Page 318 - Modern Control Systems

292 Chapter 4 Feedback Control System Characteristics

«(.?) • Y(s)
FIGURE P4.13
Closed-loop
system.

Y(s)
10(.y + 4)
R(s) -• Flighi
s(s + n)(s+ 1)
FIGURE P4.14 speed
Hypersonic airplane
speed control.
P4.13 One form of a closed-loop transfer function is P4.15 The steering control of a modern ship may be rep-
resented by the system shown in Figure P4.15 [16,20].
G.Gv) + kG 2(s)
=
(a) Find the steady-state effect of a constant wind force
(S)
G 3(.v) + kG 4(sY represented by T,i(s) = \/s for K = 10 and K = 25.
Assume that the rudder input R(s) is zero, without any
(a) Use Equation (4.16) to show that [1]
disturbance, and has not been adjusted, (b) Show that
- G,G 4) the rudder can then be used to bring the ship deviation
T k(G 2G 3
(G 3 + AG 4)(G, + AG 2) back to zero.
P4.16 Figure P4.16 shows the model of a two-tank sys-
(b) Determine the sensitivity of the system shown tem containing a heated liquid, where T () is the tem-
in Figure P4.13, using the equation verified in perature of the fluid flowing into the first tank and T 2
part (a). is the temperature of the liquid flowing out of the sec-
P4.14 A proposed hypersonic plane would climb to ond tank. The system of two tanks has a heater in the
1()0,0()0 feet, fly 3800 miles per hour, and cross the Pa- first tank with a controllable heat input Q. The time
cific in 2 hours. Control of the aircraft speed could be constants are r^ = 10 s and r 2 = 50 s. (a) Determine
represented by the model in Figure P4.14. Find the T 2(s) in terms of T 0(s) and T 2ll(s). (b) If T 2d(s), the
sensitivity of the closed-loop transfer function T(s) to desired output temperature, is changed instanta-
a small change in the parameter a. neously from T 2fi(s) = Ajs to T 2(l(s) = 2A/s, where
Wind disturbance
W
1 Y(s)
Rudder _^J K k A t 75 Ship

input _ 4 i + ^ . r + 10.v + 75 from
FIGURE P4.15 prescribed
Ship steering course

w I
(7,5+ 1)(7,.9+ 1)

Q(s) 1/100 r
C,.(.v) ,k> T (s )
(7,.9+ 1)(7,5+ 1) •* ' JVJ
FIGURE P4.16 1^
Two-tank
E(s) ^
temperature
— 7" 2«/(.v)
control.