Consider a thermal heating system given by where the output (s) is the temperature difference due to

Question:

Consider a thermal heating system given by

where the output Ï„(s) is the temperature difference due to the thermal process, the input q(s) is the rate of heat flow of the heating element. The system parameters are Ct, Q, S, and Rt. The thermal heating system is illustrated in Table 2.5.
(a) Determine the response of the system to a unit step q(s) = 1/s.
(b) As t †’ ˆž, what value does the step response determined in part (a) approach? This is known as the steady-state response.
(c) Describe how you would select the system parameters Ct, Q, S, and Rt to increase the speed of response of the system to a step input.