Observer design for a bilinear model of a continuous countercurrent ion exchange process

Abstract

The paper describes a method and proposes an algorithm for a bilinear observer design as part of a state estimation solution for a Continuous Countercurrent Ion Exchange (CCIX) process used for desalination of water. The aim of the design is to determine immeasurable process state variables using real CCIX measurement data obtained from a different study. The solution requires determination of the observer gain matrix and it is formulated on the basis of the pole placement method. The contribution of the paper is in the developed bilinear dynamic models of the process and the observer and in the extending of the pole placement method for the special matrices of the bilinear observer. An analytical procedure is developed and implemented for calculation of the characteristic equation of the observer as part of calculation of the observer gain matrix. Matlab and SIMULINK software programs for determining the estimated states are developed. Investigation of the performance of the bilinear observer and the closed loop system under various constant values of the control input and different state initial conditions is performed. The results are presented and discussed.