I. M. Appelpolscher, supervisor of the process control group of the Ideal Gas Company, has installed a 25 x 40 x 5-ft swimming poe1 in his backyard. The poo1 contains level and temperature sensors used with feedback controllers to maintain the pool level and temperature at desired values. Appelpolscher is satisfied with the Level control system, but he feels that the addition of one or more feedforward controllers would help maintain the pool temperature more nearly constant. As a new member of the process control group, you have been selected to check Appelpolscher’s mathematical analysis and to give your advice. The following information may or may not be pertinent to your analysis:

(i) Appelpolscher is particular about cleanliness and thus has a high-capacity pump that continually re-circulates the water through an activated charcoal filter.

(ii) The poo1 is equipped with a natural gas-flied heater that adds heat to the pool at a rate Q(i) that is directly proportional to the output signal from the controller pQ).

(iii) There is a leak in the pool, which Appelpolscher has determined is constant equal to F (volumetric flow rate). The liquid level control system adds water from the city supply system to maintain the level in the pool exactly at the specified level. The temperature of the water in the city system is Tw, a variable.

(iv) A significant amount of heat is lost by conduction to the surrounding ground, which has a constant, year-round temperature T. Experimental tests by Appelpolscher showed that essentially all of the temperature drop between the poo1 and the ground occurred across the homogeneous layer of gravel that surrounded his pool. The gravel thickness is ∆x,, and the overall thermal conductivity is kG.

(v) The main challenge to Appelpalscher’s modeling ability was the heat loss term accounting for convection, conduction, radiation, and evaporation to the atmosphere. He determined that the heat losses per area of open water could be represented by

Losses = U(Tp – T0)

whore

Tp = temperature of pool

Tn= temperature of (he air1 a variable

U = overall heat transfer coefficient

Appelpolscher’s detailed model included radiation losses and heat generation due to added chemicals, but he determined that these terms were negligible.

(a) Draw a schematic diagram for the pool and all control equipment. Show all inputs and outputs. Including all disturbance variables.

(b) What additional variable(s) would have to be measured to add feedforward control to the existing pool temperature feedback controller?

(c) Write a steady-state energy balance. How can you determine which of the disturbance variables you listed in part (a) are most/least likely to be important?

(d) What recommendations concerning the prospects of adding feedforward control would you make to Appelpolscher?