m-Order Time Optimal Control Synthesis Function of Discrete System and Its Application

TL;DR

This paper introduces an m-order time optimal control synthesis function for discrete systems, deriving its formulation using generating functions, and applies it to develop a robust active disturbance rejection control method verified by simulations.

Contribution

It presents a novel m-order synthesis function derived via generating functions and applies it to create a new ADRC theory with improved immunity and robustness.

Findings

The m-order synthesis function effectively enhances control signal extraction.

The new ADRCT demonstrates strong immunity and robustness in simulations.

The approach generalizes 2nd-order control strategies to m-order systems.

Abstract

In this paper, first of all, we introduce the basic concepts of generating function in combinatorics and some combinatorial identities. In order to facilitate the understanding of m(greater than 1)-order time optimal control synthesis function of discrete system (referred as m-order synthesis function), secondly, we introduce the derivation process and control ideas of 2nd-order synthesis function fsun(), and then deduce in detail the m-order synthesis function by means of generating function. By use of the m-order tracking-form synthesis function with filter factor, the methods of signal extraction and its predictive compensation are presented in this paper, and their immunity and effectiveness are verified by numerical simulation. In the back part of this paper, we analyze the features of various components of 2nd-order active disturbance rejection control (ADRC) technology, and then by constructing the new type structures of extended state observer (ESO) and feedback controller which satisfy the separation principle, we construct a new active disturbance rejection control theory (ADRCT) based on the m-order tracking-form synthesis function with filter factor. Finally, the numerical simulation shows that the new ADRCT has good immunity and robustness.