F T₁ 1/(rs+1) and (2) e/(rs + 1). (b) Include the following inputs for all systems: (1) ramp (Cr) and (2) pulse of finite duration. 5.9. The dynamic response of T6 in the heat exchanger and stirred-tank sys- tem in Figure Q5.9 is to be determined for a step increase in the flow to the exchanger Fex. with the total coolant flow Fe constant. (Assume that negligible transportation lag occurs in the pipes.) (a) Derive the models for both stirred tanks. (b) Determine the individual transfer functions. (c) Derive the overall transfer function. (d) Which of the general system structures covered in this chapter de- scribes this system? (e) Explain the numerator zeros (if any) and poles in the system. (f) Describe the dynamic response of this system for the input step change in Fex- F-constant To T₁ T₁ T₁ FIGURE 95.9 171 Questions