init

FOTF Toolbox/fpidfuns.m

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+function [fy,C]=fpidfuns(x)
+% fpidfuns - general objective function for optimum fractional-order PID
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+% Last modified 18 May, 2022 
+   global G t key1 key2 C
+   s=fotf('s'); t=t(:); 
+   switch key1
+      case {'fpid',1}, C=x(1)+x(2)*s^(-x(4))+x(3)*s^(x(5));
+      case {'fpi',2}, C=x(1)+x(2)*s^(-x(3));
+      case {'fpd',3}, C=x(1)+x(2)*s^x(3);
+      case {'fpidx',4}, C=x(1)+x(2)/s+x(3)*s^x(4);
+      case {'pid','PID',5}, C=x(1)+x(2)/s+x(3)*s;
+   end
+   dt=t(2)-t(1); e=step(feedback(1,G*C),t); e=e(:).';
+   switch key2
+      case {'itae','ITAE',1}, fy=dt*abs(e)*t;
+      case {'ise','ISE',2}, fy=dt*sum(e.^2);
+      case {'iae','IAE',3}, fy=dt*sum(abs(e));
+      case {'itse','ITSE',4}, fy=dt*e.^2*t;
+      otherwise
+         error('Available criteria are itae, ise, iae, itse.')
+   end
+   disp([x(:).' fy])
+end