The following problems relate to the turntable-
1. Derive the system model. Show the O.D.E. as well as the Transfer Function. Clearly explain the model and all assumptions made in the process including an explanation of the parameter values used.
2. Design a PID velocity controller for the system. The angular velocity of output shaft should be controllable in the range -3000 to 3000 RPM. Clearly describe and document the controller you used as well as how you chose the controller gains.
3. Consider the system subject to a step input of 2000 RPM from 0 RPM. Show 3 time response plots of the output shaft velocity as described below.
(a) plot I - optimal gains for least steady state error
(b) plot 2 - optimal gains for fastest response
(c) plot 3 - unstable gains.
