ME 4710 Motion and Control
Homework #3
The following problems are from Dorf and Bishop, 12th Ed., Prentice-Hall, 2011. Generate your results
using M-files in MATLAB, publish the results in PDF format, and email your M-file and the published
results to the instructor. Any “hand” calculations may be included in the M-file (so they appear in your
published results), as a separate PDF document, or you can submit them on paper.
1. Consider the system described in problem E8.6. Using the forward-path transfer function
500 K
Gc ( s )G ( s ) 
, and assuming the system has negative unity feedback, complete the
s( s  5)( s  100)
following using MATLAB:
o Plot the Bode diagram for the system with K  10 using the “bode” command. Using this diagram,
calculate the additional gain K a required to make the system marginally stable. The limiting gain for
stability is then K limit  K  K a .
o Use the “margin” command to verify the value of K limit calculated above. That is, verify that the gain
and phase margins are close to zero for a gain of K limit .
o Use the “rlocus” and “rlocfind” commands to verify the value of K that you found above. That is,
using a root locus diagram, verify that a gain of K limit will cause the closed loop system to be
marginally stable.
2. DP 8.1. Complete parts (a) – (e) as given in the text. In completing part (d), you can use Figure 8.11
to help you estimate an appropriate damping ratio for the complex poles of the closed loop system to
make the raw magnitude at resonance M r  2 (and 20 log( M r )  6 (dB) ). Note: The text uses the
symbol M p to represent the raw magnitude at resonance, and the ME 4710 course notes use the
symbol M r .
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