Code clean

defaultGrid.m

+function w = defaultGrid(P)
+% Get default angular frequency grid based on process dynamics.
+%
+% P   - LTI process model.
+%
+% Downloaded from git@gitlab.control.lth.se:kristian/PIDopt.git
+% See the git repo for further documentation.
+
+N = 5e2; % Number of grid points
+[~,~,w]=bode(P); % Grequenies Matlab considers interesting
+wMax = w(end);
+wMin = min(w(1),wMax/100); % ensure to include low frequencies
+w=logspace(log10(wMin),log10(wMax),N)';
\ No newline at end of file

example.m

@@ -13,24 +13,26 @@ s = zpk('s');
 P = 1/(s^2+2*.5*s+1)*exp(-0.5*s);
 
 % Robustness consraints
-Ms = 1.6; % Maximum allowed sensitivity function magnitude
-Mt = 1.6; % Maximum allowed complementary sensitivity function magnitude
+Ms = 1.8; % Maximum allowed sensitivity function magnitude
+Mt = Ms; % Maximum allowed complementary sensitivity function magnitude
 Mks = 2; % Maximum allowed magnitude of transfer function from process
           % output to control signal, sometimes referred to as noise
           % sensitivity.
           
 %% Design
-% IE-optimal design
 p0 = [0 0 0]'; % Parameters of any PID controller, which stabilizes P.
              % See pidIE.m for details. Use p = [0 0] to synthesize PI
-             % controller.
-[K1,p1] = pidIE(P,Ms,Mt,Mks,p0)
+             % controller
+
+ w = defaultGrid(P); % default angular frequency grid
+             
+[K1,p1] = pidIE(P,Ms,Mt,Mks,p0,w) % IE-optial PID controller without filter
 
 % IAE-optimal design
-[K2,p2] = pidIAE(P,Ms,Mt,Mks,p1) % Hot-start with K1 parameters
+[K2,p2] = pidIAE(P,Ms,Mt,Mks,p1,w) % Hot-start with K1 parameters
 
 % IAE-optimal design with filter
-[K3,p3,w] = pidfIAE(P,Ms,Mt,Mks,p2); % Hot-start with K2 parameters
+[K3,p3,w] = pidfIAE(P,Ms,Mt,Mks,p2,w); % Hot-start with K2 parameters
 K3
 p3
 
@@ -40,7 +42,7 @@ L = @(K)series(P,K);
 S = @(K)feedback(1,L(K));
 T = @(K)feedback(L(K),1);
 KS = @(K)feedback(K,P);
-PS = @(K)feedback(P,K)
+PS = @(K)feedback(P,K);
 
 wMin = w(1);
 wMax = w(end);

pidIAE.m

-function [K,p,w] =pidIAE(P,Ms,Mt,Mks,p)
+function [K,p,w] =pidIAE(P,Ms,Mt,Mks,p,w)
 % Computes PID controller that maximizes the integral gain subject to
 % constraints on the magnitude of the sensitivity, complementary
 % sensitivity and noise sensitivity fu nctions.
 % The length of p decides if the controller is of PI or PID type.
 %
-%   K(s) = kp + ki/s + kd*s
+% K(s) = kp + ki/s + kd*s
 %
-%   P   - LTI process model.
-%   Ms  - Maximum allowed sensitivity.
-%   Mt  - Maximum allowed complementary sensitivity.
-%   Mks - Maxium allowed noise sensitivity.
-%   p   - Vector of initial controller parameters. Length must be 2 (PI)
-%         or 3 (PID). Controller must stabilize plant.
+% P   - LTI process model.
+% Ms  - Maximum allowed sensitivity.
+% Mt  - Maximum allowed complementary sensitivity.
+% Mks - Maxium allowed noise sensitivity.
+% p   - Vector of initial controller parameters. Length must be 2 (PI)
+%       or 3 (PID). Controller must stabilize plant.
+% w   - angular freqency grid. Use [] for default grid.
 %
 % Downloaded from git@gitlab.control.lth.se:kristian/PIDopt.git
 % See the git repo for further documentation.
@@ -26,9 +27,9 @@ else
 end
 
 % Frequency grid (heuristic) - change as needed
-N = 500; % Number of grid points
-[~,~,w] = bode(P);
-w = logspace(log10(w(1)),log10(w(end)),N)';
+if isempty(w)
+    w = defaultGrid(P);
+end
 
 % Helper functions
 mdot = @(x,y)(bsxfun(@times,x,y)); % (row vector)-matrix column-wise dot

pidIE.m

-function [K,p,w] = pidIE(P,Ms,Mt,Mks,p)
-%Computes PID parameters
+function [K,p,w] = pidIE(P,Ms,Mt,Mks,p,w)
 % Computes PID controller that maximizes the integral gain subject to
 % constraints on the magnitude of the sensitivity, complementary
 % sensitivity and noise sensitivity functions.
@@ -13,16 +12,15 @@ function [K,p,w] = pidIE(P,Ms,Mt,Mks,p)
 % Mks - Maxium allowed noise sensitivity.
 % p   - Vector of controller parameters. Length must be 2 (PI)
 %       or 3 (PID). Controller must stabilize plant.
+% w   - angular freqency grid. Use [] for default grid.
 %
 % Downloaded from git@gitlab.control.lth.se:kristian/PIDopt.git
 % See the git repo for further documentation.
 
 % Frequency grid (heuristic) - change as needed
-N = 500; % Number of grid points
-[~,~,w]=bode(P);
-wMax = w(end);
-wMin = min(w(1),wMax/100);
-w=logspace(log10(wMin),log10(wMax),N)';
+if isempty(w)
+    w = defaultGrid(P);
+end
 
 % Frequency response
 P = squeeze(freqresp(balreal(P),w));

pidfIAE.m

-function [KF,p,w]=getK2F(P,Ms,Mt,Mks,pK)
+function [KF,p,w]=pidfIAE(P,Ms,Mt,Mks,pK,w)
 % Computes PID parameters, that minimize load step IAE, and filter for
 % noise attenuation.
 %
-%   K(s) * F(s) = (kp + ki/s + kd*s) * 1/((s*T)^2+2*z*T*s+1)
+% K(s) = F(s) * C(s) = (kp + ki/s + kd*s) * 1/((s*T)^2+2*z*T*s+1)
 %
-%   P   - LTI process model.
-%   Ms  - Maximum allowed sensitivity.
-%   Mt  - Maximum allowed complementary sensitivity.
-%   Mks - Maxium allowed noise sensitivity. This is only meaningful if
-%         there is high-frequency roll-off (through e.g. a filter).
-%   pK  - Vector of initial controller parameters [kp ki kd].
-%         Length must be 2 (PI)
-%         or 3 (PID). Controller must stabilize plant.
+% P   - LTI process model.
+% Ms  - Maximum allowed sensitivity.
+% Mt  - Maximum allowed complementary sensitivity.
+% Mks - Maxium allowed noise sensitivity. This is only meaningful if
+%       there is high-frequency roll-off (through e.g. a filter).
+% pC  - Vector of initial controller parameters [kp ki kd].
+%       Length must be 2 (PI)
+%       or 3 (PID). Controller must stabilize plant.
 %
 % Downloaded from git@gitlab.control.lth.se:kristian/PIDopt.git
 % See the git repo for further documentation.
@@ -26,9 +26,9 @@ else
 end
 
 % Frequency grid (heuristic) - change as needed
-N = 500; % Number of grid points
-[~,~,w] = bode(P);
-w = logspace(log10(w(1)),log10(w(end)),N)';
+if isempty(w)
+    w = defaultGrid(P);
+end
 
 % Ensure LP filter breakdown within grid
 Tmin = 1/w(end);