MATLAB Plotting of Bode Plots, Nyquist Plots, and Root Locus Plots with Implementation Insights

In control system analysis and design, Bode plots, Nyquist plots, and root locus plots are three commonly used tools for frequency response and stability analysis. While MATLAB has built-in functions for generating these plots (such as `bode`, `nyquist`, and `rlocus`), manually programming simple plotting routines helps deepen the understanding of their underlying principles and offers greater flexibility for teaching demonstrations.

### 1. Bode Plot A Bode plot consists of magnitude-frequency and phase-frequency characteristic curves, providing intuitive visualization of how system gain and phase vary with frequency. When programming in MATLAB, one can generate logarithmic frequency points, compute the magnitude and phase of the transfer function, and then use `subplot` to separately plot magnitude and phase curves. This implementation approach works for any transfer function and is particularly suitable for analyzing first-order and second-order system characteristics in exercises. Code implementation typically involves using `freqs` or `bode` calculations with custom plotting logic to demonstrate frequency response principles.

### 2. Nyquist Plot Nyquist plots display the frequency response trajectory of a system on the complex plane, used for determining closed-loop system stability. When programming manually, one can first compute the frequency response in complex form, then plot the relationship between real and imaginary parts. Compared to built-in functions, custom programs allow more flexible adjustments to frequency ranges and plotting styles, making them ideal for teaching demonstrations. The algorithm involves evaluating the transfer function at various frequencies and plotting imag(G(jω)) versus real(G(jω)) to create the Nyquist contour.

### 3. Root Locus Plot Root locus plots show the movement trajectory of system poles as the open-loop gain varies. Although MATLAB's `rlocus` function can automatically generate these plots, manual calculation and plotting provide more intuitive understanding of how gain changes affect system stability. By iterating through different gain values and solving the roots of the characteristic equation, one can progressively trace the root locus variation trend. Implementation typically involves using root-finding algorithms like `roots()` for polynomial equations while sweeping through gain parameter values.

These simplified MATLAB plotting programs, while less powerful than built-in functions, prove highly practical for teaching and exercise analysis, helping learners better understand control system frequency characteristics and stability criteria through hands-on implementation.