## 1 Introduction  
Wastewater treatment plant (WWTP) is a complicated system in which processes of removing contaminants from municipal and/or industrial wastewater take place. Physical, biological and chemical processes are used to remove contaminants before their discharge to the receiver. The activated sludge treatment approach, which uses bacteria and other microorganisms to remove contaminants by assimilating them, has been widely adopted in most WWTPs. Batch type WWTP, sequencing batch reactor (SBR), is a popular method of municipal wastewater treatment. SBRs are a special form of activated sludge treatment in which all processes take place in the reactor tank. SBR is used for small-scale wastewater treatment and also becomes useful as a decentralized wastewater treatment technology for on-site treatment and/or water reuse technologies related to the sustainable water system. A typical sequence for an SBR system is: filling, biological reactions (aerobic, anaerobic), sedimentation, decantation and idle state [1]. From the control point of view, a WWTP is a very complex, dynamic, nonlinear, multivariable, hybrid control system where interactions between the components are strong. In addition, only limited measurements are available during plant operation. Unfortunately, simple linear control systems are very often used there, which cannot provide good control results at different points of operation. The right amount of dissolved oxygen (DO) is one of the key parameters influencing the effectiveness of biological processes taking place in the WWTP. This allows the microorganisms in the activated sludge to develop and to successively reduce nitrogen and phosphorus compounds in wastewater. Air is delivered into the aerobic zones by the aeration system (blowers, pipes and diffusers). Air allows oxygen to be transferred from the air to the liquid phase wastewater. The appropriate DO value in the SBR has a great effect on the treatment efficiency, operational costs and system stability. Moreover, the electricity consumption associated with the operation of the aeration system amounts to more than 50% of the operating costs at a WWTP [2]. Therefore, effective DO control is the key to savings. The dynamics of DO is nonlinear. Unfortunately, in industrial practice DO is usually controlled by a simple feedback loop (e.g., rule-based control, linear PI algorithm with constant parameters). Therefore, good control performance for all operating conditions cannot be achieved. In other words, the effective operation of WWTPs requires the use of modern control and optimization techniques. Their implementation is justified in view of increasingly stringent standards. The costs of implementing effective control and optimization algorithms in a WWTP are much lower than its modernization. Previous studies reported various structures and technologies of the DO control system. The cascade nonlinear adaptive control system, extended by the anti-windup filter, was applied [3]. Furthermore, the parameter analysis of the adaptive controller used for quality control was performed. Optimization of aeration profiles in the WWTP was shown [4]. First, the total rate of aeration was manipulated while employing equal rates of local aeration across. Then, scenarios with a nonuniform distribution of local aeration rates were investigated. The advanced control system of DO was designed [5]. Fuzzy PID control and a conventional PID control system were composed in a cascade structure. The control results showed that the control strategy reduced aeration energy consumption and guaranteed the stability of the system. In 2009, multivariable PID control system for biological WWTP with nitrification and denitrification was proposed [6]. The results showed that the performance of WWTP improved and it could potentially lead to energy saving and improvement in the removal of nitrogen. The multiregional PI controller for dissolved oxygen and aeration system control at biological WWTP was applied [7].