Your code works correctly here and in MATLAB Online --
clear all; close all; clc;
%% System Parameters
% Physical parameters of the DC motor
Ra = 1.0; % Armature resistance (Ohm)
La = 0.5; % Armature inductance (H)
J = 0.01; % Moment of inertia (Nms^2/rad)
b = 0.1; % Damping coefficient (Nms)
KT = 0.01; % Torque constant (Nm/A)
Ke = 0.01; % Back EMF constant (Nm/A)
K = Ke; % In SI units, Ke = Ki = K
%% Transfer Function Definition
% Open loop transfer function: θ(s)/Ea(s)
% G(s) = K / [(Js + b)(Las + Ra) + K^2]
% Coefficients calculation
num = K;
den_coeff = [J*La, (J*Ra + b*La), (b*Ra + K^2)];
den = den_coeff;
% Create transfer function
G = tf(num, den);
% Display the transfer function
fprintf('Open Loop Transfer Function:\n');
fprintf('G(s) = %.4f / (%.4fs^2 + %.4fs + %.4f)\n', num, den(1), den(2), den(3));
%% Performance Specifications
% Desired specifications:
% - Settling time (Ts) < 2 seconds
% - Percentage Overshoot (PO) < 5%
% - Steady State Error (SSE) < 1%
fprintf('\nDesired Specifications:\n');
fprintf('- Settling time (Ts) < 2 seconds\n');
fprintf('- Percentage Overshoot (PO) < 5%%\n');
fprintf('- Steady State Error (SSE) < 1%%\n\n');
%% Step 1: Open Loop Response
fprintf('=== STEP 1: OPEN LOOP RESPONSE ===\n');
figure(1);
[y1, t1] = step(G);
plot(t1, y1, 'b-', 'LineWidth', 2);
title('Open Loop Step Response');
xlabel('Time (seconds)');
ylabel('Angular Position (rad)');
grid on;
% Calculate performance metrics for open loop
stepinfo_ol = stepinfo(G);
fprintf('Open Loop Performance:\n');
fprintf('Rise Time (Tr): %.4f seconds\n', stepinfo_ol.RiseTime);
fprintf('Settling Time (Ts): %.4f seconds\n', stepinfo_ol.SettlingTime);
fprintf('Peak Overshoot: %.2f%%\n', stepinfo_ol.Overshoot);
% Steady state error calculation (for unit step)
% For Type 0 system: ess = 1/(1+Kp) where Kp = lim s->0 G(s)
Kp_ol = dcgain(G);
ess_ol = 1/(1+Kp_ol) * 100; % Convert to percentage
fprintf('Steady State Error: %.2f%%\n', ess_ol);
fprintf('Comments: Open loop system is unstable or has poor performance\n\n');
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