.97Magnitude (dB): 0.95System: untitled1-10110Frequency (rad/sec):10 3.1310FrequencyPhase (deg): -171(rad

4、/sec)num/den =1.2347 s + 1-0.20154 s + 1校正之后的系统开环传递函数为:num/den =6.1734 s + 5-0.20154 s4 + 1.6046 s3 + 3.4031 s2 + 2 salpha =6.1261;专业技术资料.il,ii=min(abs(mag1-1/sqrt(alpha);wc=w( ii); T=1/(wc*sqrt(alpha);numc=alpha*T,1; denc=T,1;num,den=series(num0,den0,numc,denc);gm,pm,wcg,wcp=margin(num,den);printsy

5、s(numc,denc)disp( 'D ?y?oó ?í 3?a?· ?Yo:'ê);printsys(num,den)y?a mag2,phase2=bode(numc,denc,w); mag,phase=bode(num,den,w);subplot(2,1,1);semilogx(w,20*log10(mag),w,20*log10(mag1), '-' ,w,20*log10(mag2 ), '-.' );grid;ylabel(' ·ù ?(db)');ti

6、tle('-Go,-Gc,GoGc');subplot(2,1,2);semilogx(w,phase,w,phase1,'-',w,phase2, '-',w,(w-180-w),':');grid;ylabel('? à?(0)' ); xlabel('? ?ê(rad/sec)' );title('D ?y?° o·ù ?,num2str(20*log10(gm1),á?=''db' , '?

7、à?á ?=',num2str(pm1),'0' ;'D ?yoó o·ù ?,num2str(20*log10(gm),á?=''db' , '? à?á ?=',num2str(pm), '0' );-Go,-Gc,GoGc4020)bd0(值-20幅-40-60 -1012101010101000)0(位 -100相-200-300 -110012101010频 率 (rad/sec)矫正后系统的伯德图专业技术资料.矫正之

8、前系统单位阶跃响应矫正之后系统的单位阶跃响应：比较矫正前后系统的响应情况： 可以看出超前矫正使系统的调节时间变短， 响应更加迅速，但是超调量偏大，对改善系统的动态性能起到了巨大的作用。k2某单位负反馈控制系统的开环传递函数为G( s)( s1)3 ，试设计一个合适的滞后校正网络，使系统阶跃响应的稳态误差约为0.04 ，相角裕量约为 450 。原系统的伯德图：ans =专业技术资料.0.3200 -30.00451.73222.7477num0=25; den0=conv(1,1,conv(1,1,1,1); w=logspace(-1,1.2); gm1,pm1,wcg1,wcp1=margi

9、n(num0,den0); mag1,phase1=bode(num0,den0,w);gm1,pm1,wcg1,wcp1margin(num0,den0)grid;由此可以看出，相位裕量小于0，系统不稳定。)Bd(edtuingaM)ged(esahPBode DiagramGm = -9.9 dB (at 1.73 rad/sec) , Pm = -30 deg (at 2.75 rad/sec)40200-20-400-90-180-270-101101010Frequency (rad/sec)num0=25; den0=conv(1,0,conv(1,0,1,0); w=logspa

10、ce(-1,1.2); gm1,pm1,wcg1,wcp1=margin(num0,den0); mag1,phase1=bode(num0,den0,w);gm1,pm1,wcg1,wcp1margin(num0,den0)grid;e=10; r=45; r0=pm1;phi=(-180+r+e);il,ii=min(abs(phase1-phi);wc=w( ii); beit=mag1(ii); T=10/wc; numc= T,1; denc= beit*T,1; num,den=series(num0,den0,numc,denc); gm,pm,wcg,wcp=margin(nu

11、m,den);printsys(numc,denc)disp('D ?y?oó ?í 3?a?· ?Yoêprintsys(num,den)y?a:'mag2,phase2=bode(numc,denc,w);mag,phase=bode(num,den,w);subplot(2,1,1);semilogx(w,20*log10(mag),w,20*log10(mag1),'-',w,20*log10(mag2), '-.' );grid;ylabel(' ·ù ?(db)

12、9;); title('-Go,-Gc,GoGc' );subplot(2,1,2);semilogx(w,phase,w,phase1,'-' ,w,phase2,'-',w,(w-180-w), ':' );专业技术资料.grid;ylabel('? à?(0)' ); xlabel('? ?ê(rad/sec)');title('D ?y?° o·ù ?á,num2str(20*log10(gm1),?=''d

13、b', '? à?á ?=',num2str(pm1),'0''D ?yoó o·ù ?,num2str(20*log10(gm),á?=''db', '? à?á ?=',num2str(pm),'0');-Go,-Gc,GoGc10050)bd0(值-50幅-100-15010100)00(位相 -100-200 10-1012101010-1012101010频 率 (rad/sec)矫正后系的伯德图统矫正

14、前系统的单位阶跃响应专业技术资料.矫正后系统的单位阶跃响应由矫正前后系统的单位阶跃响应比较可以看出，系统进过矫正之后由不稳定变为稳定。3某单位负反馈控制系统的开环传递函数为K，试设计一滞后 - 超G (s)s(s 1)(s 2)前校正装置，使校正后系统的静态速度误差系数K v 10s 1 ，相位裕量500 ，增益裕量20 lg K g 10dB 。原系统伯德图及程序：)Bd(edutingaM)ged(esahPBode DiagramGm= 1.58 dB (at 1.41 rad/sec) , Pm = 5.02 deg (at 1.29 rad/sec)500-50-100-150-90

15、-135-180-225-270-101210101010Frequency(rad/sec)专业技术资料.程序： num0=5;den0=conv(1,0,conv(1,1,1,2); w=logspace(-1,1.2);gm1,pm1,wcg1,wcp1=margin(num0,den0);mag1,phase1=bode(num0,den0,w);gm1,pm1,wcg1,wcp1margin(num0,den0)grid;ans =1.20005.02391.41421.2885系统稳定裕量过小，临界稳定。-Go,-Gc,GoGc50)0bd(值幅 -50-100-101210101

16、010校 正 后 ： 幅 值 裕 量 =24.4406db相 位 裕 量 =71.58701000)0(位 -100相-200-300 -101210101010频 率 (rad/sec)矫正后系统伯德图矫正程序及结果：num/den =14.9975 s2 + 9.1921 s + 1-14.9975 s2 + 70.9235 s + 1校正之后的系统开环传递函数为:专业技术资料.num/den =74.9877 s2 + 45.9604 s + 5-14.9975 s5 + 115.916 s4 + 243.7654 s3 + 144.8469 s2 + 2 swc=1.4142; bei

17、t=10; T2=10/wc;lw=20*log10(w/1.58)-9.12;il,ii=min(abs(lw+20);w1=w(ii);numc1=1/w1,1;denc1=1/ (beit*w1),1;numc2= T2,1;denc2= beit*T2,1;numc,denc=series(numc1,denc1,numc2,denc2);num,den=series(num0,den0,numc,denc);printsys(numc,denc)disp('D ?y?oó ?í 3?a?· ?Yoê); y?a:'printsy

18、s(num,den)mag2,phase2=bode(numc,denc,w);mag,phase=bode(num,den,w);gm,pm,wcg,wcp=margin(num,den);subplot(2,1,1);semilogx(w,20*log10(mag),w,20*log10(mag1),'-',w,20*log10(mag2),'-.');grid;ylabel(' ·ù ?(db)'); title('-Go,-Gc,GoGc' );subplot(2,1,2);semilogx(w,phase,w,phase1,'-' ,w,phase2, '-',w,(w-180-w), ':' );grid;ylabel('? à?(0)' ); xlabel('? ?ê(rad/sec)');title('D ?yoó o·ù ?,num2str(20*log10(gm),?='á'd