Notes-4A

Notes-4A - 90%. Settling time: t s = the time for the step...

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4. Time Domain Analysis Impulse response Step Response Sinusoidal Response Impulse response of first order systems
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Impulse response Natural frequency ω Damping ratio ζ Undamped ζ =0 Underdamped 0< ζ <1 Criticlly damped ζ =1 Overdamped ζ >1 Damped frequency
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Transient and steady state responses y t (t) is transient response y ss (t) is steady state response
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Transient and steady state responses
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Transient and steady state responses
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Step Response Analysis Some typical step responses Note the different shapes of the responses
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Performance Criteria P eak time : t p = the time for the step response to reach the peak value. Overshoot: M p = the maximum amount the system overshots, often in % = M p x100% Bottom Time t b and Percentage Undershoot PU Rise time: t r = the time for the system to reach the vicinity of its new set point = time from 10% to
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Unformatted text preview: 90%. Settling time: t s = the time for the step response to reach within 1% (2% or 5%) of its steady state. 1 st Order System 2 nd Order Systems 2 nd Order Systems Underdamped System: Percentage Overshoot (PO) Settling Time Settling Time Rise Time: Hard to find. Approximation by step response reaching 100% of its final value. Example High Order Systems Additional pole The additional pole will slow the response (longer rise time, longer settling time), reduce overshoot (smaller overshoot). Additional Zeros Minimum zero Nonminimum zero Shorter rise time, bigger overshoot Settling time: no change. Undershoot Dominant Poles and Zeros Dominant poles and zeros Desired dominant poles and zeros Example...
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This note was uploaded on 02/03/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.

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Notes-4A - 90%. Settling time: t s = the time for the step...

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