1. A given open loop room heating system has a gain of 1.2 and atime constant of 15 seconds. Derive the transfer function of thesystem in Laplace domain.
2. A closed loop proportional controller was implemented for thesystem described in Task 1 Q1 above to reduce the time constant to10 seconds.
a. Draw the block diagram of the system, assuming that the errorsignal is the difference between the set and actual measured roomtemperatures.
b. Calculate the gain value (K) of the proportional controlaction that achieve the above response.
c. Derive the overall closed-loop transfer function in Laplacedomain.
