Stablity analysis in closed loop

The stability of the system is defined by the equation.

mtr

upa

VICTOR ANDRES DIAZ ESTRADA_UP170114

MTR08B

DIGITAL CONTROL

2

or because of the roots of the characteristic equation

3

Rules for a stable system

if a single pole is presented in z=1, then the system is critically stable.

zeroes do not affect absolute stabilising.

rules for a stable system for the system to be stable, closed-looppoles or characteristic equation roots must be presented on the z-plane within the unit circle.

methods to test the stability of the system.

Jury stability

stability by Schur-Cohn

Routh stability

Liapunov stability

characteristic equation

P(z)= a0z^4+a1z^3+a2z^2+a3z+a4

Characteristic equation

w= z+1/z-1
P(z)=a0z^n´+a1z^n-1+...~an-1z+an=0