文档介绍：Handout #4
Prof. J. P. How September 14, 2007
. TBD Due: September 21, 2007
Homework Assignment #2
1. The open loop transfer function of a closed-loop control system with unity negative
gain feedback is
K
G(s) =
s(s + 2)(s2 + 6s + 36)
• Use Matlab to plot the root locus for this system
• Determine the closed-loop gain that gives an effective damping ratio of for
the closed-loop poles closest to the origin.
• Compare the step response with a second order system with poles that have the
same frequency and damping ratio as these closed-loop poles – to what extent do
you think the response of Gcl(s) is dominated by the response of these poles?
2. A unity gain negative feedback system has an open-loop transfer function given by
K(1 + 5s)
G(s) =
s(1 + 10s)(1 + s)2
Use Matlab to draw a Bode diagram for this system and determine the loop gain K
required for a phase margin of 20 degs. What is the gain margin?
(a) A pensator
1 + 10s
G (s) =
c 1 + 50s
is added to this system. Use Bode diagrams to find the reduction in steady state
error following a ramp change to the reference input, assuming that the 20 deg
phase margin is maintained.
3. Plot the Nyquist diagram for the plant with the unstable open-loop transfer function
K(s + )
G(s) =
s(s2 + 2s − 1)
Determine the range of