2) You are to optimize the turntable for moves of 45° and 90°. For all the following parts provide plots of the angular displacement, the angular velocity, and the drive value. Show all calculations and provide your reasoning for any assumption.
a. Define a proportional gain Kp based on an assumed linear range, then perform angular moves of 45° and 90°.
Select your own linear range. A general guideline is to select a linear range close to the smallest move one expects to move.
b. Perform angular moves of 45° and 90° with double the value Kp used in part a.
c. Using the value Kp from part a, calculate a value of Kd assuming a theoretical damping factor ζ= 0.9, then perform angular moves of 45° and 90°.
d. Repeat part c but with Kd equal to 0.5X (ζ= 0.45) and 2X (ζ= 1.8) of what was calculated in part c.
e. Repeat part c with the addition of integral gain Ki to eliminate any offsets. Describe any limits you put on the integral gain. Compare results with and without integral gain.
f. Comment on what you would do next to optimize your control response.