1. In the heater example we performed step tests on the jacket flowrate. Perform step tests on the other inputs: (i) Tank flowrate, (ii) Tank inlet temperature, (iii) Jacket inlet temperature. Find the transfer functions relating the inputs and outputs. Discuss the linear vs. nonlinear effects.
2. Show that a decrease in jacket volume will cause the difference in magnitude between the fast and slow poles to increase.
3. Find the nonlinear steady-state relationships between jacket flowrate and the two temperatures (tank and jacket). Plot the input (jacket flowrate) vs. the outputs for the physical parameters given. Discuss how the gain changes with coolant flowrate.
4. Develop a simple model with imperfect mixing on the jacket side. Assume that the jacket can be modeled as two compartments, where the flow is from one compartment to another, as shown in the diagram below.