1 / 44

Lead Controller Design

Lead Controller Design. p lead. z lead. 20log(Kz lead /p lead ). Lead Design. From specs => PM d and w gcd From plant, draw Bode plot Find PM have = 180 + angle(G(j w gcd ) D PM = PM d - PM have + a few degrees

zavad
Download Presentation

Lead Controller Design

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lead Controller Design

  2. plead zlead 20log(Kzlead/plead)

  3. Lead Design • From specs => PMd and wgcd • From plant, draw Bode plot • Find PMhave = 180 + angle(G(jwgcd) • DPM = PMd - PMhave + a few degrees • Choose a=plead/zlead so that fmax = DPM and it happens at wgcd

  4. Lead design example • Plant transfer function is given by: • n=[50000]; d=[1 60 500 0]; • Desired design specifications are: • Step response overshoot <= 16% • Closed-loop system BW>=20;

  5. n=[50000]; d=[1 60 500 0]; figure(1); margin(n,d); Mp = 16/100; zeta =0.5; PMd = 100*zeta + 3; BW=20; w_gcd = BW*0.7; PM = pi+angle(polyval(n,j*w_gcd)/polyval(d,j*w_gcd)); phimax= PMd*pi/180-PM; alpha=(1+sin(phimax))/(1-sin(phimax)); zlead= w_gcd/sqrt(alpha); plead=w_gcd*sqrt(alpha); K=sqrt(alpha)/(abs(polyval(n,j*w_gcd)/polyval(d,j*w_gcd))); ngc = conv(n, K*[1 zlead]); dgc = conv(d, [1 plead]); figure(1); hold on; margin(ngc,dgc);hold off; [ncl,dcl]=feedback(ngc,dgc,1,1); figure(2); step(ncl,dcl); figure(3); margin(ncl*1.414,dcl);

  6. After design Before design

  7. Closed-loop Bode plot Magnitude plot shifted up 3dB So, gc is BW

  8. n=[50]; d=[1/5 1 0]; figure(1); clf; margin(n,d); grid; hold on; Mp = 20/100; zeta = sqrt((log(Mp))^2/(pi^2+(log(Mp))^2)); PMd = zeta * 100 + 10; ess2ramp= 1/200; Kvd=1/ess2ramp; Kva = n(end)/d(end-1); Kzp = Kvd/Kva; figure(2); margin(Kzp*n,d); grid; [GM,PM,wpc,wgc]=margin(Kzp*n,d); w_gcd=wgc; phimax = (PMd-PM)*pi/180; alpha=(1+sin(phimax))/(1-sin(phimax)); z=w_gcd/sqrt(alpha); p=w_gcd*sqrt(alpha); ngc = conv(n, alpha*Kzp*[1 z]); dgc = conv(d, [1 p]); figure(3); margin(tf(ngc,dgc)); grid; [ncl,dcl]=feedback(ngc,dgc,1,1); figure(4); step(ncl,dcl); grid; figure(5); margin(ncl*1.414,dcl); grid;

  9. n=[50]; d=[1/5 1 0]; figure(1); clf; margin(n,d); grid; hold on; Mp = 20/100; zeta = sqrt((log(Mp))^2/(pi^2+(log(Mp))^2)); PMd = zeta * 100 + 10; ess2ramp= 1/200; Kvd=1/ess2ramp; Kva = n(end)/d(end-1); Kzp = Kvd/Kva; figure(2); margin(Kzp*n,d); grid; [GM,PM,wpc,wgc]=margin(Kzp*n,d); w_gcd=wgc; phimax = (PMd-PM)*pi/180; alpha=(1+sin(phimax))/(1-sin(phimax)); z=w_gcd/alpha^.25; %sqrt(alpha); p=w_gcd*alpha^.75; %sqrt(alpha); ngc = conv(n, alpha*Kzp*[1 z]); dgc = conv(d, [1 p]); figure(3); margin(tf(ngc,dgc)); grid; [ncl,dcl]=feedback(ngc,dgc,1,1); figure(4); step(ncl,dcl); grid; figure(5); margin(ncl*1.414,dcl); grid;

  10. n=[1]; d=[1/5/200 1/5+1/200 1 0]; figure(1); clf; margin(n,d); grid; hold on; zeta = 0.4; PMd = 100*zeta + 3; ess2ramp= 0.01; Kvd=1/ess2ramp; Kva = n(end)/d(end-1); Kzp = Kvd/Kva; figure(1); margin(Kzp*n,d); grid; [GM,PM,wgc,wpc]=margin(Kzp*n,d); w_gcd=wgc; phimax = (PMd-PM)*pi/180; alpha=(1+sin(phimax))/(1-sin(phimax)); z=w_gcd/alpha^.25; %z=w_gcd/sqrt(alpha); p=w_gcd*alpha^.75; %p=w_gcd*sqrt(alpha); ngc = conv(n, alpha*Kzp*[1 z]); dgc = conv(d, [1 p]); figure(1); margin(tf(ngc,dgc)); grid; [ncl,dcl]=feedback(ngc,dgc,1,1); figure(4);step(ncl,dcl); grid; figure(5); margin(ncl*1.414,dcl); grid;

  11. n=[1]; d=[1/5/200 1/5+1/200 1 0]; figure(1); clf; margin(n,d); grid; hold on; zeta = 0.4; PMd = 100*zeta + 10; ess2ramp= 0.01; Kvd=1/ess2ramp; Kva = n(end)/d(end-1); Kzp = Kvd/Kva; figure(1); margin(Kzp*n,d); grid; [GM,PM,wgc,wpc]=margin(Kzp*n,d); w_gcd=wgc; phimax = (PMd-PM)*pi/180; alpha=(1+sin(phimax))/(1-sin(phimax)); z=w_gcd/alpha^.25; %z=w_gcd/sqrt(alpha); p=w_gcd*alpha^.75; %p=w_gcd*sqrt(alpha); ngc = conv(n, alpha*Kzp*[1 z]); dgc = conv(d, [1 p]); figure(1); margin(tf(ngc,dgc)); grid; [ncl,dcl]=feedback(ngc,dgc,1,1); figure(4);step(ncl,dcl); grid; figure(5); margin(ncl*1.414,dcl); grid;

More Related