A transfer function model from fluid flow to fluid temperature for a parabolic trough collector was introduced in Problem69, Chapter 2. A more detailed model for the response of this system is given under specific operation conditions (Camacho, 2012) by:

Find an appropriate state-space representation for the system.

Data From Problem69, Chapter 2:

In a significant number of cases, the open-loop transfer function from fluid flow to fluid temperature in a parabolic trough collector can be approximated (Camacho, 2012) by:

a. Write an analytic expression for the unit step response of the open loop system assuming that h(t) represents the output temperature and q(t) the input fluid flow.

b. Make a sketch of the unit step response of the open-loop system. Indicate on your figure the time delay, the settling time, the initial and final values of the response, and the value of the response
when t = τ + T.

c. Call the output temperature h(t) and the input fluid flow q(t). Find the differential equation that represents the open-loop system.

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