Hydraulic Servo Systems
Dynamic Properties and Control
by
Karl-Erik Rydberg
K-E Rydberg Feedbacks in Electro-Hydraulic Servo Systems 7
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Figure 12: A linear valve controlled position servo with velocity feedback
If the bandwidth of the valve is relatively high and threshold and saturation is neglected the velocity feedback will give the effect on the hydraulic resonance frequency and damping as shown in Figure 13.
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Figure 13: A linear position servo with velocity feedback included
From Figure 13 the new resonance frequency and damping ( hv and hv) caused by the velocity feedback can be evaluated as
vfv h hv vfv h
hv K K1
, , where the velocity loop gain is
p qi sav fv
vfv A
K K K
K 1 .
Designing the position control loop for the same amplitude margin as without velocity feedback gives the following relations:
Steady state loop gain without velocity feedback: f
p qi sa
v K
A K K K
Steady state loop gain with velocity feedback: f
vfv p
qi sav
vv K
K A K K K
A certain amplitude margin means that Kv h h. In this case h h hv hv, which implies that Kv Kvv and thereby the servo amplifier gain Ksav KsaKvfv. With velocity feedback, the servo amplifier gain (Ksav) can be increased in proportion to the velocity loop gain Kvfv and the servo amplifier gain without velocity feedback, Ksa. The open loop gain (Au(s)) for a position servo without (Kv = 20) and with velocity feefback (Kvfv = 10 and Kvv =20) is shown in Figure 14.
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Karl-Erik Rydberg, Linköping University, Sweden 21
Closed loop stiffness for a position servo with velocity feedback
K s V
K s K
s K
s K K A K S
ce e
t h vfv
h h vfv vv
ce p vfv vv c
1 4
2 1
1 2
2 2
K s V A K
A K K K s K K s
K s X S F
ce e
t p ce
p qi sav f vfv h
vfv h h vfv p
L c
1 4 2 1
2 2 2
p qi sav fv
vfv A
K K K K 1
f vfv p qi sav
vv K
K A K K
K 1
Steady state loop gain [1/s]
For the same amplitude margin, Kvmust have the same value in the system with and without velocity feedback.
Velocity feedback increases the steady state stiffness with the factor Kvfv.
feedback) elocity (without v
v
vv K
K
Karl-Erik Rydberg, Linköping University, Sweden 22
Closed loop stiffness for a position servo with velocity feedback
Without velocity feedback, Kv=20 1/s With velocity feedback, Kvv= 20 1/s, Kvfv= 9.0
hv= 387 rad/s
Am= 6 dB
