Bode Plot Analysis with BodePlotA

Plot the Bode Diagram

Function Overview: Bode Plot Analysis with BodePlotA

The BodePlotA function is a robust tool designed to calculate and visualize the frequency response of a transfer function in the Laplace domain. It allows users to analyze how a system behaves across a specified range of frequencies, offering flexible options for plotting the Bode diagram and interacting with the data.

Inputs

1. num (numerator coefficients): Coefficients of the transfer function's numerator.
2. den (denominator coefficients): Coefficients of the transfer function's denominator.
3. Alternatively, H (MATLAB Transfer Function Class): The transfer function can also be provided directly using MATLAB's tf class.
4. fi (initial frequency in Hz): Starting frequency for the frequency response analysis.
5. ff (final frequency in Hz): Ending frequency for the frequency response analysis.
6. res (frequency resolution in Hz): Determines the granularity of the frequency response calculation.
7. p (plot flag):

• 0: No Bode diagram is plotted.
• 1: The Bode diagram (magnitude and phase) is plotted.

1. cursor (cursor flag, optional):

• 0: Cursor is disabled on the plot.
• 1: Cursor is enabled for detailed inspection.

Outputs

1. F (frequency vector in Hz): A vector containing the frequencies used for the analysis.
2. Gain (frequency response in dB): The magnitude response of the transfer function at each frequency.
3. Phase (phase response in degrees): The phase of the transfer function at each frequency.

Example 1: Using num and den Coefficients MATLAB Code

wn = 2*pi*100; % Natural frequency in rad/s

xi = 0.707; % Damping ratio

num = [0 0 wn^2]; % Numerator coefficients

den = [1 2*xi*wn wn^2]; % Denominator coefficients

fi = 0.1; % Initial frequency (Hz)

ff = 10000; % Final frequency (Hz)

res = 0.1; % Frequency resolution (Hz)

[F, Gain, Phase] = BodePlotA(num, den, fi, ff, res, 1, 1);

Explanation

1. System Definition:

• The system's natural frequency is set at 100 Hz, and the damping ratio is 0.707, which corresponds to a critically damped response.
• The transfer function is defined using the numerator num and denominator den coefficients.

1. Frequency Range:

• The frequency response is computed from 0.1 Hz to 10,000 Hz, with a resolution of 0.1 Hz.

1. Visualization:

• The plot flag p = 1 ensures that the Bode diagram is displayed.
• The cursor flag cursor = 1 enables interactive exploration of the plot.

Example 2: Using a Transfer Function Object MATLAB Code

wn = 2*pi*100; % Natural frequency in rad/s

xi = 0.707; % Damping ratio

num = [0 0 wn^2]; % Numerator coefficients

den = [1 2*xi*wn wn^2]; % Denominator coefficients

s = tf('s'); % Define the Laplace variable

H = (wn^2) / (s^2 + 2*xi*wn*s + wn^2); % Transfer function in MATLAB's tf format

fi = 0.1; % Initial frequency (Hz)

ff = 10000; % Final frequency (Hz)

res = 0.1; % Frequency resolution (Hz)

[F, Gain, Phase] = BodePlotA(H, fi, ff, res, 1, 1);

Explanation

1. Transfer Function Object:

• The transfer function is defined directly using MATLAB's tf class as ( H(s) = \frac{\omega_n2}{s2 + 2\xi\omega_n s + \omega_n^2} ).

1. Frequency Range and Resolution:

• Similar to Example 1, the frequency range is 0.1 Hz to 10,000 Hz, and the resolution is 0.1 Hz.

1. Visualization and Interaction:

• The Bode diagram is plotted (p = 1), and the cursor is enabled (cursor = 1).

Practical Applications

These examples show how to use the BodePlotA function to analyze the frequency response of a system, either by specifying numerator and denominator coefficients or by using MATLAB's transfer function object. The flexibility of the function makes it a valuable tool in control systems, signal processing, and system dynamics analysis.