Howtosignalprocessing
- What is Nyquist contour and the effect of poles at the origin?
- How many poles does a Nyquist plot have?
- What is poles in Nyquist plot?
- What is the gain at the origin of the Nyquist plot?
- What is the necessary condition for Nyquist plot?
What is Nyquist contour and the effect of poles at the origin?
For a single pole at the origin, the Nyquist curve will approach infinity as approaches zero from both the positive and negative direction. The Nyquist curve can then be "closed" by tracing around a small semicircle to the left of the pole (as shown in Figure 9.3a).
How many poles does a Nyquist plot have?
The system has 1 unstable poles. If K>2, then −0.5K<−1, the Nyquist plot encircle −1 counterclockwise once.
What is poles in Nyquist plot?
Nyquist stability criterion states the number of encirclements about the critical point (1+j0) must be equal to the poles of characteristic equation, which is nothing but the poles of the open loop transfer function in the right half of the 's' plane.
What is the gain at the origin of the Nyquist plot?
We can check this by finding the location of the zeros of the characteristic equation: This has roots at s=-4.64, -0.18±2.07 so the system is stable as expected. Since the gain margin is 3.52 dB (=1.5), this tells us that we could increase the gain by up to a factor of 1.5 before the system goes unstable.
What is the necessary condition for Nyquist plot?
must be equal to the number of open-loop poles in the RHP. Any clockwise encirclements of the critical point by the open-loop frequency response (when judged from low frequency to high frequency) would indicate that the feedback control system would be destabilizing if the loop were closed.
