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