One of the systems I want to control with PID is the state space equation with disturbances. Can someone help me to design matlab function of the system? Please

I have given the space state parameters I want to use below. Can you help design and control this matlab function with PID?

[Sam Chak]

Hi @veysel burçak

This question looks familiar. I vaguely remember that the previous question was answered by @Paul, and you designed a PID controller based on the information provided in an excerpt from a journal paper.

The information provided in the MATLAB function above is incomplete. The output matrix and the disturbance vector are unknown. Furthermore, the MATLAB code was shown as an image file, making it impossible to copy and paste for testing purposes.

[veysel burçak]

Thank you for your answer. I designed a controller by converting space state equaition to transfer function. However, since the transfer function gets initial condition 0, the graph does not give the correct result, the graph value does not start from 300, even though I set the step input, so I have to write this function. @Paul @Sam Chak

function [y,x_out] = fcn(x,u,d)

ny=1;

nx=2;

y = zeros(ny,1);

x = zeros(nx,1);

A=[-0.00446566 0.00445684; 0.00515227 -5.15227];

B=[0.00316315;0];

E=[0.00292761 0;0 -2.0315.10^(-8)]

C=[1;0];

x_out = A*x+B*u+E*d;

y = C*x;

[veysel burçak]

Before attempting to solve the identification problem, we first performed sensitivity estimations with respect to the unknown model parameters (CpW and KW ) and the disturbance variables TI and Wloss by using the known and roughly estimated model parameters as nominal values.

During the measurements, the disturbance variable TI was measurable and constant and the cold water inlet flow rate m was constant. Furthermore, it was assumed that the environmental heat loss Wloss of the system was constant (which is an acceptable approximation of reality, since the outside temperature during the measurements was approximately constant and the temperature variation within the pressurizer was small).

Can you check disturbances vector from this paper please; https://www.sciencedirect.com/science/article/pii/S1474667015353416 @Sam Chak @Paul

Answer 1

[Sam Chak]

Hi @veysel burçak

I have fixed the code in the MATLAB Function block. The initial condition is assigned in the Integrator block. It should be working correctly now.

function dx = fcn(w, u, x)

A = [-4.46566e-3 4.45684e-3;

5.15227e-3 -5.15227e-3];

B = [ 3.16315e-3;

0];

E = [ 2.92761e-3 0;

0 -2.03150e-8];

dx = A*x + B*u + E*w;

[veysel burçak]

Thank you very much.I learned a lot in Matlab simulink thanks to you.

[veysel burçak]

When I use the controller that I control another system, the reference signal does not follow. It does not increase to 305 after 20 seconds. Can you check the value when you are available? @Sam Chak

[Sam Chak]

Hi @veysel burçak

Can you save the .slx file in R2017a format?

In general, there is no guarantee that a controller from another system will stabilize the current system. A stability analysis needs to be performed. Ideally, you should design a new controller for the current system that satisfies the performance requirements. Can you show the design methodology?

[veysel burçak]

Even though I change the parameters, the result does not change. I want the value to remain constant until the 20th second. From 20 to 25 it should be 305. I want to produce a better result than PID control. Thank you. An Bn En are mutable values. I need to produce a better result by changing the KSC and lambda @Sam Chak

[Sam Chak]

Hi @veysel burçak

I have examined the .slx file and identified some issues with the design methodology. However, I'm not familiar with handling mismatched disturbances. Moreover, no stability proof is provided to demonstrate that the proposed sliding mode controller can effectively track the reference input. If the existing PI controller can solve the tracking problem, perhaps you can apply some modifications to it.

Currently, I don't have a solution for the control design. Therefore, I recommend that you post a new question, and hopefully, experts in the field can offer guidance.