This is the code I created and it solves that problem.
clc clear % Declaration of Omega_n Value wn = 3; % Zeta Values for Each Variation z1 = 1; z2 = 2; z3 = 0.1; z4 = 0.5; z5 = 0; % Numerator and Denominator Values for Each Variation num1 = wn^2; den1 = [1 2*z1*wn wn^2]; num2 = wn^2; den2 = [1 2*z2*wn wn^2]; num3 = wn^2; den3 = [1 2*z3*wn wn^2]; num4 = wn^2; den4 = [1 2*z4*wn wn^2]; num5 = wn^2; den5 = [1 2*z5*wn wn^2]; figure; % When Zeta = 1 sys_tf1 = tf(num1, den1); % Pole Zero Map subplot(2,5,1) pzmap(sys_tf1); title(['Pole Zero Map (Zeta = ', num2str(z1), ')']) % Step Response subplot(2,5,6) step(sys_tf1); title(['Step Response (Zeta = ', num2str(z1), ')']) % When Zeta = 2 sys_tf2 = tf(num2, den2); % Pole Zero Map subplot(2,5,2) pzmap(sys_tf2); title(['Pole Zero Map (Zeta = ', num2str(z2), ')']) % Step Response subplot(2,5,7) step(sys_tf2); title(['Step Response (Zeta = ', num2str(z2), ')']) % When Zeta = 0.1 sys_tf3 = tf(num3, den3); % Pole Zero Map subplot(2,5,3) pzmap(sys_tf3); title(['Pole Zero Map (Zeta = ', num2str(z3), ')']) % Step Response subplot(2,5,8) step(sys_tf3); title(['Step Response (Zeta = ', num2str(z3), ')']) % When Zeta = 0.5 sys_tf4 = tf(num4, den4); % Pole Zero Map subplot(2,5,4) pzmap(sys_tf4); title(['Pole Zero Map (Zeta = ', num2str(z4), ')']) % Step Response subplot(2,5,9) step(sys_tf4); title(['Step Response (Zeta = ', num2str(z4), ')']) % When Zeta = 0 sys_tf5 = tf(num5, den5); % Pole Zero Map subplot(2,5,5) pzmap(sys_tf5); title(['Pole Zero Map (Zeta = ', num2str(z5), ')']) % Step Response subplot(2,5,10) step(sys_tf5,5); title(['Step Response (Zeta = ', num2str(z5), ')']) % Displaying damping mode information and time domain specifications for z = [z1, z2, z3, z4, z5] if z == 0 disp(['Mode of damping for Zeta = ', num2str(z), ': Undamped']); elseif 0 < z && z < 1 % Displaying damping mode information disp(['Mode of damping for Zeta = ', num2str(z), ': Underdamped']); % Calculating and displaying time domain specifications % Rise Time tr = pi / (wn * sqrt(1 - z^2)); disp(['Rise Time: ', num2str(tr)]); % Settling Time ts = 4 / (z * wn); disp(['Settling Time: ', num2str(ts)]); % Natural Frequency of Oscillation fn = wn * sqrt(1 - z^2); disp(['Natural Frequency of Oscillation: ', num2str(fn)]); elseif z == 1 disp(['Mode of damping for Zeta = ', num2str(z), ': Critically Damped']); elseif z > 1 disp(['Mode of damping for Zeta = ', num2str(z), ': Overdamped']); end disp(' '); % Empty line break end
