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% ===============================================================================
% optiPIDfun Lukas Reichlin July 2009
% ===============================================================================
% Objective Function
% Reference: Guzzella, L. (2007) Analysis and Synthesis of SISO Control Systems.
% vdf Hochschulverlag, Zurich
% ===============================================================================
function J = optiPIDfun (C_par)
% Global Variables
global P t dt mu_1 mu_2 mu_3
% Function Argument -> Controller Parameters
kp = C_par(1);
Ti = C_par(2);
Td = C_par(3);
% PID Controller with Roll-Off
C = optiPIDctrl (kp, Ti, Td);
% Open Loop
L = P * C;
% Sum Block: e = r - y
SUM = ss ([1, -1]); % Matlab converts to SS (and back) for MIMO TF connections
% Group Sum Block and Open Loop
SUML = append (SUM, L);
% Build System Interconnections
CM = [3, 1; % Controller Input with Sum Block Output
2, 2]; % Sum Block Negative Input with Plant Output
inputs = [1]; % Input 1: reference r(t)
outputs = [1, 2]; % Output 1: error e(t), Output 2: output y(t)
SUML = connect (SUML, CM, inputs, outputs);
% Simulation
[y, t_y] = step (SUML, t);
% ITAE Criterion
itae = dt * (t_y.' * abs (y(:, 1)));
% Sensitivity
S = inv (1 + L);
Ms = norm (S, inf);
% Objective Function
J = mu_1 * itae + mu_2 * (max (y(:, 2)) - 1) + mu_3 * Ms;
end % function
% ===============================================================================
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