1γ=50 20-=sK0原系统的伯德图：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 s^4 + 1.6046 s^3 + 3.4031 s^2 + 2 salpha =6.1261;P h a s e (d e g )Bode DiagramGm = Inf dB (at Inf rad/sec) , P m = 9.04 deg (at 3.14 rad/sec)-20020406080M a g n i t u d e (d B )[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); printsys(numc,denc)disp('УÕýÖ®ºóµÄϵͳ¿ª»·´«µÝº¯ÊýΪ:');printsys(num,den) [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('·ùÖµ(db)'); title('--Go,-Gc,GoGc'); subplot(2,1,2);semilogx(w,phase,w,phase1,'--',w,phase2,'-',w,(w-180-w),':'); grid; ylabel('Ïàλ(0)'); xlabel('ƵÂÊ(rad/sec)');title(['УÕýÇ°£º·ùÖµÔ£Á¿=',num2str(20*log10(gm1)),'db','ÏàλԣÁ¿=',num2str(pm1),'0';'УÕýºó£º·ùÖµÔ£Á¿=',num2str(20*log10(gm)),'db','ÏàλԣÁ¿=',num2s tr(pm),'0']);10-110101102-60-40-2002040幅值(d b )--Go,-Gc,GoGc10-110101102-300-200-1000100相位(0)频率(rad/sec)矫正后系统的伯德图矫正之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。
2．某单位负反馈控制系统的开环传递函数为3)1()(+=s ks G ，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045。
原系统的伯德图： ans =0.3200 -30.0045 1.7322 2.7477num0=25; den0=conv([1,1],conv([1,1],[1,1])); w=logspace(-1,1.2);[gm1,pm1,wcg1,wcp1]=margin(num0,den0); [mag1,phase1]=bode(num0,den0,w); [gm1,pm1,wcg1,wcp1]margin(num0,den0) grid;由此可以看出，相位裕量小于0，系统不稳定。
-40-202040M a g n i t u d e (d B )101010-270-180-90P h a s e (d e g )Bode DiagramGm = -9.9 dB (at 1.73 rad/sec) , P m = -30 deg (at 2.75 rad/sec)Frequency (rad/sec)num0=25; den0=conv([1,0],conv([1,0],[1,0])); w=logspace(-1,1.2); [gm1,pm1,wcg1,wcp1]=margin(num0,den0); [mag1,phase1]=bode(num0,den0,w); [gm1,pm1,wcg1,wcp1]margin(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(num,den);printsys(numc,denc)disp('УÕýÖ®ºóµÄϵͳ¿ª»·´«µÝº¯ÊýΪ:'printsys(num,den) [mag2,phase2]=bode(numc,denc,w);[mag,phase]=bode(num,den,w);),'-.');grid; ylabel('·ùÖµ(db)'); title('--Go,-Gc,GoGc');subplot(2,1,2); semilogx(w,phase,w,phase1,'--',w,phase2,'-',w,(w-180-w),':'); grid; ylabel('Ïàλ(0)'); xlabel('ƵÂÊ(rad/sec)');title(['УÕýÇ°£º·ùÖµÔ£Á¿=',num2str(20*log10(gm1)),'db','ÏàλԣÁ¿=',num2str(pm 1),'0';'УÕýºó£º·ùÖµÔ£Á¿=',num2str(20*log10(gm)),'db','ÏàλԣÁ¿=',num2str(pm),'0']);101010102-150-100-50050100幅值(d b )--Go,-Gc,GoGc101010102-200-100100相位(0)频率(rad/sec)矫正后系的伯德图统矫正前系统的单位阶跃响应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)2)(1()(++=s s s Ks G ，试设计一滞后-超前校正装置，使校正后系统的静态速度误差系数110-=s K v ，相位裕量050=γ，增益裕量dB K g 10lg 20≥。
原系统伯德图及程序：-150-100-5050M a g n i t u d e (d B )10101010-270-225-180-135-90P h a s e (d e g )Bode DiagramGm = 1.58 dB (at 1.41 rad/sec) , P m = 5.02 deg (at 1.29 rad/sec)Frequency (rad/sec)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,wcp1]margin(num0,den0) grid; ans =1.2000 5.0239 1.4142 1.2885系统稳定裕量过小，临界稳定。