control mode (velocity, position, and vision) for accomplishing the desired response of each

joint. These lag-lead compensators had the form

 Kc('dS+ 1)
 HP (s) =K S1)
 "is+1 (8-3)

where s = Laplace operator (sec-1)

 Kc = controller gain,
 units:
 joints 0 and 1:
 velocity control: (D/A Word)/(deg/sec)
 position control: (D/A Word)/(deg)
 vision control: (D/A Word)/(pixel)
 joint 2:
 velocity control: (D/A Word)/(cm/sec)
 position control: (cm/sec)/(cm)

 d = time constant of the lead controller (sec), and

 zi = time constant of the lag controller (sec).


 In response to the high static friction (stiction) of the slider bearing, a minor velocity

loop was added to the position control loop of joint 2 to increase the major loop stiffness

(Merritt, 1967). The advantage of the velocity minor loop was the ability to increase the gain

in the minor loop to reduce the errors due to drift and load friction. Also noted by Merritt was

the fact that the inclusion of a minor loop would cause a decrease of bandwidth in the major

loop. The minor velocity control loop involved the inclusion of the velocity control feedback

loop between the position controller and the robot joint. Thus, the output from the position

controller for joint 2 would be the input to the velocity controller which calculated the valve

control signal for joint 2.


 Control System Discretization

 Implementation of the lag-lead controller in the software environment required that

the controller be converted to the discrete form. The discretized version of the controllers was

accomplished by approximating the Laplace variable of the continuous domain function by

Tustin's bilinear transformation. According to Tustin's rule (Franklin and Powell, 1980),