each of the joints and aid in the selection and implementation of the controllers of the orange-
picking robot.
The joints' responses to the step input signals gave important information to be used in
the design of the respective controllers. For joints 0 and 1, the ranges in the natural frequencies
and damping ratios were related to the position of joint 2 during the tests. Higher natural
frequencies were calculated for joint 0 when the weight of joint 2 was being lifted. For example,
the highest natural frequencies resulted when the tube was extended with the end-effector
being lifted or when the tube was retracted with the end-effector being lowered. Likewise, the
highest damping ratios for joint 0 were calculated for those responses in which the most weight
was being lifted. When this information was checked against the parameters of equations 6-2
and 6-3, the damping ratio follows the expected trend that increased load inertia would result
in increased damping. However, the natural frequency contradicts the inverse relationship
with the inertia load as indicated in equation 6-2. This contradiction indicated that the
position of the sliding joint influenced the system more as an external torque load than an
inertia load used in equation 6-2.
The step tests for joint 1 involved moving the end-effector in horizontal directions. For
this joint, a steady-state gain of 0.05 (deg/sec)/(D/A word) was calculated for every trial. In
this case, the second-order parameters varied with the position of joint 2 and the direction of
travel. The hydraulic natural frequencies were smallest when the sliding joint was extended
and the highest inertia was expected. This followed the relationship of equation 6-2. On the
other hand, the established damping ratios did not follow the relationship of equation 6-3.
The only evident pattern of the change in damping ratio was that the damping ratio for the
positive direction was smaller than that for the negative direction. This variance could have
been caused by improper alignment of the outer frame causing binding in the bearings or from
different friction values for the different directions of travel.
As previously discussed, the model of joint 2 could not be determined due to the high
static friction values in the bushing and its unpredictable behavior. The behavior of joint 2