compensators. These constraints were a maximum phase lag of 2.5 degrees at 3.1 rad/sec or 10

degrees at 6.9 rad/sec. Because the experimentally determined natural frequency for joint 0 was

slower than joint 1, design of a stable compensator for joint 0 would almost certainly provide a

stable compensator for joint 1. Also, the lack of ability to meet the requirements by joint 0 would

also indicate that the same shortcoming would carry over to joint 1.

 Observations of the Bode plots for the vision plant of joint 0 (Figure 8.25) indicated

that these requirements could not be met. An increase in the gain of the overall system would

have caused the position of the peak to rise above unity, causing the system to be unstable.

Since a slope of -1 was also desired at the crossover frequency, the addition of the lag factor at

a frequency less than the crossover frequency would have to be countered by placing the lead

breakpoint less than the crossover frequency. Even with an increased gain of the system to move

the peak to a value near unity, the required open-loop system gains as specified could not be

met. Therefore, the fact was recognized that some motions of the fruit would create an

impossible picking situation for the robot.



 100
 100^------------------)----------------------|nvauesfo
 24 -- ) Required gain values for
 10 tracking observed fruit motions
 4.9

 1





 .001
 .001
 .1 1 10 100
 3.1 6.9
 6.9
 to (rad/sec)

Figure 8.25. Open-loop Bode diagram for joint 0 vision system indicating the gain requirements
 for picking worst case fruit motions.