m-Order Time Optimal Control Synthesis Function of Discrete System

TL;DR

This paper introduces an m-order time optimal control synthesis function for discrete systems using generating functions, detailing its derivation, control strategies, and validating their effectiveness through simulations.

Contribution

It presents a novel m-order synthesis function for discrete systems, extending the 2nd-order case with a generating function approach and new control methods.

Findings

Effective signal extraction and predictive compensation methods

Immunity and effectiveness verified by numerical simulation

Extension of 2nd-order synthesis to m-order using generating functions

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-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, 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.