How do I set the saturation output for PID objects in MATLAB?

I want to set the saturation output of a PID object in MATLAB to enable the implementation of an anti-windup PID control scheme.

Answer 1

[MathWorks Support Team]

PID objects in the Control System Toolbox are LTI (linear time-invariant) systems of a special type. Because of that, there is no property for output saturation in PID objects. To simulate "anti-windup" in MATLAB, you can setup a custom state-space system and call the "lsim" function to simulate the time response of that system with nonlinear properties such as saturation. Below is a simple script that performs closed-loop PI control with back calculation that can be used as a starting point.   

UseBackCalculation = true; % enable/disable anti-windup (back calculation)
G = ss(tf(1,[1 2 1])); % plant
Kp = 2; Ki = 2; % PI controller gains (parallel)
Ts = 0.1; % controller sample time
tau = 1; % reset time constant
UB = 1.2; LB = -1.2; % saturation limits

% initial condition
r = 1;
y = 0;
x = zeros(2,1);
actionI = 0;

% closed-loop simulation (200 steps)
N = 200;
for ct=1:N
    % error
    e = r - y;
    
    % control action
    actionP = Kp*e;
    u = actionP + actionI;
    
    % saturation control action
    u_sat = max(min(u,UB),LB);
    
    % anti windup
    if UseBackCalculation
        actionI = actionI + (Ki*e + (u_sat-u)/tau)*Ts;
    else
        actionI = actionI + Ki*e*Ts;
    end
    
    % plant output
    [Y,T,X] = lsim(G,[u_sat;u_sat],[0;Ts],x);
    
    % for next iteration
    x = X(end,:)';
    y = Y(end);
    y_vec(ct) = y;
    u_vec(ct) = u_sat;
end

clf;
figure(1);
plot(1:N,y_vec,'*r',1:N,u_vec,'+b');
xlabel('Time'); ylabel('Signal');
legend('Model Response','Control Signal')
if UseBackCalculation
    title('With Anti-Windup (Back Calculation)');
else
    title('Without Anti-Windup');
end