In Problem 49, Chapter 9, and Problem 39, Chapter 10, we considered the radial pickup position control of a DVD player. A controller was designed and placed in cascade with the plant in a unit feedback configuration to stabilize the system. The controller was given by

and the plant by (Bittanti, 2002)

It is desired to replace the continuous system by an equivalent discrete system without appreciably affecting the system performance.

a. Find an appropriate sampling frequency for the discretization.

b. Using the chosen sampling frequency, translate the continuous compensator into a discrete compensator. 

c. Use Simulink to simulate the continuous and discrete systems on the same graph. Assume a unit step input. Are there significant differences in the system’s performance?

Data from Problem 49 Chapter 9:

Digital versatile disc (DVD) players incorporate several control systems for their operations. The control tasks include (1) keeping the laser beam focused on the disc surface, (2) fast track selection, (3) disc rotation speed control, and (4) following a track accurately. In order to follow a track, the pickup-head radial position is controlled via a voltage that operates a voice coil embedded in a magnet configuration. For a specific DVD player, the transfer function is given by

Transcribed Image Text:

0.5(s +1.63) s(s + 0.27) M(s) =