Implement PID in ode45 code

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Kashish Pilyal 2022-8-16

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评论： Kashish Pilyal 2022-8-17

So, I have a ode45 function and I have an error defined in it which changes at different iterations of the solver. I was able to define the derivative part by just differentiating the error formula but I am unable to implement the integral part. The error expression is:

, where q represents position and v represents velocity. Is it possible to get the PID part in the ode function.

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Answer 1

Sam Chak 2022-8-16

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https://ww2.mathworks.cn/matlabcentral/answers/1780265-implement-pid-in-ode45-code#answer_1027565

编辑：Sam Chak 2022-8-17

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Hi @Kashish Pilyal

If the error is defined as

then

P part is

I part is

D part is

and you can arrange then in the state-space form. For example, a Double Integrator system

can be rewritten in state-space as:

.

The PID has 3 terms, and the state-space is in differential form. So you have no issue with the P and the D part, because they are part of the state variables. The I part is in integral form, so you have to create an additional state variable. See Example below:

[t, x] = ode45(@DIsystem, [0 20], [0; 0; 0]);

plot(t, x(:,1), 'linewidth', 1.5)

grid on, xlabel('t'), ylabel('y(t)'), % ylim([-0.2 1.2])

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 = [0 1; 0 0]; % state matrix

B = [0; 1]; % 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

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Sam Chak 2022-8-17

Hi @Kashish Pilyal

I have provided an example in the Answer using a Double Integrator system:

You will get the idea of how to implement that. Hope it works out for your system.

Kashish Pilyal 2022-8-17

在 MATLAB Online 中打开

Thanks I got the idea, in my case I have the error:

e_1=x(1)-( x(4)+(h_i*x(5)) );

So, If I am right I need to introduce a new state which I will be equal to this error at the end of every iteration like you did with dxdt=x(3) and in the next iteration use this state as the integral of the error.

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