CONTINUOUS CONTROL OF NONLINEAR NON-AFFFINE OBJECTS

Abstract

The paper proposes a method for constructing continuous control of non-affine control objects with differentiable nonlinearities and a measurable state vector. The method is based on the use of quasilinear models of nonlinear objects, which are created on the basis of their equations in Cauchy form while maintaining the accuracy of the description. It is shown that control by state and influences exists if the nonlinear object is completely controllable by state and satisfies the criterion of output controllability. To determine the control, it is necessary to find a number of polynomials using the object model and solve polynomial and nonlinear algebraic equations. The method is analytical and allows us to provide some primary quality indicators. The region of attraction of the equilibrium position of a closed system is determined by the region of state space in which the controllability condition of the quasi-linear model of the object is satisfied. Depending on the nonlinearity properties of the object, control is defined either as a function of state and deviation variables, or is a numerical solution obtained by an iterative method. The required control is oriented towards implementation by a computing device. The article provides the formulation of the problem, the conditions for its solvability, as well as analytical expressions for finding the control action. A numerical example is given with the results of synthesis and modeling, which allows us to conclude that the above relations lead to finding continuous control of a non-affine object with differentiable nonlinearities and a measurable state vector, which ensures the required properties of a closed-loop control system