Stability part 1

Stability part 1 - Chapter Chapter 6 Stability (c) 2010...

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hapter 6 Chapter 6 Stability (c) 2010 Farrokh Sharifi
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bjectives Objectives o learn: To learn: How to determine the stability of a LTI system using Routh-Hurwitz criterion How to determine system parameters to yeild stability (c) 2010 Farrokh Sharifi
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troduction ection 6 1) Introduction (section 6.1) ontrol Design Requirements: Control Design Requirements: - Transient Response tability (in this chapter) - Stability (in this chapter) - Steady-state Errors (next chapter) • Transient response and Steady-state Error are eaningless for an unstable system meaningless for an unstable system. • This chapter investigates stability for linear time- variant (LTI) systems (c) 2010 Farrokh Sharifi invariant (LTI) systems.
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troduction Introduction • What is stability? y • System total response: ) () t c t c t • If results in then the LTI system is forced natural ct  t  natural unstable. • If results in then the LTI system is b l t 0 natural stable. • If results in remaining constant or scillating then the LTI system is marginally stable t natural (c) 2010 Farrokh Sharifi oscillating, then the LTI system is marginally stable.
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troduction Introduction • If the input is unbounded, forced response could be unbounded as well. (Hard to determine the stability) ounded put Bounded utput (BIBO) Stability: Bounded-Input Bounded-Output (BIBO) Stability: - systemis able every ounded put yields a A system is stable if every bounded input yields a bounded output. (stable systems) - A system is unstable if every bounded input yields a unbounded output. (marginally stable and unstable systems) (c) 2010 Farrokh Sharifi
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troduction Introduction ow to determine if a system is stable? How to determine if a system is stable?
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This note was uploaded on 02/20/2011 for the course MEC 709 taught by Professor Sharifi during the Fall '11 term at Ryerson.

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Stability part 1 - Chapter Chapter 6 Stability (c) 2010...

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