Stability ppt
- 1. Stability of a Control System Topic:
- 2. CONTENTS 01 I n t r o d u c t i o n 03 H u r w i t z a n d R o u t h S t a b i l i t y c r i t e r i o n 02 C o n c e p t o f S t a b i l i t y 04 C o n c l u s i o n
- 3. Stability means whether the system is stable or unstable. Stability is of three types : • Stable system • Unstable system • Marginally stable system
- 4. Types of System • Stable system: The system is said to be stable when only the output is bounded for bounded input. • Unstable system: For a bounded input the output is unbounded in the system. • Marginally stable system: If given an impulse of infinite magnitude as input and given unbounded output, but neither will the output return to zero.
- 5. Stability of a Control System can be classified into 5 chategories: • BIBO(Bounded Input Bounded Output): Output should be bounded for bounded input. • Asymptotic Stability(Zero stability): There will be zero output for zero input. • Absolute Stability: For a bounded input, the system is stable for all the values of system parameters. • Relative Stability: It indicates how close the system is to instability. • Conditional Stability: Stability of a system for a particular range of any or some parameters.
- 6. • If all the coefficient of characterstics equation may lie on the LHS of s-plane. • This is necessary but not sufficient condition to ensure the stability of closed loop system or to ensure that roots of characterstics equation are on the left hand side of s-plane for that we propose Routh Table or Routh Array. • The characterstics equation of the nth order continuous system can be written as: • The stability criterion is applies using a Routh table which is defined as: Routh Hurwitz Criteria • Where an, an-1 ,....a0 are coefficients of the characterstics equation.
- 7. Limitations of Hurwitz Criterion 1. Very time consuming and combursion technique to solve large determinants for higher order systems. 2. It doesn't tell the exact no. of Right half poles. 3. Determinants of marginal stability becomes tough using this method.
- 8. Conclusion • So from the above ppt we were able to know about the basics of stability and also the cocept of stability. • The verification of stability using the Routh Hurwitz criteria helps us to know if a sysytem is stable or not, so in practice it is desired to follow Relative stability.
- 9. • Class notes • Control System- Stability Tutorials • Slideshare-Circuit network analysis- Chapter 5 Reference