Table 6.2. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 1 in relation to position of joint 2 and direction of
motion.
steady-state
joint 1 gain hydraulic hydraulic natural
position direction (deg/sec) damping frequency
of joint 2 of motion (D/Aword) ratio rad/sec HZ
retracted negative 0.054 0.29 28 4.5
positive 0.055 0.18 32 5.1
centered negative 0.055 0.32 28 4.5
positive 0.055 022 28 45
extended negative 0.056 0.31 22 3.5
positive 0.058 0.26 22 3.5
other hand, the response of joint 2 to large control values would increase stiffness requirements
for positioning the joint.
Results and Discussion
Design of the control systems for the orange-picking robot required a knowledge of the
each joint's transfer function. Merritt (1967) suggests that the transfer function of most
electrohydraulic servo systems can be estimated as a second-order system. Open-loop step tests
were conducted on each of the robot's joints for verification of Merritt's assumptions and for
establishing the parameters which define the behavior of a second-order system. After
defining the systems' parameters, the second-order systems were simulated for comparison with
the actual systems and verification of the determined parameters.
Analysis of the open-loop step tests responses of joint 0 for various positions of the
sliding tube yielded a range of hydraulic natural frequencies and damping ratios. Repetitions
of the step tests suggested average hydraulic natural frequencies ranging from 17 to 33 rad/sec
(2.8 to 5.2 HZ) and average damping ratio ranging between 0.18 and 0.34 (Table 6.3). The open-
loop gain (Kv) for joint 0 was averaged to be approximately 0.039 (deg/sec)/(D/A word) as the
ratio of the output signal to the computer's D/A converter in deg/sec to the input signal from the
computer's A/D converter in deg/sec.