Implement PID in ode45 code
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Kashish Pilyal
el 16 de Ag. de 2022
Comentada: Steven Lord
el 8 de Ag. de 2024
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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Sam Chak
el 16 de Ag. de 2022
Editada: Sam Chak
el 17 de Ag. de 2022
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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Banaan Kiamanesh
el 8 de Ag. de 2024
This is not right.
You are assuming that the derivative of the reference signal is 0 which is correct in this particular case. But what if it is not?
The main question in here is that how can we do differentiation in ode functions when we dont have any access to the data from previous iterations.
It is possible beacuse it is being done in simulink models. but I'm not sure how in MATLAB... :/
Steven Lord
el 8 de Ag. de 2024
The main question in here is that how can we do differentiation in ode functions when we dont have any access to the data from previous iterations.
If your differential equation requires historical information about the solution from earlier times as part of evaluating the solution at the current time, you don't have an ordinary differential equation (ODE). You have a delay differential equation (DDE). There are three solvers in MATLAB for solving DDEs listed on this page: dde23, ddesd, and ddensd.
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