Identification of hammerstein systems by the hermite series estimate with application to flexible robot manipulators control

In this paper we study the identification of single-input, single-output discrete Hammerstein system. Such a 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 Newton-Gauss method. The main results concern the estimation 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 the density-free pointwise and global convergence of the estimate, that is, convergence is proven for inputs with arbitrary density function and virtually all nonlinearities. The rates of pointwise as well as global convergence are obtained for smooth input densities and for nonlinearities of Lipschitz type. The application of the proposed algorithm to the compensation of a flexible manipulator deflection in robot assembly is presented.