Unformatted text preview: o a first-order system.
Then, what is the output?
0 0 TF from motor input voltage to
motor speed is 1st-oder
1stmotor position is 2nd-order
2nd(Partial fraction expansion)
5 How to eliminate steady-state error
Make a feedback system with a controller having
an integrator (copy of Laplace transform of a unit
step function): Meaning of K and T
K : Gain
K=1,T=1 Final (steady-state) value
Final (steady- 1 0.8 Controller T : Time constant
Time 1 Time when response
rises 63% of final value
Indication of speed of
Response is faster as T
becomes smaller. 0 One has to select controller parameters
to stabilize the feedback system.
Suppose K=T=1, and obtain such parameters!
7 Amplitude u(t)
u(t) 6 0.6 0.4 0.2 0
0 1 2 3
Time 4 5 6 8 DC gain for a general system Settling time of 1st-order systems DC gain : Final value of a unit step response
For first-order systems, DC gain is K.
For firstFor a general stable system G, DC gain is G(0).
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- Spring '08