ch8p2.m

this the matlab tuning of pid with root locus

'(ch8p2) Example 8.8'               % Display label.
clear                               % Clear variables from workspace.
clf                                 % clear graph on screen.
j=.21
numg=j*[1 .055];                       % Define numerator of G(s).
deng=[3.984e-007 0.0001931 1.292 0];              % Define denominator of G(s).
'G(s)'                              % Display label.
G=tf(numg,deng)                     % Create and display G(s).

rlocus(G)                           % Draw root locus (H(s)=1).
title('Original Root Locus')        % Add title.
pause
K=0:.5:50;                          % Specify range of gain to smooth
                                    % root locus.
rlocus(G,K)                         % Draw smoothed root locus (H(s)=1).
title('Smoothed Root Locus')        % Add title.
pos=input('Type %OS  ');            % Input desired percent overshoot
                                    % from the keyboard.
z=-log(pos/100)/sqrt(pi^2+[log(pos/100)]^2)
                                    % Calculate damping ratio.
sgrid(z,0)                          % Overlay desired damping ratio line
axis([-3 3 -15 15])
                                    % on root locus.
title(['Root Locus with ',num2str(pos),'% overshoot line'])
                                    % Define title for root locus
                                    % showing percent overshoot used.
[K,p]=rlocfind(G)                   % Generate gain, K, and closed-loop 
                                    % poles, p, for point selected 
                                    % interactively on the root locus.
pause
'T(s)'                              % Display label.
T=feedback(K*G,1)                   % Find closed-loop transfer function
                                    % with selected K and display.
step(T)                             % Generate closed-loop step response
                                    % for point selected on root locus.
title(['Step Response for K=',num2str(K)])            
                                    % Give step response a title which 
                                    % includes the value of K.