Nonlinear observer design: Theory and applications to automotive control.

Abstract

In this thesis, a new approach to observer design for nonlinear discrete-time systems is developed and subsequently shown to be applicable to the problem of air charge estimation in automotive engines. The problem of reconstructing state information from a sequence of measurements is cast in the form of root finding problems for systems of nonlinear equations. For the latter, a variety of methods is available in the literature. We first show that Newton's method, properly interpreted, yields an exponential observer with limited, but not necessarily small domain of attraction, and explore the connections between this so called Newton observer and the well-known extended Kalman filter. Then we investigate modifications to the Newton observer with two different and generally conflicting objectives in mind: increasing the region of convergence and decreasing the computational complexity. The former is achieved by employing the continuous Newton method, which, under the appropriate conditions, yields a global exponential observer; the latter may be possible by using Broyden's method--a quasi-Newton method in which Jacobian matrices are approximated by secant updates in order to avoid costly explicit function evaluations or finite difference approximations. It is also shown how the proposed design method naturally leads to reduced-order observers in the case that some of the state variables are measured directly. As a final theoretical issue we investigate the topic of detectability and the design of observers for detectable systems, a problem which, to date, has received virtually no attention. After the introduction of a new definition of detectability for nonlinear discrete-time systems, it is demonstrated how the basic Newton observer can be modified to yield an exponential observer for detectable systems. The second main part of the thesis is concerned with the problem of air charge estimation of individual cylinders in an automotive engine. A novel, control oriented model of the induction process is presented and validated with actual engine data. Using this model, a Newton-like observer is constructed to estimate individual cylinder air charge in a four cylinder engine from a single pressure sensor located in the intake manifold. This latter work is only an initial investigation. It illustrates, however, the potential of the Newton observer in practical applications.