Análise de Sistemas de Controle

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Problem 6.71 PP
Consider the system shown in Fig. 1{a). 
(a) Construct a Bode plot for the system.
(b) Use your Bode plot to sketch an inverse Nyquist plot. (See Appendix W6.9.2.)
(c) Consider closing a control loop around G(s), as shown in Fig. 1 (b). Using the inverse Nyquist 
plot as a guide, read from your Bode plot the values of GM and PM when K = 0.7,1.0.1.4. and 2. 
What value of K yields PM = 30“?
(d) Construct a root-locus plot, and label the same values of K on the locus. To what value of ^
Ho p s panh nair nf PM/f^M valupa m rrpR nnnri? C nm narp (^vpraiiR P M with thp rniinh
(d) Construct a root-locus plot, and label the same values of K on the locus. To what value of ^ 
does each pair of PM/GM values correspond? Compare ^ versus PM with the rough 
approximation in Fig. 2.
Figure 1 Control system
Figure 2 Damping ratio versus PM
Phue niMgtn
Step-by-step solution
step 1 of 4
Step 2 of 4
Step 3 of 4
K=0.7 ; GM=15.1dB, PM=54.7" 
K=1.0 ; GM=12dB , PM=44.1® 
K=1.4 ; GM=9.12dB, PM=33.1* 
K=2.0 ; GM=6.02dB, PM=21.4"
AtK=1.54, PM=30“
Step 4 of 4
PMd. The s^roximation of ---- is valid in all die cases
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