Repeat Problem 1.1-4 with the transfer functions Problem 1.1-4 A feedback control system is illustrated in Fig.

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Repeat Problem 1.1-4 with the transfer functionsH(s) = 1 For part (e), recall that the transfer-function underdamped pole term [(s+ a) + b] yields a time =

Problem 1.1-4

A feedback control system is illustrated in Fig. P1.1-4. The plant transfer function is given byR(s) 5 0.2s +1 Compensator Ge(s) G (s) = E(s) Sensor H(s) M(s) Fig. Pl.1-4 Plant Gp(s) C(s)

(a) Write the differential equation of the plant. This equation relates c(t) and m(t) .

(b) Modify the equation of part

(a) to yield the system differential equation; this equation relates c(t) and r(t). The compensator and sensor transfer functions are given byG. (s) = 10, H(s) = 1

(c) Derive the system transfer function from the results of part (b).

(d) It is shown in Problem 1.1-2

(a) that the closed-loop transfer function of the system of Fig.
P1.1-4 is given byG (1)G, (s) R(s) 1+ G.(s) G (s)H(s) Gp c(s)

Use this relationship to verify the results of part (c).

(e) Recall that the transfer-function pole term (s +

a) yields a time constant τ = 1 a , where a is real. Find the time constants for both the open-loop and closed-loop systems.

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Digital Control System Analysis And Design

ISBN: 9780132938310

4th Edition

Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty

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