1. (10 pts) Consider the following dynamic temperature data from a 4-cell DMFC in the University of Florida laboratory facility. The cathode inlet temperature and flowrate are 23C and 13 SLPM or L/min for 10 seconds. In Figure 1, there is a step change in the cathode flowrate, which assumed to be uniform throughout the cathode flow pathway or channels in the fuel cell. Due to the step change, the cathode outlet temperature response is measured as shown in Figure 2. (4 pts) What is the process gain K of the step response in C/(L/min)? Show work. Hints: a. Find the net value of the step change (M) in L/min. b. Find the initial and final steady state values of the step response data in C. (6 pts) What is the approximate time constant in s? Show work and which method was used. Hint: c. Assume time delay is approximately 1 second. d. Assume it is FOPTD model in canonical form. e. Choose and specify a method that you learned to find time constant. 14 13 12 11 10 00 ON 9 Cathode (Air) Inlet Flowrate (SLPM) 6 5 4 3 2 N 1 0 3130 3330 3530 3930 4130 4330 3730 Time (s) Figure 1. Step input function of cathode air flow rate Cathode (air) temperature out (C) 51.5 51.25 51 50.75 50.5 50.25 50 49.75 49.5 49.25 49 48.75 48.5 48.25 48 47.75 47.5 3130 3330 3530 3730 3930 4130 4330 Time(s) Figure 2. Temperature data from DMFC