Numerical Design Method of Quasilinear Models for Nonlinear Objects

Abstract

Design modern methods of nonlinear control systems of nonlinear objects in the majority assume transformation of initial object model to some special forms. In these cases, it is reasonable to use quasilinear models as they can be designed on condition only of differentiability of the nonlinearities of the initial objects models. These models allow to find control analytically, i.e. as a result of the solution of some equations system, if the object, naturally, meets the controllability condition. The quasilinear models are synthesized traditionally analytically, bytransformation of initial nonlinear models using operation of the taking of partial derivatives from the nonlinearities of the initial objects models and the subsequent integration of these derivatives on the auxiliary variable with application of the known formulas of differentiation and integration. However, in many cases, the objects nonlinearities have so complicated character, that the operations of the differentiation and, in particular, the integration are executed very difficult by shown way. This complexity can be overcome by application of the new numerical design method of the quasilinear models, which excludesneed of the analytical differentiation and integration, but demands considerable number of the arithmetic operations. But now it is not the big problem since the modern multiprocessor controllers can carry out all the necessary operations for a short time. The developed method allows to receive rather exact, approximate piecewise-constant quasilinear models for the objects with the complicated nonlinearities. It is convenient to apply such models at numerical control of the nonlinear objects. The efficiency of a numerical method is shown by comparison of phase portraits of piecewise constant quasilinear and nonlinear models of a simple object and also by comparison of the state variables values of these models. The offered method can be applied to nonlinear control systems design for the nonlinear, characterized by complicated characteristics objects ship, aviation, chemical, agricultural and other industries.