Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K = 2. The complete Nyquist plot of the transfer function G(s) is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume G(s) has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ___________.
- A0
- B1
- C2
- D3
Solution & Step-by-step Explanation
Concept:
Nyquist stability criterion:
N = P – Z
N is the number of encirclements of (-1+j0) point by the Nyquist contour in an anticlockwise direction.
P is the open-loop RHP poles
Z is the closed-loop RHP poles
Analysis:
For K = 1,
For K = 2, the plot will be
N = No. of encirclement about (-1, 0) in anticlockwise.
P = Total number of open loop poles, in R.H.S.
Z = P - N
N = -2, P = 0
Z = 0 - (-2) = 2
Z = 2
Two poles in right side.
Nyquist stability criterion:
N = P – Z
N is the number of encirclements of (-1+j0) point by the Nyquist contour in an anticlockwise direction.
P is the open-loop RHP poles
Z is the closed-loop RHP poles
Analysis:
For K = 1,
For K = 2, the plot will be
N = No. of encirclement about (-1, 0) in anticlockwise.
P = Total number of open loop poles, in R.H.S.
Z = P - N
N = -2, P = 0
Z = 0 - (-2) = 2
Z = 2
Two poles in right side.