Can anybody give me the idea for implementing PID control for dc motor using state space equations through ode45 solver?

function dxdt = DIsystem(t, x)

dxdt = zeros(3, 1);

% construction of PID

r = 1; % reference signal

e = x(1) - r; % error signal

Kp = 1 + sqrt(2); % proportional gain

Ki = 1; % integral gain

Kd = 1 + sqrt(2); % derivative gain

u = - Kp*e - Ki*x(3) - Kd*x(2); % the PID thing

% the dynamics

  A = [-b/J K/J ; -K/L -R/L];               % state matrix
  B = [0; 1/(L*V)];                         % input matrix

dxdt(1:2) = A*[x(1); x(2)] + B*u; % the Double Integrator system

dxdt(3) = e; % for integral action in PID

end

How to modify this equation to the dc motor equation?

Answer 1

[Sam Chak]

@MOHAMED ASWER

Not sure how your DI/dc motor system, but I think the following example should give you the basic idea.

tspan  = [0 1];
x0     = [0 0 0];
[t, x] = ode45(@motor, tspan, x0);
plot(t, x(:,1)), grid on, xlabel('t')

function dxdt = motor(t, x)
    dxdt    = zeros(3, 1);
    
    % construction of PID 
    r    = 1;                               % reference signal
    err  = x(1) - r;                        % error signal
    Kp   = 3.49;                            % proportional gain
    Ki   = 52.8;                            % integral gain
    Kd   = 0.0512;                          % derivative gain
    u    = - Kp*err - Ki*x(3) - Kd*x(2);    % the PID thing
    
    % the dynamics
    J = 3.2284E-6;
    b = 3.5077E-6;
    K = 0.0274;
    R = 4;
    L = 2.75E-6;
    % V = ?;
    % A = [-b/J K/J; -K/L -R/L];              % state matrix
    % B = [0; 1/(L*V)];                       % input matrix
    
    A = [0 1; 0 -(b*R + K^2)/(J*R + b*L)];  % state matrix
    B = [0; K/(J*R + b*L)];                 % input matrix
               
    dxdt(1:2) = A*[x(1); x(2)] + B*u;       % the motor
    dxdt(3)   = err;                        % for integral action in PID
end

[MOHAMED ASWER]

Thanks for the answer brother

[Sam Chak]

You are welcome, @MOHAMED ASWER. If you find the MATLAB code is helpful, please consider accepting ✔ and voting 👍 the Answer. Thanks!