A Nyquist plot is a graphical representation used in control engineering. It is used to analyze the stability and frequency response of a system. The plot represents the complex transfer function of a system in a complex plane. The x-axis represents the real part of the complex numbers and the y-axis represents the imaginary part. Each point on the Nyquist plot reflects the complex value of the transfer function at that frequency.
Nyquist Stability Criteria
It is used to determine the stability of a control system. This criterion works on the principle of argument. It is useful for feedback control system analysis and is expressed in terms of frequency domain plot. It is applicable for minimum and non-minimum phase systems.
Nyquist PlotAccording to the Nyquist Stability Criterion the number of encirclement of the point (-1, 0) is equal to the P-Z times of the closed loop transfer function. The equation for stability analysis is given below:
N = Z - P ------ (equation 1)
Where,
P = open loop pole of the system on right hand side (RHP)
Z = close loop zero of the system on right hand side (RHP)
N = number of encirclement around (-1,0)
Note: 'N' is negative for anticlockwise encirclement around (-1,0) and positive for clockwise encirclement around (-1,0).
Stability Cases:
N (encirclements)
| Condition
| Stability
|
|---|
0 (no encirclement)
| Z = P = 0 $ Z = P
| Marginally stable
|
N > 0 (clockwise encirclement)
| P = 0, Z ≠0 & Z > P
| Unstable
|
N < 0 (anti-clockwise encirclements)
| Z = 0, P ≠0 & P > Z
| Stable
|
Principle of Argument in Nyquist Plot
It states that if