splane1

splane1 - S Plane Control Xia Hong May 14, 2004 Books: Dorf...

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S Plane Control Xia Hong May 14, 2004
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Books: Dorf and Bishop (1998) Modern Control Systems Addison and Wesley Franklin, Powell and Emami-Naeini (1994) Feedback Control of Dynamic Systems Ad- dison and Wesley. Kuo (1995) Automatic Control Systems Wi- ley. Nise (2000) Control Systems Engineering Wiley Philips and Harbor (2000) Feedback Con- trol Systems Prentice-Hall. 1
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Stability: The total response of a system is the sum of the forced and natural responses: c ( t )= c forced ( t )+ c natural ( t ) 1. A linear, time-invariant system is stable if the natural response approached zero as time approaches infinity. 2. A linear, time-invariant system is unstable is the natural response grows without bound as time approaches infinity. 3. A linear, time-invariant system is marginally stable if the natural response neither decays or grow, but remains constant or oscillates as time approaches infinity. 2
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By looking at the placement of the poles of a system in the s-plane we can draw conclusions about the stability of a system. 1. If the poles of the closed loop are in the left half of the s-plane (negative and real), the system is stable. 2. If the poles of the closed loop are in the right half of the s-place (positive and real), the system is unstable.
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This note was uploaded on 01/23/2012 for the course EE 4580 taught by Professor Gu during the Fall '10 term at LSU.

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splane1 - S Plane Control Xia Hong May 14, 2004 Books: Dorf...

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