On superposition of Hammerstein systems: Application to simultaneous hysteresis‐dynamics compensation

Abstract

Summary Superposition principle (SP)—the response (output) of a linear system to a weighted combination of inputs equals to the combination of the outputs with the same weights and each corresponding to the individual input, respectively—is one of the most fundamental properties of linear systems, and has been exploited for controls, for example, in the development of model predictive control. Extension of the superposition principle beyond linear systems, however, is largely limited. In this paper, the almost superposition of Hammerstein systems (ASHS) and its application to precision control of hysteresis‐Hammerstein systems is studied. We first show, under some minor conditions, the existence of a nonstrict form ASHS, and under one further condition, the strict‐form ASHS. We then present one application of the ASHS—simultaneous hysteresis and dynamics compensation in output tracking of hysteresis‐Hammerstein systems, where offline iterative learning control to track the output elements is integrated with online synthesis of the control input via an inverse Preisach modeling. The proposed ASHS‐based technique is further enhanced through two online optimization schemes, and then illustrated through a simulation example on piezoelectric actuators model.