Displacement Identification of Flexible Manipulator Arm using Hammerstein Model

Abstract

In this paper we study the identification of a flexible manipulator arm using SISO discrete Hammerstein model. In the first part of the paper we discuss identification of a general Hammmerstein system itself. Such system consists of two cascaded subsystems: nonlinear, memoryless subsystem followed by a dynamic, linear subsystem. We identify the parameters of the dynamic, linear subsystem by the correlation and estimate of the nonlinear, memoryless subsystem. We impose no conditions on the functional form of the nonlinear subsystem, recovering the nonlinearity using the Hermite series regression estimate. We show pointwise and global convergence of the estimate for virtually all nonlinearities. The rates of pointwise as well as global convergence are obtained for smooth input densities and for nonlinearities of Lipschitz type. In the second part of the paper mathematical model of a flexible robot manipulator is discussed. We present equations of the model and apply Hammerstein model to compensation of a flexible manipulator deflection in a robot assembly.