文档介绍：Handout #5
Prof. J. P. How September 28, 2007
. TBD Due: October 5, 2007
Homework Assignment #4
1. The goal is to design an autopilot for the altitude dynamics of an airplane. Overall,
the only important dynamics are the long period (phugoid) motion, which gives the
transfer function from elevator input to height output of
h(s) 15(s + )
=
2
δe(s) s(s + + )
The input to the autopilot also includes the desired height hc, resulting in the error
e(s) = hc(s) − h(s), and δe(s) = Gc(s)e(s).
(a) Use Matlab to obtain the Bode plot of this system. Choose a constant so that
with Gc(s) = K, the system has a crossover frequency of rad/sec. For this
value of K would the system be stable, if so, what are the gain and phase margins?
(b) For your design, what would be the steady-state error if mand was a ramp
at 3 ft/sec?
(c) Now consider a pensator for the system - choose the parameters of Gc(s)
◦
so that ωc = rad/sec as before, but the phase margin is 50 . Compare the
Bode plot of KG(s) with Gc(s)G(s). Is everything as expected?
(d) What is the steady-state error if mand was a ramp at 3 ft/sec for the
system with a lead controller? Design pensator that could decrease this
error by a factor of 2.
2. Consider the homogeneous system
x˙(t) = A(t)x(t)
with initial condition x(t0)