Design Compensation via Root Locus imtiaz hussainfaculty muet

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

Contents • Compensation – Lead Compensation – Lag-Lead Compensation

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

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

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…

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]; sgrid(b, wn) axis([-5 0 -5 5 ]) Lead Compensation contd…

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…

Pzmap of Lead Compensator Lead Compensation contd…

Bode plot of Lead Compensator Lead Compensation contd…

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…

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

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…

Compensated Vs Uncompensated System Pzmap of Compensated & Uncompensated System Uncompensated Lead Compensation contd…

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

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

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…

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…

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

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