A rate-dependent KP modeling and direct compensation control technique for hysteresis in piezo-nanopositioning stages

This paper first presents a rate-dependent Krasnosel’skii-Pokrovskii (RKP) model to capture the hysteresis of piezo-nanopositioning stages. The dynamic density function of the RKP model is obtained via neural network with frequency behavior input signal. Under the persistently exciting condition, the convergence of the neural network with Krasnosel’skii-Pokrovskii (KP) operators is proved rigorously. In order to address the hysteresis issue, a direct compensation control (DCC) approach with the KP compensation operator is proposed, where its dynamic density function is same as that of the RKP model. Some experiments with different reference signals are conducted to verify the effectiveness of the proposed modeling and DCC method on piezo-nanopositioning stages.