What does the Nyquist criterion help determine in control systems?

• A. It helps assess the stability of a closed-loop system by analyzing how the open-loop transfer function's frequency response encircles the -1 point.
• B. It determines the time-domain response to a step input.
• C. It measures the system's settling time.
• D. It defines the sampling rate of a digital controller.

Answer: (A)

Nyquist criterion tests whether a feedback system will be stable by looking at the open-loop transfer function’s frequency response. By plotting L(jω) as ω runs from 0 to ∞ (and considering the full Nyquist contour), you watch how this response encircles the critical point −1 in the complex plane. If the open-loop system has no unstable poles, zero encirclements of −1 mean the closed-loop is stable; each encirclement indicates an unstable closed-loop pole, with the exact relationship given by N = P − Z (where N is the encirclements, P is the number of unstable open-loop poles, and Z is the number of unstable closed-loop poles). This approach uses frequency-domain information to infer stability, rather than predicting time-domain responses like step response, settling time, or sampling rate.