Optimal Control of Solar Sludge Dryers

Abstract

Optimal control (OC) methodology is used to develop a control policy for a batch-operated solar sludge dryer with ventilation as the dominant control. Batch performance criteria and instantaneous optimization criteria are developed for two economic environments: quota limited and capital limited. The general formulation, as well as simplifications resulting from the multiplicative form of the evaporation (drying) rate model, are presented. The multiplicative form results in a single constant number, called here “control intensity,” which is used to guide the on-line control decisions. These decisions turn out to be independent of the dry solids content (DSC) of the sludge. Further simplification, by assuming a strictly constant weather, is used to demonstrate the general effects of the economic and physical (weather) environment on the solution.

The OC approach is used to address, via simulation under realistic weather conditions, several design, operation, and pricing problems. In particular, the following have been considered: sizing of the ventilation fans, determination of a fair fee for sludge disposal, finding the best final DSC, and evaluating the effect of the price of electricity. Regarding the particular location represented by the data, it has been shown that the installed capacity of the ventilation fans should be increased and that there seems to be sufficient economic incentive for solar drying.

Keywords:

• Economic equilibrium
• Equipment sizing
• Fair fee
• Optimal control
• Sewage sludge
• Solar drying

Notes

E is the average evaporation rate for the drying period (the evaporation rate diminishes as the sludge is drying). Units of Columns 7 to 9 in different parts of the table are not the same. Values in bold are independent of weather. Consult text for further detail. kg[s] is kg of sludge solids, kg[w] is kg of water, and m³ [a] is m³ of air.

Cases 0 (Q0 and A0; quota and area limitation) are the standard. The ventilation capacity in Cases 1 is double the standard. The cost of electricity in Cases 2 is twice the standard, and the final DSC of Cases 3 is 0.2 higher than standard (bold, columns 2, 3, and 5). The bottom frame shows the gain, mostly in percent, by changing from the quota-limiting scheme to the area-limiting one. Q _v is annual average ventilation rate. N is number of batches in year.