Page 161 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

y3=R/(sqrt( (tau*w)A2+1 ))A3; %magnitude at wand
kdisp(['at critical point mag= ' num2str(y1) ' angle
(deg) = ' num2str(y2*180/pi)])
disp(['process ampl at critical freq = 'num2str(y3) ' '
num2str(20*log10(y3)) 'dB'])
disp(' ')
% now add integral-only to three tank process with no
back flow
clear
close all
x0=[1 .001];
x=fminsearch('ThirdCriti',xO);
disp('for Third Order process with integral-only')
disp(['I = 'num2str(x(1)) ' fc = 'num2str(x(2)) ])
freq=x(2);
I=X(1);
R=10;
tau=10;
w=2*pi*freq;
y1=I*R/(w*(sqrt( (tau*w)A2+1 ))A3);% magnitude at wand k
y2=-atan(tau*w)-atan(tau*w)-atan(tau*w)-pi/2;
y3=R/(w*(sqrt( (tau*w)A2+1 ))A3); %magnitude at wand k
disp(['at critical point mag= 'num2str(y1) 'angle
(deg) = ' num2str(y2*180/pi)])
disp(['process ampl at critical freq = 'num2str(y3)
num2str(20*log10(y3)) 'dB'])
%-------------------
function y=ThirdCrit(x)
% called by critpars.m
k=X(1);
W=X(2)*(2*pi);
R=10;
tau=10;
y1=k*R/(sqrt( (tau*w)A2+1 )A3) - 1;
y2=-atan(tau*w)-atan(tau*w)-atan(tau*w)+pi;
Y=Y1A2+y2A2;
%--------------------------------
function y=ThirdCriti(x)
% called by critpars.m
k=X(1);
w=x(2)*(2*pi); %convert to radian freq
R=10;
tau=10;
y1=k*R/(w*(sqrt( (tau*w)A2+1 ))A3) - 1;
y2=-atan(tau*w)-atan(tau*w)-atan(tau*w)-pi*.S+pi;
Y=Y1A2+y2A2;
Note that the above script calls two functions, Thirdcrit and
Thirdcriti. It also uses a built-in Matlab function fminsearch.
Using the integral gain from these calculations for a simula-
tion would result in marginal stability, namely sustained but not-
growing oscillations. Decreasing the integral gain by a factor of
0.5 to 0.004 provides a little better gain margin and produces a
new Bode plot shown in Fig. 5-9. Note that the circles in this