Application Of Some Approximate Methods For Distributed Parameter Systems

Distributed parameter systems are those the behaviour of which is described by partial differential equations or integral equations and are of infinite dimension. In general, it is impossible or very difficult to get analytic solution for partial differential equations describing distributed parameter systems. In order to be convenient for computation and implementation in practice, the application of approximate methods for solving partial differential equations and dealing with the problems of distributed parameter systems is very important. There are lots of approximate methods for solving the problems of distributed parameter systems in this dissertation, and their essence is to use finite-dimensional systems to approximate infinite-dimension systems. This dissertation investigates the applications of some approximate methods for the optimal control and identification of distributed parameter systems, the numerical computation of interior ballistic two-phase fluid dynamics model and the analysis of distributed parameter circuits, which are further concluded as follows:The origin, development and application of distributed parameter systems and their approximate computation methods are reviewed first, and then the applications of some approximate methods are introduced for the control and identification of distributed parameter systems, computational fluid dynamics and distributed parameter circuits.An approximate computation method of optimal control for distributed parameter systems (DPS) is presented. Based on exact and explicit representations of differential operators, the proposed method can translate the computation of optimal control for DPS into that for lumped parameter systems. The method need not construct new basis functions for boundary conditions and need not consider the effect of boundary conditions when partial differential equation is approximated with differential equation and the error can be estimated.An identification method for distributed parameter systems is presented. The proposed method translates DPS into lumped parameter systems using the matrix representations, which are obtained by projecting differential operators onto wavelet space, and then identification can be made via the once algorithm of least square parameter estimate. The complexity of computation is decreased because boundary conditions need not be considered in the process of translation.The mixed system of gas phase and solid phase in chamber is investigated as a distributed parameter system in the fire process of a tank gun. Distributed parameter...