Nyquist relation is:

• A. N = P − Z
• B. N = Z / P
• C. N = P + Z
• D. N = Z - P

Answer: (D)

The Nyquist relation in control theory and systems engineering expresses the relationship between the number of poles, zeros, and the system's overall behavior. Specifically, it defines the number of system's poles (P), zeros (Z), and the system's transfer function (N).

The correct form of the Nyquist relation can be expressed as N = Z - P, where N represents the number of outward encirclements of the critical point in the Nyquist plot. In this equation, Z indicates the number of zeros of the closed-loop transfer function, and P signifies the number of poles. This relationship is essential because it helps in understanding system stability and how the poles and zeros of a transfer function relate to its frequency response.

By focusing on how many times the Nyquist plot encircles the critical point, which depends on the poles and zeros, engineers can ascertain the stability and response of the system effectively. Thus, the correct answer encapsulates this important concept in control theory, allowing practitioners to analyze and design systems with a clearer understanding of their dynamics.