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