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!
