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 “blackbox” 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 1storder system Ramp response for 1storder system
K =1 ,T =1
5 Input a unit ramp function to a 1storder 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 steadystate 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 1storder systems
Time
Step and ramp responses
Step
Time constant and DC gain
Time
System identification
System Next, time response for 2ndorder 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.
 Spring '08
 KHAN
 Laplace

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