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Design & Compensation via Root Locus

Design & Compensation via Root Locus. imtiaz.hussain@faculty.muet.edu.pk. Contents. Compensation Lead Compensation Lag Compensation Lag-Lead Compensation. Compensator. Plant. G. (. S. ). G. (. S. ). c. -. H. (. S. ). Compensation .

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Design & Compensation via Root Locus

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  1. Design & Compensation via Root Locus imtiaz.hussain@faculty.muet.edu.pk

  2. Contents • Compensation • Lead Compensation • Lag Compensation • Lag-Lead Compensation

  3. Compensator Plant G ( S ) G ( S ) c - H ( S ) Compensation • Used to Improve the performance of stable or unstable systems.

  4. Compensator Plant G ( S ) G ( S ) c - H ( S ) Lead Compensation • Used to Improve the Transient behavior of the system.

  5. Lead Compensation • Consider the Following Unity feedback system k=4 p=[0 -2 ] z=[]; usys=zpk(z,p,k) rlocus(usys) csys=feedback(usys,1) [wn b]=damp(csys) sgrid(b,wn) axis([-3 0 -3 3 ]) Lead Compensation contd…

  6. Design Requirements • It is desired to increase ωn to 4 rad/sec without changing damping ratio of closed loop poles. k=4 p=[0 -2 ] z=[]; usys=zpk(z,p,k) rlocus(usys) wn=[2 4]; b=[0.5 0.5]; sgrid(b,wn) axis([-5 0 -5 5 ]) Lead Compensation contd…

  7. Lead Compensator (Follow the Class Work) kc=4.68 pc=-5.4 zc=-2.9 lc=zpk(zc,pc,kc) ltiview(lc) Lead Compensation contd…

  8. Pzmap of Lead Compensator Lead Compensation contd…

  9. Bode plot of Lead Compensator Lead Compensation contd…

  10. Compensated Vs Uncompensated System Root locus of Compensated & uncompensated Systems b=0.5; wn=[2 4]; ku=4 pu=[0 -2 ] zu=[ ]; usys=zpk(zu,pu,ku) k=18.7 p=[0 -2 -5.4] z=-2.9 csys=zpk(z,p,k) rlocus(usys, ‘g’,csys,’b’) Sgrid(b,wn) Lead Compensation contd…

  11. Root locus of Compensated & uncompensated Systems Compensated Vs Uncompensated System Uncompensated compensated Lead Compensation contd…

  12. Compensated Vs Uncompensated System Response of compensated & Uncompensated system numu=4; denu=[1 2 4]; numc=[18.7 54.23]; denc=[1 7.4 29.5 54.23]; csys=tf(numc,denc); usys=tf(numu,denu); ltiview(usys, ‘g:’,csys,’b’) Lead Compensation contd…

  13. Compensated Vs Uncompensated System Pzmap of Compensated & Uncompensated System Uncompensated compensated Lead Compensation contd…

  14. Compensated Vs Uncompensated System Step response of Compensated & Uncompensated System Uncompensated compensated Lead Compensation contd…

  15. Compensated Vs Uncompensated System Bode plot of Compensated & Uncompensated System Uncompensated compensated Lead Compensation contd…

  16. Compensated Vs Uncompensated System Steady State Error of Compensated & Uncompensated System According to final value theorem Steady state error is given by In MATLAB limit(f(x),x,0) Returns the limit of a function f(x) as x 0. Lead Compensation contd…

  17. Compensated Vs Uncompensated System Steady State Error of Compensated & Uncompensated System clear syms s numu=4 denu=s^2+2*s Gu=numu/denu numc=18.7*s+54.23 denc=s^3+7.4*s^2+10.8*s Gc=numc/denc kvu=limit(s*Gu,s,0) kvc=limit(s*Gc,s,0) essu=1/kvu essc=1/kvc Lead Compensation contd…

  18. Exercise#1 Repeat the same tutorial using SISO Design tool. Exercise#2Design another lead compensator for the same system and compare the results.

  19. End of tutorial You can download this tutorial from:http://imtiazhussainkalwar.weebly.com/control-system-design-and-analysis.html

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