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Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Feedback Control of Dynamic Systems (7th edition) - Problem 7.25

Transcribed Image Text:Consider the system in Fig. 7.87.
7.25
Figure 7.87
System for Problem 7.25
-o Y
s2+4
(a) Write a set of equations that describes this system in the standard canonical
control form as x = AxBu and y Cx
(b) Design a control law of the form
u
Ki K2
2j
which will place the closed-loop poles at s= -2
Expert Solution
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- An operational-amplifier circuit that may be used as a controller is shown in Figure Qla. (a) R4 ww R1 R3 e Co Figure Qla R1, R2, R3 and R4 are resistors and C1 and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: (i) obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and Eo(s)/E(s). (ii) hence obtain the complete transfer function for the system, i.e. Eo(s)/Ei(s). (iii) Determine D(s) = Eo(s)/E:(s) when R1 = R2 = R3 = R4 = 1 N and C1=1 F, C2= 2 F. %3D (b) Consider the closed-loop control system shown in Figure Qlb. 1 Σ K.D(s) (s +2) Figure Qlb K is the gain and D(s) is the transfer function obtained in part (a)-iii. (i) Plot open loop zeros and poles for the above system in the s-plane. [. Determine whether the point (-1+j) is a closed loop pole for any value of K, by considering the angle criterion at this point. (ii) (c) Briefly summarise the steps, which need to be…arrow_forwardB pleasearrow_forward
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