Relation between Open and Close Loop System Routh table coefficient of characteristics equation. Note: Routh is only applicable for closed loop system and for implementation of Of poles on imaginary axis (System has undamped natural frequency), system is “If Characteristics Equation contain only even power of S “ or “elements of any oddĬomplete row of Routh table is zero” represents system will contain at least one pair SYSTEM EXHIBITS INSTABILITY DUE TO RESONANCEįor a stable system all elements of first column in Routh table should have same The relative stability of system is improves.Īt least one of the system poles on the imaginaryĪxis is present in the form of a pole in R(s) If poles moves away from imaginary axis towards the left of s-plane If there are repeated poles or roots on imaginary axis, then alsoĥ. If roots lie on the positive half side of s-plane, system if un-stable.Ĥ. If roots lie on imaginary axis, system is called marginally stable orģ. System) must lie in negative half of s plane.Ģ. For a stable system, all roots of characteristic equation (Poles of the Negative direction, has higher stability.ġ. System having poles away from the imaginary axis of S-Plane, in
In term of Damping Ratio, Gain Margin and Phase Margin) Oscillation die out with time and how fast steady state reached. Relative Stability: This is a quantitative measure of how fast system (inīounded Input, Bounded Output: Output must be bounded forĪsymptotic Stability: If system input is remove from the system, thenĪbsolute Stability: A system is stable for all values of system Generally for a stable system oscillations must die out asĮarly as possible or steady state should be reached fast. In Control System STABILITY cab be judged by observing the
Stability of any system is a very important characteristic of
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