# Optimal Control of an Ultraviolet Water Disinfection System
## 1 Introduction  
Disinfection of drinking water is clearly a highly important sanitary objective. This treatment may be accomplished through chemical or physical processes. Among these, UV treatment is widely used due to its numerous advantages: The odor, PH, taste, and other properties of the water are not affected; it does not affect minerals in water; it needs relatively small exposure time to UV radiation; it does not add chemicals to the water and does not yield by-products (or yields a very small amount, see [1]); and, a simple operational procedure is required for the UV system. The most important advantage of UV disinfection of water is its effectiveness against wide-ranging pathogens, including protozoans and chlorine-resistant viruses. Comprehensive action against viruses may be an essential quality that compels the use of UV disinfection. The UV rays damage the genetic components of viruses, parasites, bacteria, or molds, thus preventing reproduction, i.e., they are inactivated. UV disinfection of drinking water is widely used and has been the subject of many research studies because of these advantages. UV disinfection is a complex process whose model requires the use of multidisciplinary, scientific aspects. Previous studies have applied chemical and physical approaches (see [2; 3]) and generated models that allow mainly qualitative analysis. When authors model the process and propose equipment to perform disinfection, they adopt a discourse based on biological and engineering considerations (see [4; 5; 6]). Numerical techniques such as computational fluid dynamics are also used to jointly solve and simulate the flow, radiation, and disinfection equations (see for example [7; 8]). To systematically construct a UV system model, the paper [9] proposes a bond graph approach that can cope with the nonlinear characteristic of a pilot disinfection water system. The resulting model allows parameters and the water disinfection kinetics to be computed. Other studies address the static optimization of the reactor's configuration through the evaluation of potential performance indexes (see, for example [10]). This study regards the optimal control of a UV disinfection system (UVDS) that places our work at the optimization level, namely above the basic automation level (if any). The latter aims to automatically adjust the values of the UVDS control inputs to equal the setpoint values to ensure the inactivation of pathogens. The UVDS control inputs are, in most cases, the water flow rate and the UV light intensity. Sometimes these physical parameters are manually controlled because the basic automation level does not exist. The optimization level has just the task of establishing the setpoint values jointly for the control inputs. An optimization algorithm considers optimum criteria (e.g., minimizing energy consumption or maximizing the water quality) and searches for the optimal values using a specific technique to fulfil this task. To study the optimal control of a UVDS, the work presented in this study tackled the following mandatory matters: dynamic model of the UVDS; statement of the optimization problem; optimization algorithm; and examination of optimal solutions. The dynamic model of the UVDS depends obviously on the equipment's structure and its technical performances. To obtain a dynamic model for a specific UVDS is a complex task related to our work's main objective: the disinfection model. The task is yet more complex in the case of flow reactors (like in our paper). An integrated UV disinfection process model should involve the modelling of fluence rate, flow field, and microbial inactivation kinetics. Computational fluid dynamics has been used to simulate the UV disinfection process (see [8; 11]). Usually, this methodology is used by research specialists during scientific investigations. Certain specialists consider that it is not adequate for practitioners working with water systems because of its lack of flexibility (it is tailored for a specific single case).