Some Applications of State and Parameter Estimation to Machine Tool Problems: I—Applications of Nonsequential Estimation

Abstract

A general introduction to the area of off-line and on-line identification of systems is given, and applications of these techniques to machine tool problems, especially adaptive or optimal control, are discussed. The problem of identifying the dynamic model of the metal cutting process is given special emphasis. A general formulation of the nonsequential or off-line estimation problem is presented using state variable notation, so that nonlinearities and time varying parameters may be present. Two techniques tailored to the use of the high-speed digital computer are developed to solve this general problem. The first utilizes a direct multivariable search to match the output, of an assumed dynamic model to actual experimental observations in a least squares sense. The second method uses a modified quasilinearization procedure. Controlled digital experiments are used to refine and test the proposed techniques. The two algorithms are then applied to actual experimental cutting process data. Estimates of the cutting stiffness and damping factor in the dynamic model of the cutting process are obtained, thus demonstrating the effectiveness of the developed nonsequential identification schemes, and showing that the assumed linear dynamic model adequately represents the cutting process. A later paper will consider sequential estimation applications.