From these points, the lag and lead factors and the controller gain were adjusted to give the

maximum possible low-frequency gain with the highest possible bandwidth while retaining

stability. Final values for the parameters of the controller are presented in Table 8.5.

 For joint 1, the worst case occurred when the following system parameters were

determined: Kv = 0.056 (deg/sec)/(D/A word), oh = 31.8 rad/sec, and 8 = 0.18. Again, this

system possessed the highest peak at the hydraulic natural frequency. The controller for this

system was also initialized with the lag factor at ri = 1.0 sec and the lead factor as rd = 0.01 sec.

The gain, Kc, for the controller was set to 2.0 (D/A word)/(deg/sec). Similar to the controller

for joint 0, the parameters of this controller were tuned on line to achieve the best possible

controller for joint motion in both directions and any position of joints 0 and 2. Again, the final

parameters are presented in Table 8.5.

 The process for determining values for the parameters of the velocity controller for joint

2 proved to be much more difficult due to the lack of a well defined open-loop transfer function.

However, Merritt's (1967) discussion of hydraulic control systems gave information that the

system could be modeled as an ill-behaved second-order system. Initial values of the controller

were established: Kc = 1.0 (D/A word)/(cm/sec), Ti = 1.0 sec, and td = 0.01 sec. During

implementation, however, these values did not produce a stable system. The gain and lead

factor were held constant while the value of Ti was increased, dropping the resonant peak well

below unity. A stable system was finally achieved, and the tuning process was continued until a

suitable controller for joint 2 was in operation. The final parameters for the lag-lead velocity

controllers are presented in Table 8.5.


Table 8.5. Final velocity controller parameters for joints 0, 1, and 2.

 Ti "Cd
 Joint Kc (sec) (sec)
 0 2.50 (D/A word)/(deg/sec) 0.50 0.05
 1 6.00 (D/A word)/(deg/sec) 2.00 0.01
 2 10.00 (D/A word)/(cm/sec) 20.00 0.10