leaddesign.m

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function Lead=LeadDesign(Kp,Kv,PM,plant);
%% Use of a simple lead to compensate for a control system.
%% See P.696 of Nise's Control Systems Engineering, 
%% Wiley, 3rd Edition, 2000.
%% For Example:
%Kp=[];Kv=30;PM=30;LeadDesign(Kp,Kv,PM,tf(1,[1 1 0]))
%%
%% PenChen Chou. 2003-5-9

s=tf('s');
% If Kp is empty the use Kv to find K
if ~isempty(Kp)
    [num,den]=tfdata(plant,'v');
    N=length(num);D=length(den);Limit=num(N)/den(D);
    K=Kp/Limit;
else
    P1=plant*s; P1=minreal(P1);
    [num,den]=tfdata(P1,'v');
    N=length(num);D=length(den);Limit=num(N)/den(D);
    K=Kv/Limit;
end
% K must be finite
if K<inf
    [Gm,Pm,wcg,wcp]=margin(K*plant);
    MorePhase=(PM-Pm+7)/57.3;
    alpha=(1-sin(MorePhase))/(1+sin(MorePhase));
    NewCrossOver=1.2*wcp;
    tau=1/NewCrossOver/sqrt(alpha);
    Gc=K*(tau*s+1)/(alpha*tau*s+1);
    open2=Gc*plant;open1=K*plant;
    figure(2);bode(open1,open2);grid;ylabel('Figure 2');
    figure(3);margin(open2);ylabel('Figure 3');
    clo=open2/(1+open2);clo=minreal(clo);
    figure(4);subplot(211);step(clo);ylabel('Figure 4');
    figure(4);subplot(212);step(clo);ylabel('Figure 4');
    if Kv>0
        [y,t]=step(clo);
        [y]=lsim(clo,t,t);N=length(y);Ess=t(N)-y(N);
        subplot(212);plot(t,t,t,y);grid;
        title(['Ramp response with Ess=' num2str(Ess)]);
        xlabel('Time (sec.)');
    end
else
    error('===>Simple Lead compensator wouldnot work for this case.');
end
fprintf('Figure 2 shows the Bode plots of uncompensated and compensated systems\n');
fprintf('Figure 3 shows GM, PM of the compensated systems\n');
fprintf('Figure 4 shows the Time Responses of the  compensated systems\n');
Lead=Gc;