16 SERVO SYSTEMS
[SE(. 11
descriptiousof early scrvolike devices can bcfounclin literature at least
as far back as the time of I,eonardo da Vinci.
The accumulated knowl-
edge and experience that comprise the present-day scicncc of servo
design, ho\vcvcr, rcccivcd a grrat initial ‘impulse from the ]vork and
publications of Nicholas Minorsky ’ in 1922 and 11. 1,. IIazcn’ in 193-!.
Minorsky’s \rork on the automatic strrring of ships and Irazcn’s on shaft,-
positionirrg types of servomechanisms both cont~ined mathmnatical
analyses based on a direct study of the solutions of dilfcrcntial equations
similar to those of Sec. 1.3. “1’his approach to the design problem IVUS
the only one availalic for many years, and it was exploited \ritil signifi-
cant success by intelligent and industrio(ls drsigrmrs of sc’rvt)nl(~cll:~nisms.
In 1932 h’yquist’ published a proccdurc for studying the stal)ility
of feedback amplifiers by the usc of steady-state techniques. 1[is po\rm-
ful theorcm for studying the stability of fcccfback aml~lifirrs bccamc
known as the N“yquist stability criterion.
In Xyquist’s analysis the
behavior of the servo systcm \viththe feedback l(Jop broken is consi{leu,d.
The ratio of a (complex) amp]itudc of the servo output to the (L’L)IT)])]CY)
error amplitude is plottccf in the complex plane, with frrq(lency as LL
variable parameter. If the resulting curve rlocs not encircle tlw critical
point ( —1, O), the system is stable; in fact, the farther the locu~ c:m he
kept away from the critical point the greater is the stability of t]w system.
The theory and application of this criterion arc discussed in (haps. 2
and 4. From the designer’s viewpoint, the best advantage of this mrthod
is that even in complicated systems time can be saved in analysis and a
great insight can be obtained into the detailed physical phcnomrna
involved in the servo loop.
Some of the earliest w-ork in this field \ras
done by J. Taplin at .Nfassachusetts Institute of Technology in 1937,
and the work was carried further by H. Harris,
3 also of Massacblwtts
Institute of Technology, who introduced the concept of transfer functions
into servo theory.
The ~varcreated a great demand for high-performance
servomechanisms and greatly stimulated the whole subject of servo
design. The supposed demands of military security, however, confined
the results of this stimulation within fairly small academic and industrial
circles, certainly to the over-all detriment of the \var effort, and pre-
vented, for example, the early publishing of the fundamental work of
G. S. Brown and A. C. Hall.’ The restricted, but nevertheless fairly
IN. Minorsky,“Directional Stability of AutomaticallySteeredBodies,” J. Am.
SOS. Naual Eng.,
34, 280 (1922); H. L. Hazen, “Theory of Servomechankms,”
J. Franklin~TMt.,218, 279 (1934).
ZH. h“yquist, “RegenerationTheory,”
Belt System Tech. J., XI, 126 (1932).
3 H. Harris,
“The Analysis and Design of Servomechanisms,”OSRD Report
454, January1942.
4G. S. Brown and A. C. Hall,
“Dynamic Behavior and Design of Servo-
mechanisms,” Trans.,
ASME, 68, 503 (1946).