What is a Nyquist plot used for in control and feedback systems?

• A. The plot shows the time-domain response to a step input.
• B. Nyquist plots complex loop gain L(jω) around the -1 point; stability is assessed by encirclements of -1.
• C. Nyquist plots only the magnitude response and ignores phase.
• D. Nyquist criterion guarantees stability for all systems.

Answer: (B)

Nyquist plots the complex loop gain L(jω) as frequency ω sweeps, so you see both how big the gain is and how its phase shifts in one picture. The key point is the -1 point on the real axis: when the loop gain equals one with a phase of -180 degrees, the feedback effectively becomes positive and can make the system unstable. The Nyquist criterion uses this by counting how many times and in which direction the plot encircles the point -1 as ω goes from 0 to ∞, while also knowing how many right-half-plane poles the open-loop transfer function has. From that encirclement count, you can determine how many unstable poles the closed-loop system will have. If there are no right-half-plane open-loop poles and the plot does not encircle -1, the closed-loop system is stable. So this plotting approach is about the loop’s complex gain and encirclements around -1 to judge stability. It’s not a time-domain step response, it doesn’t show only magnitude, and stability isn’t guaranteed for all systems without considering the open-loop pole structure and the encirclement count.