I understand that you want to know how to define a dynamic system in MATLAB with two state variables,
The state-space representation is typically given as,
x˙=Ax+Bu+Ew
where ”w” is the process disturbance.
Regarding your question about whether to consider “δf” as a measured disturbance, it depends on whether you have a sensor that can measure it. If you do, then you can include it as a measured disturbance. Otherwise, you can treat it as an unmeasured disturbance.
To define the system in state space form, you can use the following code:
% Define the system matrices
A = [a11 a12; a21 a22];
B = [b1; b2];
E = [e11 e12; e21 e22];
C = eye(2);
% Define the state space model
sys = ss(A, [B E], C, 0);
% Display the state-space model
disp('State-Space Model:')
disp(sys)
% Save the system to a MATLAB file
save('vehicle_system.mat', 'sys');
Here, “a11”, “a12”, “a21”, “a22”, “b1”, “b2”, “e11”, “e12”, “e21”, and “e22” are the elements of the matrices “A”, “B”, and “E”. The State Space function is used to create a state-space model. The “[B E]” input matrix combines the control input “u” and the fixed input “δf” into a single input vector.
To create the Simulink model, you can follow these steps:
- Open Simulink and create a new model.
- Drag and drop the "State-Space" block from the Simulink Library Browser onto the model canvas.
- Double-click the "State-Space" block to open its block parameters dialog.
- Enter the system matrices “A”, “E”, and “B” into the appropriate fields.
- Connect the output of the "State-Space" block to the input of the MPC controller block.
- Connect the output of the MPC controller block to the input of the plant block.
- Add any other necessary blocks to the model, such as disturbance inputs or output signals.
- Save the model with a name of your choice.
Hope this Helps!
Thanks.
