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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
Amplitude Amplitude 1 5
K=2,T=1 1 Unknown 5
Time Obtain step response
Obtain 10 10 2
Amplitude Amplitude Suppose that we have a “black-box” system
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?
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.
Then, what is the output?
y(t) 0 0 4
u(t)=t K=1,T=1 y(t)
u(t)=t 3 slope 2 1 0 0 1 2 T im e
Time 3 4 5 Steady state response
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
a double integrator (copy of Laplace transform of
u(t)=t Controller 14 Summary and exercises
Time response for 1st-order systems
Step and ramp responses
Time constant and DC gain
System Next, time response for 2nd-order systems
Exercises 0 Review examples in this lecture.
One has to select controller parameters
to stabilize the feedback system.
Suppose K=T=1, and obtain such parameters!
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- Spring '08