2. Description of the process NBI control

In order to facilitate the understanding of the possibility of implementing the NBI algorithm in controllers, let us take, for example, an industrial effluent treatment plant, which operates with a certain constant flow, due to the residence time necessary for part of the organic load to be degraded via bacteria and protozoa in an aerobic process. As a base of the input variables, we will work with initial organic load in terms of biochemical oxygen demand (BOD) and pH. As controllable factors, we will use the air or oxygen flow (aeration) and residence time. As desired responses, we will use as an illustration the removal of the organic load in terms of biochemical oxygen demand (BOD) and chemical oxygen demand (COD).

Modeling a typical problem processes, we could write that both responses have a direct relationship with the two factors presented as X1 and X2. However, keeping the process steady relative to the inputs becomes virtually impossible. By establishing, the two responses used, as an illustration of the application of the method, is it feasible to predict the aeration rate and residence time required. Certainly, the answer would be positive, if the entries were kept constant. However, if this standardization is not possible, how can we keep the responses within desirable patterns? Imagine in a situation of actual biological treatment process, where some changes can lead to periodic changes in the conditions of entry. For example, an increase in the rainfall rate may lead to the dilution of the organic matter present in the tributary and consequently the decrease of the initial BOD. The decrease of the initial BOD requires a lower concentration of dissolved oxygen so that bacteria and protozoa can decompose the organic matter in order to meet the exit standards, which would lead to the conclusion of shorter residence times required. There is a relationship as presented that can be considered a certainty. However, what is the relationship between them? What would be the best condition, to decrease aeration or increase residence time? These responses can only be met if we have this problem modeled. When working with models, we can easily predict the relationship of each of the factors to the expected response. This fact helps us reduce process costs and increase effectiveness in the targeted response. Through the use of models created from response surfaces, which have quadratic models, it is easily possible to determine local or global minimum or maximum points.
