0195136047.pdf

822 BASIC CONTROL SYSTEMS

Rfg

vfg

ifg

Lfg

Ifm =

constant

eg

ωm

+ −

R i

G

−

+

MJb

−

+

Figure P16.2.17

Servo

amplifier Va^ ∠^ ±^90 °

Vm ∠ 0 °

Σ

+

−

Eref

θref θ

θ

E

+V

Figure P16.2.19

16.2.19For the position control system shown in Figure

P16.2.19, let the potentiometer transducers give a

voltage of 1 V per radian of position. The transfer

function of the servoamplifier isG(s)= 10 ( 1 +

0. 01571 s)/( 7 +s). Let the initial angular position

of the radar be zero, and the transfer function

between the motor control phase voltageVaand

the radar positionθbeM(s)= 2. 733 /s( 1 +

0. 01571 s).

(a) Obtain the transfer function of the system.

(b) For a step change in the command angle of

180° (=πradians), find the time response of

the angular position of the antenna.

*16.2.20A separately excited dc motor has the following
parameters:Ra= 0. 5 , La∼= 0 ,andB∼=0.
The machine generates an open-circuit armature
voltage of 220 V at 2000 r/min, and with a field
current of 1.0 A. The motor drives a constant load
torqueTL =25 N·m. The combined inertia of
motor and load isJ = 2 .5kg·m^2. With field
currentIf= 1 .0 A, if the armature terminals are
connected to a 220-V dc source:

(a) Obtain expressions for speedωmand armature

currentiaas functions of time.

(b) Find the steady-state values of speed and ar-

mature current.

16.2.21The process of plugging a motor involves revers-

ing the polarity of the supply to the armature of

the machine.Pluggingcorresponds to applying

a step voltage of−V u(t)to the armature of the

machine, whereVis the rated terminal voltage.

A separately excited 200-V dc motor operates at

rated voltage with constant excitation on zero load.

The torque constant of the motor is 2 N·m/A, its

armature resistance is 0.5, and the total moment

of inertia of the rotating parts is 4 kg·m^2. Neglect

the rotational losses and the armature inductance.

Obtain an expression for the speed of the machine

after plugging as a function of time, and calculate

the time taken for the machine to stop.

16.2.22The schematic diagram of a Ward–Leonard system

is shown in Figure P16.2.22, including a separately

excited dc generator, the armature of which is con-

nected directly to the armature of the separately