Analysis

NyquistPlot Block

Visualizes the complex plane frequency response (Real vs Imaginary).

Description

The Nyquist Plot block visualizes the frequency response of a system as a polar plot in the complex plane. It plots the real part of the frequency response on the horizontal axis and the imaginary part on the vertical axis.

The Nyquist plot is a powerful tool for analyzing closed-loop stability using the open-loop frequency response. It captures both magnitude and phase information in a single, intuitive trajectory.

Mathematical Model

The plot maps the loop transfer function $L(j\omega)$ for $0 \leq \omega < \infty$.

Real Axis: $Re[L(j\omega)]$
Imaginary Axis: $Im[L(j\omega)]$

Stability can be determined by counting encirclemtents of the critical point $(-1, j0)$.

Parameters

Title (`title`)

Heading shown above the plot area.

Type: string
Default: Nyquist Plot

Show Unit Circle (`showUnitCircle`)

Toggle visibility of the unit circle (radius=1) centered at the origin.

Type: boolean
Default: true
Use Case: Helps visualize the gain margin and phase margin transition points.

Examples

Stable First-Order System

System: $G(s) = \frac{1}{s + 1}$. The Nyquist plot is a semi-circle in the right half-plane, starting at (1, 0) for $\omega=0$ and ending at (0, 0) for $\omega \to \infty$.

Conditionally Stable System

A higher-order system might pass close to the $(-1, j0)$ point. The Nyquist plot helps visualize how much phase lag or gain can be added before the system becomes unstable.

Remarks

Polar Interpretation: The distance from the origin is the magnitude $|L(j\omega)|$, and the angle from the positive real axis is the phase $\angle L(j\omega)$.
Stability Analysis: A closed-loop system is stable if the number of counter-clockwise encirclements of the $(-1, j0)$ point equals the number of open-loop poles in the right-half plane.
Interactive Update: Like the Bode plot, the Nyquist plot updates in real-time as the simulation frequency sweep progresses.