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SUMMARYIn this paper we propose a fractional‐order proportional‐integral‐derivative controller design based on the solution of an scriptHMathClass-rel∞ model matching problem for fractional first‐order‐plus‐dead‐time processes. Starting from the analytical solution of the problem, we show that a fractional proportional‐integral‐derivative suboptimal controller can be obtained. Guidelines for the tuning of the controller parameters are given in order to address the robust stability issue and to obtain the required performance. The main differences with respect to the integer‐order case are highlighted. Simulation results show that the design methodology is effective and allows the user to consider process with different dynamics in a unified framework. Copyright © 2013 John Wiley & Sons, Ltd.

The improvement of the dissolved oxygen control is one of the main objectives in the research works on control of wastewater treatment plants. In the research literature, most of the works are based on benchmark simulation models, where ideal sensors and ideal actuators are commonly considered. However, it is important to note that the main difficulty of the dissolved oxygen control is due to noise and delay in the sensors and actuators. These are taken into account in this article with the aim of dissolved oxygen control improvement using the benchmark simulation model no. 1. The main purpose of this work is to highlight the need to take them into account and conduct a first step in analyzing how they affect the usually considered dissolved oxygen control approaches. The work proposes an approach for dissolved oxygen control improvement within non-ideal sensors and actuators using the benchmark simulation model no. 1, where a precise catalog and characterization of sensors and actuators are also provided (although not used). Filters are used to reduce the noise of the sensors. Artificial neural networks are designed to predict the value of dissolved oxygen, to compensate the delay produced by filters and sensors, as well as to anticipate the time needed by the actuator to obtain the desired value. The artificial neural networks take into account the microorganisms present in the wastewater, as well as their food and energy source, to predict the value of dissolved oxygen. The article shows different options of artificial neural networks for dry weather, rain, storm, and variable set-point. The results show meaningful integral of square error improvements, around 80% in dry weather and greater than 50% with rain and storm influents, as well as a significant reduction of abrupt changes in the actuator.

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