The schematic (below) indicates a room heated with an electric heater

The schematic (below) indicates a room heated with an electric heater. The inside of the room is at temperature Tr and the walls are assumed to be at temperature Tw.

If the outside temperature is To, develop a model of the system to show the relationship between the supplied heat g and the room temperature Tr

Write the state space model of the system in a matrix form and solve this equation using MATLAB. Plot the figures showing temperature variation for this thermal system in terms of

Tr vs. cand Tw vs. ¢ itimel. (Assume that Rr-O.5. Rw- 1.8. Tr-8. Tw-4. Te 3. and q-10)

Produce this assignment ina report format, with additional explanations on:

- Why do we linearized the behavior of a Fluid Systems normal operating points? (on your own words)

- Explain the assumptions needed to be consider tar linearization.