The inside of the room is at temperature 𝑇𝑟and 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 𝑞 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. 𝑡 and 𝑇𝑤 vs. 𝑡 (𝑡𝑖𝑚𝑒). (Assume that 𝑅𝑟=0.5, 𝑅𝑤=1.8, 𝑇𝑟=8, 𝑇𝑤=4, 𝑇𝑜=3, and 𝑞=10)
Produce this assignment in a 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 for linearization.