## 1 Introduction
At the same time, the gradient descent algorithm is used to optimize the center, width and output weight of the membership function online to ensure the convergence of SOFNN. Finally, experimental verification was carried out in the international benchmark simulation platform BSM1. Experimental results on the BSM1 show that, compared with control strategies of PID, fuzzy logic control (FLC) and FNN with fixed structure, SOFNN has a better performance on tracking accuracy, control stability and adaptive ability [22]. Although there are many studies on how to control the DO concentration in wastewater treatment system by using neural networks and predictive control methods with great outcomes, these kinds of methods have complicated structures and require large amount of computations. They are difficult to implement in practical engineering applications. Basically, most of the existing wastewater treatment plants (WWTPs) are still using PID, a simple and practical control strategy, to control the process. Unfortunately, since the parameters of the PID control algorithm are difficult to set up in advance which are strongly affected by the nonlinearity and large time-delay characters of the wastewater treatment process the control effect maybe unsatisfactory and the key problem is the parameters are not self-adjusted [23]. Therefore, combining intelligent algorithm with the PID algorithm becomes an effective way to realize simple structures and the control requirements of wastewater treatment process in actual WWTPs. When we use intelligent algorithm into PID, the parameters can be adjusted real-time according to the control effect of current strategy (such as gradient descent method) to avoid the problem of difficult-to-adjust PID parameters. At the same time, they can be adaptively adjusted according to the change of operation environment and dynamic disturbances. There are two ways to improve the control accuracy: one is to improve the accuracy of the measurement equipment of dissolved oxygen concentration, and another is the selection of the center point and the node width of the neural network. In this paper, a neural network-based adaptive PID control algorithm is proposed. The radial basis function (RBF) neural network is employed which has good generalization ability besides the strong self-learning and adaptive abilities and has a simple network structure. The proposed network already has research and application basis for the control of practical processes in some other areas [24; 25; 26]. Compared with the traditional PID control algorithm, the proposed RBF neural network-based adaptive PID (RBFNNPID) control algorithm comprises the advantages of these two methods. It is simple, easy to implement and has better control accuracy. More importantly, one does not need to set up the best parameters of PID in advance; that is to say, it can solve the problem of traditional PID controller that has difficulty in adjusting parameters online. Considering the control problem of DO concentration level in the wastewater treatment process, in this paper, the Benchmark model of BSM1 is introduced and the implementation of the RBF neural network-based adaptive PID control algorithm is discussed. It can be seen from the comparison simulation results that RBFNNPID control algorithm can effectively improve the control accuracy of dissolved oxygen concentration under the Benchmark as opposed to traditional PID.