As a process engineer with the Complex Pole Corporation, you are assigned a unit with an exothermic chemical reactor. In order to learn more about the dynamics of the process, you decide to make a step change in the input variable, the coolant temperature, from 10C to 15C. Assume that the reactor was initially at a steady state. You obtain the following plot for the output variable, which is reactor temperature (notice that the reactor temperature is in F). Use Figure 3-9 to help answer the following questions. 290 285 280 275 270 reactor temperature, deg F 265 260 235 250 0 20 40 60 30 100 time, minutes i. What is the value of the process gain? (show units) ii. What is the value of t? (show units) iii. What is the value of C? (show units) iv. What is the decay ratio? v. What is the period of oscillation? (show units) vi. Write the second-order transfer function. Figure 3-9. Step response of a second-order underdamped system as a function of the damping factor (). Interpolate between the curves for the behavior of other damping factor values. 1.8 0.1 1.6 0.25 1.4 1.2 1 0.5 0.75 dimensionless output 1.0 0.8 0.6 0.4 0.2 various damping factor values 5 10 15 t/tau