In 49, Chapter 9, and 39, Chapter 10, we considered the

Chapter 13, Problem 30

(choose chapter or problem)

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

\(M(s)=\frac{0.5(s+1.63)}{s(s+0.27)}\)

and the plant by (Bittanti, 2002)

\(P(s)=\frac{0.63}{\left(1+\frac{0.36}{305.4} s+\frac{s^2}{305.4^2}\right)\left(1+\frac{0.04}{248.2} s+\frac{s^2}{248.2^2}\right)}\)

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?