Repeat Problem 1.1-4 with the transfer functions

Problem 1.1-4

A feedback control system is illustrated in Fig. P1.1-4. The plant transfer function is given by

(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 by

(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 by

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.

H(s) = 1 For part (e), recall that the transfer-function underdamped pole term [(s+ a) + b] yields a time = 1/a. constant, T = G(s) = 2, 3s +8 s+25+2 G (s) =