% Define the transfer function of the plant K = 1; % You can adjust this value as needed numerator = K; denominator = conv([1 1], [1 4]); % (s 1)(s 4) G = tf(numerator, denominator); % Desired peak time and damping ratio Tp = 1.047; % seconds zeta = 0.8; % Calculate the natural frequency wn = pi / (Tp * sqrt(1 - zeta^2)); % Define the characteristic equation s = tf('s'); desired_char_eq = s^2 2*zeta*wn*s wn^2; % Calculate PID controller gains manually Kp = wn^2; Ki = 2*zeta*wn; Kd = 1; % Create the PID controller transfer function controller = pid(Kp, Ki, Kd); % Calculate the closed-loop transfer function closed_loop_system = feedback(series(controller, G), 1); % Display the PID gains disp(['Proportional Gain (Kp): ' num2str(Kp)]); disp(['Integral Gain (Ki): ' num2str(Ki)]); disp(['Derivative Gain (Kd): ' num2str(Kd)])