Page 207 - MATLAB an introduction with applications

192 ——— MATLAB: An Introduction with Applications

R(s) + K C(s)
s(s+3)(s+5)(s+7)
–

s ( + 25 )
s ( 2 + 10 s + 100 )
Fig. P3.6

P3.7: Write a program in MATLAB to obtain a Bode plot for the transfer function
(5s + 51s + 20s + 400)
3
2
() =
Gs
(s + 12s + 60s + 300s + 250)
4
2
3
P3.8: Write a program in MATLAB for the unity feedback system with G(s) = K/[s(s + 7) (s + 15)] so that
the value of gain K can be input. Display the Bode plots of t, a system for the input value of K. Determine
and display the gain and phase margin for the input value of K.
P3.9: Write a program in MATLAB for the system shown in Fig. P3.9 so that the value of K can be input
(K = 40).
R(s) + E(s) K s ( + ) 3 C(s)
2
s ( s + 4 s+ 20 )
–

Fig. P3.9

(a) Display the closed-loop magnitude and phase frequency response for unity feedback system
with an open-loop transfer function, KG(s).
(b) Determine and display the peak magnitude, frequency of the peak magnitude and bandwidth for
the closed-loop frequency response for the input value of K.
P3.10: Write a program in MATLAB for a unity feedback system with the forward-path transfer function
given by
7(s + 3)
() =
Gs
2
( ss + 4s + 12)
(a) Draw a Nichols plot of an open-loop transfer function
(b) The user can read the Nichols plot display and enter the value of M p
(c) Obtain the closed-loop magnitude and phase plots.
(d) Display the expected values of percent overshoot, settling time and peak time
(e) Plot the closed-loop step response.

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