%%Example-9.6%% Lag-lead Compensator Design
%%Root Locus for Uncompensated system%%
Gu=zpk([],[0 -6 -10],1);
figure(1)
rlocus(Gu)
grid off
sgrid(0.456,0)
title('Root Locus for Un-compensated system')
%%Root Locus for Lead Compensated system%%
Gc1=zpk([-6],[-29.1],1); %for lead
Gce1=Gu*Gc1;
figure(2)
rlocus(Gce1)
grid off
sgrid(0.456,0)
title('Root Locus for Lead Compensated system')
%%Root Locus for Lag-lead Compensated system%%
Gc2=zpk([-0.04713],[0.01],1); %for lag-lead
Gce2=Gu*Gc1*Gc2;
figure(3)
rlocus(Gce2)
grid off
sgrid(0.456,0)
title('Root Locus for lag-lead Compensated system')
% Lag-lead compensator Output Response
Gu=zpk([],[0 -6 -10],192.1)
G_lead=zpk([],[0 -10 -29.1],1977) G_lag_lead=zpk([-0.04713],[0 -10 -29.1 -0.01],1971) T_u=feedback(Gu,1,-1);
T_lead=feedback(G_lead,1,-1);
T_lag_lead=feedback(G_lag_lead,1,-1);
figure(4)
step(T_u,'-r')
hold on
step(T_lead,'b')
hold on
step(T_lag_lead,'k')
legend('Uncompensated response','Lead response','Lag-lead response')