5.2. A heated process is used to heat a semiconductor wafer operates with first-order dynamics, that is, the transfer function relating changes in temperature T to changes in the heater input power level P is T'(s) P'(s) 8. K TS+1 where K has units [C/Kw] and T has units [minutes]. The process is at steady state when an engineer changes the power input stepwise from 1 to 1.5 Kw. She notes the following: (i) The process temperature initially is 80 C. Four minutes after changing the power input, the temperature is 230 C. (iii) Thirty minutes later the temperature is 280 C. (a) What are K and 7 in the process transfer function? (b) If at another time the engineer changes the power input linearly at a rate of 0.5 kW/min, what can you say about the maximum rate of change of process temperature: When will it occur? How large will it be?

transfer function relating changes in temperature T to changes in the heater input power level P is P(s)T(s)=s+1K where K has units [CKK ] and has units [minutes]. The process is at steady state when an engineer changes the power input stepwise from 1 to 1.5Kw. She notes the following: (i) The process temperature initially is 80C. (ii) Four minutes after changing the power input, the temperature is 230C. (iii) Thirty minutes later the temperature is 280C. (a) What are K and in the process transfer function? (b) If at another time the engineer changes the power input linearly at a rate of 0.5kW/min, what can you say about the maximum rate of change of process temperature: When will it occur? How large will it be