0195136047.pdf

PROBLEMS 823

excited dc motor driving a mechanical load. Let

Jbe the combined polar moment of inertia of

the load and motor, andBthe combined viscous

friction constant of the load and motor. Assuming

that the mechanical angular speed of the generator

ωmGis a constant, develop the block diagram for

the system and obtain an expression for the transfer

functionmM(s)/VfG(s).

16.2.23Consider the elementary motor-speed regulator
scheme shown in Figure P16.2.23 for a separately
excited dc motor, whose armature is supplied from
a solid-state controlled rectifier. The motor speed
is measured by means of a dc tachometer genera-
tor, and its voltageetis compared with a reference
voltageER. The error voltageER−etis amplified
and made to control the output voltage of the
power-conversion equipment, so as to maintain
substantially constant speed at the value set by the
reference voltage. Let the armature-circuit param-
eters beRaandLa, and the speed–voltage constant

of the motor beKm, with units of V·s/rad. Assume

that the combination ofAandPis equivalent to

a linear controlled voltage sourcevs=KA(error

voltage), with negligible time lag and gainKA.

Assume also that the load torqueTLis independent

of the speed, with zero damping. Neglect no-load

rotational losses.

(a) Develop the block diagram for the feedback

speed-control system withER/Kt, the steady-

state no-load speed setting, as input, andm

as output.Ktis the tachometer speed–voltage

constant in V/(r/min).

(b) WithTL=0, evaluate the transfer function

m/ER.

(c) WithER=0, obtain the transfer function

m/TL.

(d) Find the expressions for the underdamped nat-

ural frequencyωn, the damping factorα, and

the damping ratioξ=α/ωn.

eaG eaM

ωmM

TeM

TL

ifg

ifM

ωmG

Rfg

vfg

Lfg

+ − R = RaG + RaM L = LaG + LaM

LfM

vfM

RfM

ia

−

+

−

+

+−

Figure P16.2.22

ER Σ AP

If = constant

ωm

TL J

Ac power

Tachometer

et = Ktωm

−

+

Figure P16.2.23