natural frequency and the hydraulic damping ratio for each joint. The steady-state gain of a
joint was the ratio of the achieved steady-state velocity to the input value. The gain for each
joint was determined as
K Vout
K,-
V*P (6-4)
where: Kv a steady-state gain ((deg/sec)/(D/A word)),
Vout steady-state output velocity (deg/sec), and
Vsp = velocity control signal (D/A word).
The damping ratio was approximated with (Palm, 1983):
In ln(os) )2
Sh= ( I
2
1+ (In (os))
-IC ) (6-5)
where: 5h hydraulic damping ratio dimensionlesss), and
V max-V
os overshoot (decimal value) Vmax
V sa
The hydraulic natural frequency was approximated with (Palm, 1983)
tPv l- (6-6)
where oh = hydraulic natural frequency (rad/sec),
kh = damping ratio dimensionlesss), and
tp = time to peak (sec).
A typical response of joint 0 of the orange-picking robot to a step input is shown in
Figure 6.4. The response signals from the A/D converters were converted from the bit values as
used by the control computer to deg/sec by the conversion factor 0.033 (deg/sec)/bit from Table
4.2. For a step input to the actuator of 1200 D/A bits, the joint started from a velocity of 0
deg/sec (0 A/D bits) and peaked at a velocity of 65 deg/sec (1980 A/D bits) before returning to
an average steady-state velocity of 46 deg/sec (1400 A/D bits). Thus, the steady-state gain for