Identification of a class of precision motion systems with uncertain hysteretic nonlinearities

In this paper, we propose a nonrecursive identification algorithm for a class of precision motion systems with uncertain hysteresis nonlinearities. This class of precision motion systems can be modeled by a Hammerstein system with a hysteresis nonlinearity. The hysteresis nonlinearity can be symmetric, asymmetric, rate-independent, or rate-dependent. The proposed identification algorithm is a two-stage algorithm that identifies the hysteresis nonlinearity and the linear system using measurements of the input and output of the Hammerstein system. The first stage of the algorithm uses a delayed impulse signal with simple least squares to identify the linear part of the Hammerstein system. The delayed impulse signal is shown to be persistently exciting of a sufficient order for the considered model structure. The second stage of the algorithm uses a sinusoidal input and the identified linear model obtained from the first stage to construct an estimate of the unknown intermediate signal, which represents the output of the hysteresis nonlinearity. Finally, a model of the hysteresis nonlinearity is obtained using the sinusoidal input and the constructed estimate of the intermediate signal. The identification algorithm is demonstrated on an experimental setup that includes a piezoelectric actuator, which exhibits a hysteresis nonlinearity and badly damped dynamics.