How can I enter a variable disturbance as a matrix input

the following system contains linear system and a augmented representation, how do I inlude the same disturbance knowing that it is a function of x1(t) and x2(t)m and occures in a specific time in a form of matrix to respect the appropriate dimensions .

Answer 1

[Suraj Kumar]

Hi @Mohamed Amine TAIB,

To include a variable disturbance in a MATLAB system, especially when dealing with state-space representations or augmented systems, you need to appropriately define the disturbance as a function of your state variables and incorporate it into your system equations.

1. Define the disturbance (d(t)) as a function of the state variables ( x_1(t) ) and ( x_2(t) ) that occurs at specific times.Replace f1 and f2 with your specific disturbance functions and t_start and t_end with the times during which the disturbance occurs.

function d = disturbance(t, x)
    if t >= t_start && t <= t_end
        d = [f1(x(1), x(2)); f2(x(1), x(2))];
    else
        d = [0; 0]; 
    end
end

2. Use a numerical solver to simulate the system dynamics, including the disturbance.

t_span = [0, T]; % where T is the total simulation time
x0 = [x1_0; x2_0]; % Replace with your initial state conditions
function dxdt = system_dynamics(t, x)
    % System matrices
    A = [...]; % Define your A matrix
    B = [...]; % Define your B matrix
    E = [...]; % Define your E matrix

    u = ...; % Define your control input

    % Disturbance
    d = disturbance(t, x);

    % State equation
    dxdt = A*x + B*u + E*d;
end
[t, x] = ode45(@system_dynamics, t_span, x0);

Hope this helps!