ADAR Method and Theory of Adaptive Control in the Tasks of Synthesis of the Nonlinear Control Systems

Abstract

This work continues a series of artides devoted to an illustrative comparison of the methods of modern control theory and the method of Analytical Design of Aggregated Regulators (ADAR). The ADAR method suggests two ways to ensure a nonlinear system adaptability to the external and parametric perturbations. The first way is the use of the principle of integral adaptation, when the influence of the parametric or external perturbations is compensated for by the nonlinear control laws introduced by integrators in a spedal manner. The design pгoceduгe of the adaptive control laws, according to this way, does not require a synthesis of the state and perturbation observers and consequently eliminate a real-time estimation of these perturbations. The second way is a design of the nonlinear observers of the parametric and external perturbations. In this case the designed nonlinear control laws are supplemented by a subsystem of observation, which realizes a dynamic estimation of the nonmeteringperturbations and a compensation for them. The above ways are illustrated in the artide by the known control tasks: the task of a wheel slip control in an anti-lock braking system; and the task of identification of the parameters and monitoring of the state of electгochemical pгocesses in the cell membranes in accordance with Hindmarsh and Rose model. The examples of the design procedures presented in the article demonstrate the advantages of the ADAR method concerning the analytical design of the adaptive regulators for the nonlinear objects. The theoretical results were confirmed by simulation of the closed-loop system in MATLAB software.