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Stability analysis of closed loop systems in the Z plane - Coggle Diagram
Stability analysis of closed loop systems in the Z plane
Stability of system is given by
Steps to determine the stability
If Z = 1, the system is critically damped
The poles or the roots in closed loop have to be inside of unitary circle
The zeros not affect the stability, hence these can be anywhere, inside or outside of unitary circle
Methods to prove the absolute stability
Th system is stable if
1.- |an|>ao
2.- P(z)|z=1>0
3.-P(z)|z=-1 (>0 to n odd)(<0 to n even)
4.- |q2|>|q0|
Jury's stability test
A table is constructed whose elements are the coefficients of P (Z)
Bilinear transformation and Routh stability criterion
requires transformation from Z plane to w plane
comments about the stability of closed loop systems
it can be useful to use Matlab to generate a diagram of the locus of the roots
it may be useful to use Matlab to directly determine the roots of the characteristic equation
The error signal in a closed loop control system can increase and still be stable
