response to positive and negative steps. The results of the repetitions were averaged. The

average steady-state gains, hydraulic natural frequencies, and damping ratios are presented in

Table 6.1.

 A typical response of joint 1 of the robot to a step input of -500 D/A bits is shown in

Figure 6.5. This step caused the joint to move the end-effector of the robot from left to right.

The step input was initialized at 1/2 sec (30 counter timer ticks). The joint which began from a

velocity of approximately 0 deg/sec (0 A/D bits) responded to the input by reaching a peak

velocity of -38 deg/sec (-1150 A/D bits) before returning to an average steady-state velocity of

-28 deg/sec (-850 A/D bits). The values for this step test represent an overshoot of -10 deg/sec

(-300 A/D bits) or 35 percent of the steady-state velocity. Joint 1 reached its maximum or peak

velocity in 7 counter timer ticks or 0.12 sec. Using these values in equations 6-4, 6-5, and 6-6, the

hydraulic natural frequency and damping ratio of joint 1 were found to be 28 rad/sec (4.5 HZ)

and 0.32, respectively. The steady-state gain, Kv, for joint 1 was found to be

0.056 (deg/sec)/(D/A word).

 For step test response of joint 1, the position of joint 0 was held constant while joint 1

was free to respond to the step input from the control computer. These tests included both

positive and negative step inputs from the computer resulting in horizontal motions of the end-

effector. The test was also conducted in repetition for joint 2 in the retracted, centered, and


Table 6.1. Experimentally determined steady-state gains, damping ratios, and hydraulic
 natural frequencies of joint 0 in relation to position of joint 2 and direction of
 motion.

 steady-state
 joint 0 gain hydraulic hydraulic natural
 position direction (deg/sec) damping frequency
 of joint 2 of motion (D/A word) ratio rad/sec HZ
 retracted down 0.035 0.30 33 5.2
 up 0.042 021 22 3.4
 centered down 0.033 0.18 17 2.8
 up 0.038 0.26 20 3.1
 extended down 0.044 0.31 17 2.8
 up 0.040 0.34 27 4.3