In Problem34, Chapter 11, a zero steady-state error for a unit-step input was achieved through the design of a lag compensator with integral control. In that problem, the open-loop transmission can be written as L(s) = G_c(s)G(s), where the parabolic trough plant is given by (Camacho, 2012)

and the lag compensator is given by

We want to substitute for the continuous compensator with a digital one.

a. Find a suitable sampling period for the system.

b. Find the equivalent compensator’s transfer function in z-domain.

c. Use Simulink to simulate the digital compensator with the continuous plant. Compare the resulting response with that of the original system using the continuous compensator on the same graph.

Data from Problem 34 Chapter 11

In order to reduce the steady-state error of the parabolic trough collector system, a PI controller is added to the open-loop transfer function so that (Camacho, 2012)

137.2 x 10-6 -39s G(s) s2 + 0.0224s + 196 10-6