NyquistBodeanalys

NyquistBodeanalys is a method in control theory that combines Nyquist plot analysis with Bode plot analysis to evaluate the stability and performance of a linear time-invariant feedback system. The approach uses the open-loop transfer function L(s) = G(s)H(s) and its frequency response to assess both stability margins and dynamic behavior.

The Nyquist plot represents the open-loop response in the complex plane by plotting L(jω) as ω runs from 0 to ∞ (and, when needed, from −∞ to 0). It is used with the Nyquist criterion to determine how the plot encircles the critical point −1, which relates to the location of closed-loop poles. The Bode plot shows the magnitude |L(jω)| and phase ∠L(jω) versus frequency, from which gain margin, phase margin, bandwidth, and resonance characteristics can be read. Together, the plots provide a view of robustness to gain changes and model uncertainty, and of the frequency-dependent performance.

Methodology typically involves deriving L(s) from the plant and controller, generating Bode plots to identify crossover frequencies and margins, and constructing the Nyquist plot to check stability constraints. For unity feedback, the Nyquist criterion states that the number of encirclements of −1 equals the number of unstable open-loop poles minus the number of unstable closed-loop poles. In practice, NyquistBodeanalys supports controller design and tuning by aligning phase and gain margins with desired bandwidth and disturbance rejection.

Limitations include reliance on linear time-invariant models and the need for accurate frequency response data. See also Nyquist criterion, Bode plot, control theory.