Question: P12.10 A satellite system can be modeled as a double integrator with a plant transfer function G s s 10 . 2 ( ) =
P12.10 A satellite system can be modeled as a double integrator with a plant transfer function G s
s
10
.
2
( ) =
We want to use a PID controller and a prefilter with unity feedback for the system to achieve the require
ments of P.O. = 2% and settling time Ts = 2 sec. The desired characteristic poles for third-order systems as per ITAE and Bessel polynomials normalized at
ωn = 1 rad/s are given as:

Design the PID and the prefilter. Plot the step response of the system.
(s+ 0.7081)(s + 0.5210+ 1.0681)(s + 0.5210-j1.0681) Bessel: (s + 0.9420)(s + 0.7455+ j0.7112)(s + 0.7455 - j0.7112).
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