Page 160 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

latrices ••• Hig•er-or•er Precess ••••Is 135

Alternatively, a two-dimensional valley-seeking algorithm can be
easily constructed to find the values of I and ro that minimize the fol-
lowing quantity

2
R3 I 1 )
( J<-r3ro)2 + 1J(-r2ro)2 + 1J(-rtro)2 + 1 ro
+( tan-•(~,<») + tan- ( ~,<»)+tan-·<~,<»)+ i +If r (5-15)
1

which is equivalent to solving Eq. (4-25) in Chap. 4 which is repeated
here:

or

or

or

For this case, the quantity in Eq. (5-15) is minimized by I= 0.0089
and/= ro/2tr= 0.00929 Hz.
A Matlab script to carry out this minimization is

clear
close all
xO=[l .001];
x=fminsearch('ThirdCrit',xO);
disp('for Third Order process no back flow')
disp( [ •k.c = ' mun2str(x(l)) ' fc = ' mun2str(x(2)) ] )
% get mag and angle at this w and k
freq=x(2);
k=X(l);
R=lO;
tau=lO;
w=2*pi*freq;
yl=k*R/(sqrt( (tau*w)A2+1 ))A3; %magnitude at wand k
y2=-atan(tau*w)-atan(tau*w)-atan(tau*w);