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Stability part 1

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

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Chapter 6 Stability (c) 2010 Farrokh Sharifi

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Objectives To learn: d i h bili f 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
Introduction (section 6 1) Introduction (section 6.1) • Control Design Requirements: Control Design Requirements: - Transient Response - Stability (in this chapter) - Stability (in this chapter) - Steady-state Errors (next chapter) Transient response and Steady-state Error are meaningless for an unstable system meaningless for an unstable system. This chapter investigates stability for linear time- invariant (LTI) systems (c) 2010 Farrokh Sharifi invariant (LTI) systems.

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Introduction What is stability? System total response: ( ) ( ) ( ) c t c t c t • If results in then the LTI system is forced natural t   ( ) natural c t   unstable. • If results in then the LTI system is t bl t   ( ) 0 natural c t stable. • If results in remaining constant or oscillating then the LTI system is marginally stable t   ( ) natural c t (c) 2010 Farrokh Sharifi oscillating, then the LTI system is marginally stable.