Estimation and control of some classes of dynamical systems with application to biological wastewater treatment

Tingey, David (2007) Estimation and control of some classes of dynamical systems with application to biological wastewater treatment. Doctoral thesis, Northumbria University.

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Abstract

It is well-known that there are no general approaches for observer and controller design for nonlinear systems. Instead, focus is placed upon design for classes of systems. On the other hand, a wide variety of dynamical systems belong to the class of state-affine systems. Amongst these are biological wastewater treatment processes, which are essential in order to prevent pollution in the environment and prevent disease in the consumption of recycled water. An interesting aspect found in biological wastewater treatment systems, and many typical industrial processes, are time-delays. In almost all systems there are time-delays and nonlinearities and it is not surprising that time-delay and nonlinear systems have received a great deal of attention in mathematics and control engineering. This project introduces new methodologies for the design of controllers and observers for a class of state-affine systems and a class of linear time-delay systems. Firstly, new observable and controllable canonical forms are introduced. These are then used to establish new controller and observer design methodologies for a class of state¬affine systems. In particular, an adaptive observer design is established. The methodologies are simple since they are based upon linear techniques. Secondly, a full-state controller and a separation principle are established for a class of single-input single-output linear time-delay systems. The designs are based on a new stability criterion and are derived from first principles. Finally, the new observer design methodology for the class of state-affine systems is used to produce observers for the estimation of biomass concentration in a biological wastewater treatment bioreactor. The observers are applied in theory and in simulation, where a full and a partial knowledge of the kinetic rate of reaction of biomass are considered. In addition, the performances are shown both in the absence and in the presence of measurement noise for a variety of influent flow characteristics.

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