Page 174 - Modern Control Systems

148 Chapter 2 Mathematical Models of Systems

-H 2(s)

Speed Speed
control
input

R 2(S) O r 2[s)
Tension Tension
FIGURE P2.32 control
A model of the
input
coupled motor
drives. -HM

FIGURE P2.33 Idle speed control system.

P233 Find the transfer function for Y(s)/R(s) for the idle-
speed control system for a fuel-injected engine as
shown in Figure P2.33.
P2.34 The suspension system for one wheel of an old-
fashioned pickup truck is illustrated in Figure P2.34.
The mass of the vehicle is m% and the mass of the wheel
is m 2-The suspension spring has a spring constant k^ and
the tire has a spring constant k 2. The damping con-
stant of the shock absorber is b. Obtain the transfer
function Y\(s)j'X(s), which represents the vehicle re-
sponse to bumps in the road.
P2.35 A feedback control system has the structure shown FIGURE P2.34 Pickup truck suspension.
in Figure P2.35. Determine the closed-loop transfer
function Y(s)/R(s) (a) by block diagram manipulation so that the closed-loop response to a step input is crit-
and (b) by using a signal-flow graph and Mason's sig- ically damped with two equal roots at s = -10. (d)
nal-flow gain formula, (c) Select the gains /C, and K 2 Plot the critically damped response for a unit step