How To Plot Transfer Functions In Matlab?

To plot a transfer function in MATLAB, first define the system using the Laplace variable s = tf('s') or coefficient vectors with G = tf(num, den) from the Control System Toolbox. You can then generate time-domain responses using step(G) and impulse(G), frequency-domain responses using bode(G) and nyquist(G), or stability plots using rlocus(G) (Root Locus) and pzmap(G) (Pole-Zero Map).

Step 1: Defining the Transfer Function

You can define continuous-time transfer functions using either polynomial coefficients or direct algebraic Laplace expressions:

% Method A: Direct Laplace Variable Notation (Recommended)
s = tf('s');
G = (10 * (s + 2)) / (s^3 + 4*s^2 + 6*s + 10);

% Method B: Numerator and Denominator Coefficient Vectors
% Equivalent to: (10s + 20) / (s^3 + 4s^2 + 6s + 10)
num = [10, 20];
den = [1, 4, 6, 10];
G = tf(num, den);

% Display transfer function in Command Window
disp(G);

Step 2: Time-Domain Analysis Plots

1. Step Response (Transient Metrics: Rise Time, Settling Time, Overshoot)

figure('Name', 'Step Response Analysis', 'Color', 'w');
step(G);
grid on;
title('Step Response of Closed-Loop System');

% Extract numerical step response characteristics
info = stepinfo(G);
fprintf('Rise Time: %.2f s, Settling Time: %.2f s, Overshoot: %.2f%%\n', ...
    info.RiseTime, info.SettlingTime, info.Overshoot);

2. Impulse Response & Custom Input Simulation (lsim)

% Impulse Response
figure('Color', 'w');
impulse(G);
grid on;
title('Impulse Response');

% Arbitrary Input Simulation (e.g., Sine Wave Input)
t = 0:0.01:10; % Time vector
u = sin(2 * pi * 0.5 * t); % 0.5 Hz sine wave input
figure('Color', 'w');
lsim(G, u, t);
grid on;
title('Linear Simulation with Sinusoidal Input');

Step 3: Frequency-Domain Analysis Plots

1. Bode Plot (Magnitude & Phase Margins)

figure('Name', 'Bode Analysis', 'Color', 'w');
% margin() plots the Bode diagram and displays Gain Margin (Gm) and Phase Margin (Pm)
margin(G);
grid on;

% Extract stability margins numerically
[Gm, Pm, Wcg, Wcp] = margin(G);
fprintf('Gain Margin: %.2f dB, Phase Margin: %.2f deg\n', 20*log10(Gm), Pm);

2. Nyquist Diagram & Nichols Chart

% Nyquist Plot (Evaluates encirclements of the critical -1+0j point)
figure('Color', 'w');
nyquist(G);
grid on;
title('Nyquist Diagram');

% Nichols Chart (Open-loop to closed-loop gain/phase grid)
figure('Color', 'w');
nichols(G);
grid on;
ngrid; % Overlay closed-loop M and N contours

Step 4: Stability & Pole-Zero Plots

1. Root Locus (Closed-Loop Pole Trajectory vs Gain \(K\))

figure('Color', 'w');
rlocus(G);
grid on;
title('Root Locus Diagram');
sgrid; % Overlay damping ratio (zeta) and natural frequency (wn) lines

2. Pole-Zero Map (pzmap)

figure('Color', 'w');
pzmap(G);
grid on;
title('Open-Loop Pole-Zero Map');

% Check stability directly
is_stable = isstable(G);
if is_stable
    disp('The system is open-loop stable.');
else
    disp('The system is open-loop unstable (Poles exist in right-half plane).');
end

Interactive Visual GUI: Linear System Analyzer

If you want to view the Step Response, Bode Plot, Nyquist Diagram, and Root Locus simultaneously in an interactive dashboard, launch the Linear System Analyzer by typing:

linearSystemAnalyzer(G);

Essential Transfer Function Plotting Functions