System Stability. DNT 354 - Control Principle. Date: 4 th September 2008 Prepared by: Megat Syahirul Amin bin Megat Ali Email: [email protected] Introduction System Stability Routh-Hurwitz Criterion Construction of Routh Table Determining System Stability. Contents.
Stability is the most important system specification. If a system is unstable, the transient response and steady-state errors are in a moot point.
Stable systems have closed-loop transfer functions with poles only in the left half-plane.System Stability
Unstable systems have closed-loop transfer functions with at least one pole in the right half-plane and/or poles of multiplicity greater than 1 on the imaginary axis.System Stability
Marginally stable systems have closed-loop transfer functions with only imaginary axis poles of multiplicity 1 and poles on the imaginary axis.System Stability
To determine stability of a given system, we have to consider the manner in which the system is operating, whether open-loop or closed-loop.
Routh-Hurwitz Stability Criterion: The number of roots of the polynomial that are in the right half-plane is equal to the number of changes in the first column.
an, an-1, …, a1, a0 are constants
n = 1, 2, 3,…, ∞
Equivalent closed-loop transfer function
Initial layout for Routh table
Completed Routh table