Nonlinear adaptive observer design for a reverse osmosis plant

Abstract

This thesis proposes a novel approach for a nonlinear adaptive observer design applied to a reverse osmosis desalination plant. The considered mathematical model of the de- salination system includes nonlinearities of the states and the parameters that cannot be handled with previously published estimation methods which are based on the mod- ulating function technique. Therefore, the proposed real-time capable approach uses a decoupled parameter estimator and state observer. These estimates can be utilized for developing a controller or a fault detection system of the desalination plant with the aim of improving the quality and effort of fresh water production. The parameter estimator is composed of a convolution filter with modulating func- tions and the common Extended Kalman-Bucy Filter in order to estimate nonlinear parameters of a state-linear input/output relation. To receive a regression form of the nonlinear system for the state observer and to avoid the necessity of time-derivatives of the measured input and output signals, a linearization by means of the Taylor se- ries and the modulating function technique are applied. The estimates can be non- asymptotically obtained by using a sliding window of finite length. This procedure allows a continuous and recursive update of the state estimates and extends the possi- ble applications of the modulating function technique to nonlinear systems. Comparative simulations are executed with the considered nonlinear system of a reverse osmosis desalination plant. Distinct scenarios with respect to the parameter change and the impact of noise are examined. The parameter and state coupled Ex- tended Kalman-Bucy Filter shows an asymptotic convergence of its estimates, whereas the decoupled proposed adaptive observer confirms its non-asymptotic behavior by fast estimation results.