Title Energetic Processes in Follow-up Electrical Control Systems English 2.2 MB 136
##### Document Text Contents
Page 1

INTERNATIONAL SERIES OF MONOGRAPHS ON

E L E C T R O N I C S A N D I N S T R U M E N T A T I O N

GENERAL EDITORS: D . W . FRY AND W . HIOINBOTHAM

Volume 28

ENERGETIC PROCESSES IN FOLLOW-UP
ELECTRICAL CONTROL SYSTEMS

Page 2

ENERGETIC PROCESSES IN

FOLLOW-UP ELECTRICAL

CONTROL SYSTEMS

by

A. A. BULGAKOV

Translated by

J. B . A R T H U R

Translation edited by

D . K . G H O S H

PERGAMON PRESS
OXFORD · LONDON · EDINBURGH · NEW Y O R K

P A R I S · F R A N K F U R T

1 9 6 5

Page 68

Hence the maximum mechanical power is

Pp=\<obMc. (189)

I f œb and Mc have the limiting values, i.e. are taken at the

nominal values of motor voltage, the expression

P
p.\im = Τ

œ
b. l i m ^ c . lim (190)

gives the magnitude of the limiting mechanical power, i.e.

the maximum power the motor can develop at the nominal

voltage.

This quantity depends on the overall dimensions of the

motor and its design features, but does not directly reflect

the state of heating of the motor.

Substituting from equation (190) in (185), we obtain the

relation between the amplitude of the motor power in the

harmonic regime and the maximum mechanical power of the

motor as a function of frequency

vT M
Pa. lim

=
%Pp. lim j ^ 2 ^ 2 * (191)

As the frequency is raised, the power amplitude first increases

and then decreases (Fig. 19).

PO.CR
P
T>ïim

0 I 2 3 4 5 6 7 8 9 10

F I G . 1 9 . Power as a function of frequency.

Page 69

60 ENERGETIC PROCESSES

By inspection we see that for the critical frequency

»cr = J - (192)
1
M

the power amplitude has a maximum equal to the maximum

mechanical power of the motor

Pa = P p . um- (193)

We obtain from equation (171) the amplitude of the output

angle at the critical frequency corresponding to the maximum

power amplitude

Ψ α . ^ =
ω

~ ^ φ - . (194)

In expression (191)
vTM = tan χ, (195)

where χ is the phase of the oscillations of the angular velocity

of the motor relative to the input signal of the power section,

if the other inertia parameters of this section are neglected

(64). On this basis, using elementary trigonometric identities,

formula (191) may be written in the form

^ a . um = Pp. lim sin 2χ. (196)

The power amplitude varies sinusoidally as a function of
the double angle 2χ and has a maximum at % = 45°.

The above formulae do not directly include the nominal
power of the motor, but this relation is easily obtained since
the heating of the motor is determined by the mean load power
(over a quarter period) [equation (155)] and in the harmonic
regime this is π/2 times less than the power amplitude.

Pm=yz^l=^JV0>l. (197)

Thus, the mean power as a function of frequency varies
like the power amplitude and has a maximum at the same
critical frequency [equation (192)], equal to the maximum
mechanical power of the motor, divided by π/2.

Page 135

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