Parabolic trough collector. In 34, Chapter 11, a zero

Chapter 13, Problem 41

(choose chapter or problem)

Parabolic trough collector. In Problem 34, 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)

\(G(s)=\frac{137.2 \times 10^{-6}}{s^2+0.0224 s+196 \times 10^{-6}} e^{-39 s}\)

and the lag compensator is given by

\(G_c(s)=1.12 \frac{(s+0.01)}{s}\)

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.