Page 573 - Mechatronics with Experiments

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JWST499-c07
JWST499-Cetinkunt
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 559
Similarly, the maximum force the EH system can afford to exert even under a zero accelera-
tion condition (no head-room for force) may be smaller than desired, that is F load = 15 000,
and available force at rated conditions,
6
(p max − p ) ⋅ A = (20.865 − 6.895) ⋅ 10 ⋅ 0.001 = 13 590 N (7.632)
r
a
One way to determine the approximate proportional gain of the closed loop PID
controller is to decide on the maximum position following error for which the valve should
be fully open, neglecting transient effects. This relationship would give a good estimate
of the proportional gain K . Then the rest of the PID gains K , K can be tuned, including
d
i
p
the tuning of K around the estimated value until the desired closed loop performance is
p
achieved. Let
(y (t) − y(t)) max = e max (7.633)
d
for which we would like the controller to open the valve fully, x = x vmax . Neglecting the
v
transient aspect of the amplifier and valve dynamics,
i cmd ≈ K ⋅ e max (7.634)
p
x = x vmax = x vmax ⋅ K ⋅ K ⋅ i cmd (7.635)
v
t
a
x vmax = x vmax ⋅ K ⋅ K ⋅ e max ⋅ K p (7.636)
t
a
1
K = (7.637)
p
K ⋅ K ⋅ e max
a
t
Note that this calculated value for K is only a guidance as a starting point, and a very useful
p
one. The actual values of the PID gains (K , K , K ) should be further tuned to achieve the
p
i
d
desired dynamic performance on the actual hardware.
Remarks on Simulations In order to understand the effect of different circuit
design parameters as well as to be able to confirm the accuracy of the simulation results
by our qualitative physics based reasoning, it is instructive to examine the effects of the
following different conditions in simulation;
1. In order to confirm that the overall dynamic model makes sense, simulate the system
for a condition that the servo valve is always in neutral position (no flow through
the servo valve), and initial conditions of the cylinder are stationary at a nominal
position. The simulation results should confirm that the cylinder does not move, and
pressures in A and B sides do not change, no flow through the servo valve. All of the
pump flow should be dumped back to the tank through the relief valve.
2. The next level of check in the correctness of the model and simulation is to specifiy
the servo valve spool position as a function of time, x (t), instead of having it
v
determined via a control current command and valve dynamics. Given a prescribed
valve position as a function of time, we can approximately predict and expect that the
cylinder velocity should have a similar profile to the motion of the valve spool, and
the cylinder position should be similar to the integral of the valve spool displacement.
This simulation excludes the effect of servo valve dynamics and the closed loop PID
controller.
3. Much smaller and much larger hose volumes between pump and servo valve, and
between servo valve and cylinder, can be simulated.
4. Different damping coefficient for the servo valve inertial dynamics: very small (i.e.,
c = 0.1) or very large (i.e., c = 1.0) can be simulated.
v
v