Mathematical models used for adaptive control of machine tools

Abstract

Many adaptive control (AC) systems have been developed in the laboratory, but despite this research effort, few AC systems have been applied in industrial settings in the past 25 years. The failure of AC systems for machine tools has been at an enormous cost to automated factories. There are a number of flexible manufacturing systems (FMS) in the United States that are in operation less than 10 percent of the time. Such systems are sometimes said to be “controlled by computers and operated by humans.” One of the reasons for the failures of machine tool AC is the lack of appropriate mathematical models of the metal cutting processes. Metal cutting processes are stochastic, nonlinear and ill-defined. This paper presents a review of the literature spanning the past 25 years which discusses the mathematical models used for the most common metal cutting processes used in machine tool AC systems. It is well recognized that modeling is a critical problem, and this paper imparts the evolution of the modeling approaches taken. Models used to implement the control are discussed as well. The paper will begin with a brief explanation of adaptive control; this is necessary since the term is used one way by control engineers and another way by manufacturing engineers. Classification of AC systems into adaptive control constraint (ACC) and adaptive control optimization (ACO) categories is explained. However, this paper defines categories consistent with control theoretic definitions and the literature is reviewed within this context. Two categorizations for the type of metal cutting model used are defined. Early research efforts are presented, followed by the attempts for industrial application. Problems encountered in the mechanics and methodology are discussed. After the review, the authors present their two unique approaches to adaptive control of machine tools. One approach is to develop a state space model. The model presented is for semi-orthogonal metal cutting on a lathe. The second approach is a model which includes characteristics of an actual human operator. This approach is based on fuzzy logic control and artificial intelligence to simulate the human operator.