Here, we develop a process model for the vessel in Figure M10-1a, which is a vertically oriented cylinder that can be assumed to have a constant cross-sectional area. The development of a model for the vessel in Figure M10-1b is left as an exercise for the reader. A material balance around the vessel, assuming constant density and cross-sectional area (A), yields
The deviation variables for the manipulated input, load disturbance, and measured output are
The process and load disturbance transfer ...