Hi,
Initial Condition: You can specify the initial condition 'x0' as a 3x1 matrix. This matrix represents the initial values of your state variables: supply current, angular displacement, and angular velocity. You can then simulate the system over a specified time range.
Simulating the System: You can use MATLAB's "lsim" function to simulate the response of your system to a specified input over time. This function allows you to specify the initial condition and will provide the state trajectory over time.
Have a look at the below revised code:
function [xt, x1, x2, x3] = motor1(t, x0)
% Define system parameters
L = 0.3; % H inductance
R = 2.5; % ohm resistance
Kv = 0.0195; % Vs/rad electromotive constant
Kt = 0.0195; % Nm/A torque constant
J = 17.2e-7; % kgm^2 inertia
D = 1e-6; % N.m.rad/s friction constant
% State-space matrices
A_motor = [-R/L 0 -Kv/L; 0 0 1; Kt/J 0 -D/J];
B_motor = [1/L; 0; 0];
C_motor = eye(3); % Output all states
D_motor = [0; 0; 0];
% Create state-space system
motor = ss(A_motor, B_motor, C_motor, D_motor);
% Define input voltage as a step input (e.g., 12V)
u = 12 * ones(size(t));
% Simulate the system
[y, t_out, x] = lsim(motor, u, t, x0);
% Extract state variables at t = 1 second
[~, idx] = min(abs(t_out - 1)); % Find index closest to t = 1
x1 = x(idx, 1); % Supply current
x2 = x(idx, 2); % Angular displacement
x3 = x(idx, 3); % Angular velocity
% Output the state at each time step
xt = x;
end
t = linspace(0, 5, 1000); % Time vector from 0 to 5 seconds
x0 = [0; 0; 0]; % Initial condition: all states start at zero
[xt, x1, x2, x3] = motor1(t, x0);
disp(['Angular displacement at 1 second: ', num2str(x2)]);
Hope this helps!
