Page 619 - Mechanical Engineers' Handbook (Volume 2)

610 Servoactuators for Closed-Loop Control

KKKA
p
1
a
L Lp 2 ns (116)
s
KB A 2
2
Equation (116) shows that the maximum value of loop gain depends only on the values of
the natural frequency and damping ratio of the open-loop system.
In general, the loop gain is a critical parameter. An increase in loop gain results in a
decrease in load sensitivity (or increase in stiffness), an increase in the speed of response,
and a decrease in the degree of stability.
For a given electrohydraulic position control system designed to meet certain steady-
state performance requirements (e.g., load sensitivity), an optimum or best value of loop
gain (and therefore the best feedback gain) exists. This optimum value represents the best
compromise between speed of response and degree of stability. Figure 49 illustrates responses
of the system output ( Y) to step changes in the system input ( E ) for four different values
c
of the loop gain [Eq. (112)].
46
A comprehensive study of Eq. (112) by Meyfarth has shown that the optimum response
characteristics to a step input signal are obtained when
0.5 (117)
s
K Lp 0.34 ns (118)
In many practical casess, the open-loop system damping ratio ( ) is well below 0.5.
s
The resulting load resonance places severe limitations on the maximum level of loop gain
that can be used and therefore limitations on the quality of steady-state and dynamic per-
formance that can be achieved with the closed-loop system. That is, it may not be possible
to simultaneously satisfy the steady-state load sensitivity (or stiffness) and dynamic perform-
ance requirements without special enhancements to the system.

10.5 Hydraulic Compensation

One of the features of electrohydraulic servosystems is the ease with which electronic feed-
back and forward-loop compensation networks can be employed to produce improved dy-

Figure 49 Typical step responses for a third-order linear system.