Modeling and Control of Bilinear Systems

Ekman, M. 2005: Modeling and Control of Bilinear Systems: Applications to the Activated Sludge Process. Written in English. Acta Universitatis Upsaliensis. Uppsala Dissertations from the Faculty of Science and Technology 65. 231 pp. Uppsala, Sweden. ISBN 91-554-6342-8 This thesis concerns modeling and control of bilinear systems (BLS). BLS are linear but not jointly linear in state and control. In the first part of the thesis, a background to BLS and their applications to modeling and control is given. The second part, and likewise the principal theme of this thesis, is dedicated to theoretical aspects of identification, modeling, and control of mainly BLS, but also linear systems. In the last part of the thesis, applications of bilinear and linear modeling and control to the activated sludge process (ASP) are given. In the system identification part of the thesis special emphasis is devoted to errors-in-variables (EIV) problems for linear as well as bilinear systems. The parameter estimation problem for continuous-time BLS is also investigated. One main point is that both the EIV problem and the continuous-time BLS parameter estimation problem can be treated as separable least-squares (LS) problems. A new bias-eliminating approach, based on a compensated LS solution of an overdetermined system of equations and separable LS, is introduced for identification of parameters in dynamic linear and bilinear systems with EIV, and for parameter estimation of continuous-time BLS. Two different strategies for controlling BLS are investigated. Firstly, a suboptimal control law for the continuous-time BLS is introduced. Secondly, a model predictive control (MPC) algorithm for discrete-time BLS is presented. The last part of the thesis is focused on applications to wastewater treatment plants (WWTP’s). Reduced order time varying bilinear state-space models for the ASP are derived and used for control applications. An adaptive control strategy for control of the nitrate level in an ASP is also suggested. Finally, a supervisory aeration volume control strategy for an ASP is discussed. The control strategy is evaluated in a simulation study as well as in a real pilot plant.