The Nyquist plot of the transfer functionDoes not encircle the point (...
Concept:
For Nyquist stability
N = P
P = Number of open-loop poles in RHS of s-plane
N = Number of encirclement about the point (-1 + j0)
N = +ve for anticlockwise
N = -ve for clockwise enduement
Calculation:
The polar plot is drawn as:
Let two points A and B representing -1 + j0 for different values of K,
The Nyquist plot is not encircling -1 + j 0 at A, i.e, K = 10
at B, the Nyquist plot is encircling -1 + j 0 i. e, K = 100
Let us now find the stability for K = 10 and K = 100 using Nyquist
Case: 1
K = 10
N = P - Z
Z = P - N
The Routh table can be drawn as follows:No sign change, hence P = 0 and also N = 0
∴ Z = 0 → CLTP is stable
Case: 2
Z = P - N
N = -2 (two clockwise encirclement)
∴ Z = 2.
hence, CLTP is unstable.