provide acceptable response of the joint while minimizing the effects of stiction between the

sliding tube and its support bushing. The final value of the controller gain, Kc, of 20.0

(cm/sec)/cm was used.

Vision Controller Tuning

 The open-loop transfer functions for the vision control loops were similar to the position

control loops as shown in Figure 8.2. However, the control objectives for the vision controllers

were much different. In the case of the vision controllers, the response of the system to a

frequency disturbance was much more important because the vision system would be required to

follow the sinusoidal motion of a fruit swinging from the tree. Thus, the desired performance of

the vision control scheme was based on the motion of the fruit as covered in the previous

chapter.

 As presented in equations 7-1 and 7-2, rather than being calculated as the difference

between the actual and desired positions of the joint, the error for the vision controllers would

be the error as the robot tracked a fruit in motion. These equations were used to determine

desired amplitude ratios of the system for two critical cases: AR = 0.96 for frit = 3.1 rad/sec

(0.5 HZ) and AR = 0.83 for fruit = 6.9 rad/sec (1.1 HZ). These amplitude ratios were a function

of the loop gain of the entire system, KL, as

 AR- KL
 1+KL (8-12)

where the loop gain was the produce of the open-loop system gain, Kp, and the controller gain,

Kc, (KL = Kp Kc). Equation 8-12 was solved for the open-loop system gain:

 AR
 KL.--
 1-AR (8-13)

Thus, a normalized open-loop system gain of 24 was desired for Case I at 3.1 rad/sec to give an

amplitude ratio of 0.96. And, a normalized loop gain of 4.9 was calculated as the desired value

for Case II at 6.9 rad/sec. While striving to meet these requirements of the system gain, the

requirements placed on the phase angles were also a consideration in tuning the vision