Q8Control System
Question
Q.8. Explain Nyquist stability criterion.
Answer
The Nyquist criterion states that the number of closed-loop right-half-plane poles Z equals N + P, where N is the number of clockwise encirclements of the (-1, j0) point by the G(jω)H(jω) plot and P is the number of open-loop right-half-plane poles; the system is stable if Z = 0.
The Nyquist stability criterion relates the encirclement of the critical point (-1 + j0) by the open-loop frequency response G(jω)H(jω), plotted for ω from -∞ to +∞ (the Nyquist plot), to the stability of the closed-loop system, via:
where P is the number of open-loop poles of G(s)H(s) in the right-half s-plane, N is the number of clockwise encirclements of (-1, j0), and Z is the number of closed-loop poles in the right-half plane. The closed-loop system is stable if and only if Z = 0.