Now that we are done with the Basics of Control Systems and Signal Flow Graph and Block Diagram Reduction Techniques, let us get to the next chapter – Stability of Control Systems. In these free GATE 2019 Notes, we will deal with the Concept of Stability for Linear Time Invariant (LTI) Systems. We discuss the conditions that should be satisfied for a LTI system to be stable. This article deals with the Stability of Control Systems and covers concepts like BIBO stability, Condition for Stability, Marginal Stability, Asymptotic Stability, Conditional Stability, Absolute Stability and Relative Stability
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| Event Details | Specifications |
| Exam Name | GATE (Graduate Aptitude Test in Engineering) |
| Conducting Body | IIT Madras |
| Exam Level | National Level Examination |
| Exam Mode | Online |
| Exam Duration | 180 minutes (3 hours) |
| Language | English |
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It can also be said as for input r(t) being |r(t)| ≤ M1 < ∞; the output c(t) will be
|c(t)| ≤ M2 < ∞.
For a single pair of roots on imaginary line, the system is Marginally Stable, which means a slight disturbance can push it towards instability. For double pair of roots at imaginary line, the system will be unstable. Similar case will be for a single root at origin and a pair of roots at origin. As shown above, for the roots which are in negative s-plane i.e. having negative real part the system will be stable. On the other hand, roots having positive real part constitute for an unstable system.
Another property of system which we look at is Relative Stability. It is the measure of relative response of transients dying with respect to time for different poles. The farther the poles are on left side of negative S – plane, the more quickly the transients will dry. The relative response of system with respect to position of poles is illustrated below.
This was the basic concept of S tability of Control Systems . In next article we will explore the Routh-Hurwitz Stability Criteria .
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