Lecture Notes (13)

# For g relation between time and exponential decay

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Unformatted text preview: elation between time and exponential decay Relation Final value theorem Examples Examples 5% settling time is about 3T! 2% settling time is about 4T! 9 Step response for some K & T K=1,T=1 K=1,T=2 Amplitude Amplitude 1 5 Time K=2,T=1 1 Unknown 5 Time K=2,T=2 5 Time Obtain step response Obtain 10 10 2 Amplitude Amplitude Suppose that we have a “black-box” system Suppose 0 0 10 2 1 0 0 System identification 2 2 0 0 10 5 Time 10 1 0 0 Can you obtain a transfer function? How? Can 11 12 Ramp response for 1st-order system Ramp response for 1st-order system K =1 ,T =1 5 Input a unit ramp function to a 1st-order system. Input Then, what is the output? y(t) y(t) 0 0 4 Amplitude Amplitude u(t)=t u(t)=t K=1,T=1 y(t) y(t) u(t)=t u(t)=t 3 slope 2 1 0 0 1 2 T im e Time 3 4 5 Steady state response Steady We may want to modify the system s.t. We (Partial fraction expansion) 13 How to eliminate steady-state error Make a feedback system with a controller having Make a double integrator (copy of Laplace transform of ramp function): u(t)=t u(t)=t Controller 14 Summary and exercises Time response for 1st-order systems Time Step and ramp responses Step Time constant and DC gain Time System identification System Next, time response for 2nd-order systems Next, Exercises Exercises 0 Review examples in this lecture. Review One has to select controller parameters to stabilize the feedback system. Suppose K=T=1, and obtain such parameters! 15 16...
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## This document was uploaded on 03/02/2014 for the course ME 451 at Michigan State University.

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