DESIGN AND IMPLEMENTATION OF REDUCED--ORDER OBSERVER AND IT'S CONVERGECE ANALYSIS

Abstract

As it is known that, the use of nonlinear control methods in control engineering implies, in general, the knowledge of full state vector of the system. This is an important drawback in engineering applications because all the states of the system are not measurable. In these cases, those state variables that cannot be measured must be estimated from the ones that are measured. In this dissertation work, I have developed a computer program in MATLAB software package to simulate a reduced-order state estimator for linear as well as non-linear discrete-time control systems, also called a reduced order state observer or simply a reduced order observer. Since it is not logical to estimate a state that is measured, because measurement of a state in general is more accurate than any estimate of the state, based on that measurement. Reduced order estimate also require less computational efforts. The reduced-order observer presented here is very simple and useful for a large class of multi-input-multi-output (MIMO) non-linear discrete-time systems with general non-linear dynamics and not necessarily with the presence of a linear part in the state. But the output is assumed to be linear with the state. It is worth noting that large class of physical processes (such as induction machine, robots, bio-reactors, electro-hydraulic systems, rigid body, ball and beam system) are with linear output map. High performance, from the design and implementation point of view, is shown through numerical examples of physical processes (such as Rigid body, Electro-Hydraulic manipulator and Induction machine) largely used in industrial applications. The stability analysis is achieved by the use of Lyapunov approach which lead to a LMI (Linear Matrix Inequality) condition..