The position controller for joint 1 was tuned in a similar manner. For joint 1, the highest

resonant peak was found in the experimentally determined system with parameters Kp = 0.056

deg/(D/A word), Oh = 21.7 rad/sec, and 8 = 0.26. After tuning the position controller for joint 0

and noticing that the diagram for joint 1 was similar, the values for the joint 1 controller were

initialized to Kc = 10 (D/A word)/deg, ti = 3.0 sec, and td = 0.3 sec. For these values, the system

was stable, but the response was less than desired. The tuning process was completed as

previously described resulting in a controller that minimized the steady-state error and

possessed adequate response. The joint 1 position controller parameters are also presented in

Table 8.6.

Position Controller with a Velocity Control Minor Loop Tuning

 A position controller with a minor velocity loop was implemented for controlling the

position of the sliding joint. Merritt (1967) points out that the system with the velocity minor

loop can be approximated as a system with a lag at the corrected crossover frequency and a

quadratic at the hydraulic natural frequency. The response of this system would thus be

limited by the crossover frequency rather than the hydraulic natural frequency. This new

system was similar to the uncompensated position systems previously discussed and could be

tuned accordingly.

 After tuning a stable velocity loop, the main objective in tuning the outer loop was to

increase the gain to overcome the friction of the sliding joint. Initial choices for the parameters

of the major position loop controller were a high gain and lag and lead factors that would

cancel at a frequency lower than the new crossover frequency. The initial estimates were K =

30.0 (cm/sec)/cm, ti = 15.0 sec, and rd = 1.0 sec. As the tuning process progressed, the

improvements in the system response resulted when the values for Tj and Td of the position loop

were moved closer together. Continued observance of the reaction of joint 2 to this controller

indicated that the lag-lead controller of the major loop could be replaced with a proportional

controller. Therefore, the lag and lead function was omitted, leaving a simple proportional

controller. Using the proportional controller, the gain of the major loop was increased to