I see you have an equation as plant in “state space” form, which you want to implement in Simulink or by codes. Here’s how you do this:
In Simulink:
1.) Launch Simulink and create a brand new model.
2.) Drag and drop the State-Space block from the Simulink Library Browser under Continuous.
3.) Now double click the block and in its “parameters dialog”, enter your matrices “A”, “B”, “C”, “D” in the respective slides.
A: Enter the state matrix (
).
). B: Enter the combined input matrix 
if you want to handle multiple inputs.
if you want to handle multiple inputs. C: Enter the output matrix (
).
). D: Enter the direct transmission matrix 
based on your system.
based on your system. 4.) For inputs like u, v and 
, use “Inports” and for output like z, use “Outport”.
, use “Inports” and for output like z, use “Outport”. 6.) Connect the input ports to the “State-Space block” and the output of the “State-Space block” to the output port.
7.) Lastly run the simulation and observe the system behaviour.
For implementing in MATLAB code, you can use the following code:
% Define matrices
A = [...]; % Define your A matrix
Bw = [...]; % Define your Bw matrix
Bu = [...]; % Define your Bu matrix
Bref = [...]; % Define your Bref matrix
Cz = [...]; % Define your Cz matrix
Dzw = [...]; % Define your Dzw matrix
Dzu = [...]; % Define your Dzu matrix
% Combine B matrices for multiple inputs
B = [Bu, Bw, Bref];
D = [Dzu, Dzw, zeros(size(Cz, 1), size(Bref, 2))];
% Create state-space model
sys = ss(A, B, Cz, D);
% Define input signals
t = 0:0.01:10; % Time vector
u = [...]; % Define your input signal for u
w = [...]; % Define your disturbance signal for w
vref = [...]; % Define your reference signal for vref
% Combine inputs into a single matrix
inputs = [u; w; vref];
% Simulate the system
[y, t, x] = lsim(sys, inputs, t);
% Plot the output
plot(t, y);
xlabel('Time (s)');
ylabel('Output z');
title('State-Space System Output');
I used some example values for input and got this graph:
