Approximate Decoupling and Asymptotic Tracking for MIMO Systems

摘要

This paper presents an algorithm for approximate input-output decoupling ofnonlinear MIMO systems that are either numerically ill-posed or exhibit nearly singular behavior in the application of decoupling algorithms. Although the systems considered are regular, so that the exact decoupling algorithms are applicable in this case, they require inversion of an ill-conditioned matrix, and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros. The approximate algorithms of this paper are numerically robust, and provide solutions that do not cancel far off right-half plane zeros. This latter characteristic is especially valuable when some of the far off right-half plane zeros are unstable. The algorithms are inspired by and are generalizations of some examples in the flight control literature. The nonlinear control toolbox has grown enormously in the last decade. Central to this development is the theory of feedback linearization for nonlinear systems (see 4, 5) and the solution to the multi-input multi-output (MIMO) decoupling problem. Several algorithms have been proposed in the literature for solving the problem of exact decoupling for nonlinear MIMO systems, see for example 4-9. These algorithms all require the determination of the inverse of a so-called decoupling matrix. Practical implementation of these algorithms, however, is difficult when the decoupling matrix is ill conditioned or close to singularity, in which case the decoupling of such systems needs excessively large control effort. Further, the algorithm is not numerically robust since it requires the inverse of an ill conditioned matrix. (KAR) P. 2.