The application of adaptive Luenberger observer concept in chemical process control: An algorithmic approach

Abstract

When developing a wide class of on-line parameter estimation scheme for estimating the unknown parameter vector that appears in certain general linear and bilinear parametric model will be parametrizations of LTI processes or plants as well as of some special classes of nonlinear processes or plants. The resuls is used to design one of the important tools in control, i.e., adaptive observer and for stable LTI processes or plants. In this paper it will consider the design of schemes that simultaneously estimate the plant state variables and parameters by processing the plant I/O measurements on-line and such schemes is refered to as adaptive observers. The design of an adaptive observer is based on the combination of a state observer that could be used to estimate the state variables of aparticular plant state-space representation with an on-line estimation scheme. The choice of the plant state-space representation is crucial for the design and stability analysis of the adaptive observer. The paper will discuss a class of observer called Adaptive Luenberger Observer and its application. Begin with observable canonical form one can find observability matrix of n linear independent rows. By using this fact or their linear combination chosen as a basis, various canonical forms known also as Luenberger canonical form can be obtained. Also,this formation will leads to various algorithm for computing including computation of observable canonical form, observable Hessenberg form and reduced-order state observer design.