Finite-Time Adaptive Quantized Motion Control for Hysteretic Systems With Application to Piezoelectric-Driven Micropositioning Stage

This study addresses the finite-time adaptive output feedback quantized control problem for nonstrict-feedback nonlinear systems subject to unknown hysteresis and time delays. An estimated inverse compensator (EIC) is constructed to mitigate hysteresis by resorting to a generalized Duhem model. A Lyapunov-Krasovskii functional is employed to deal with the uncertainties of time delays. However, the system performance deteriorates when the quantized signal is directly applied to the hysteretic system. To overcome this obstacle, this study proposes a new composite quantizer consisting of an adaptive state-estimation filter and a modified hysteretic quantizer, in which the former facilitates the state approximation by incorporating the feedback information of the system and the latter regulates the communication rate. With the proposed finite-time prescribed adaptive quantized control with an estimated inverse compensator (EIC-FPAQC) scheme, all solutions of the closed-loop systems are semiglobal practical finite-time stable and the tracking error can be ensured in a predefined accuracy. Finally, experiments are conducted on a piezoelectric-driven micropositioning stage to demonstrate the effectiveness of the proposed method.

Automated summary

This study considers the problem of finite-time adaptive output feedback quantized control for nonstrict-feedback nonlinear systems with unknown hysteresis and time delays. An estimated inverse compensator (EIC) is constructed to compensate for the hysteresis, while a Lyapunov-Krasovskii functional is used to handle the uncertainties of time delays. However, applying the quantized signal directly to the hysteretic system leads to degraded system performance. To overcome this issue, a new composite quantizer is proposed, which consists of an adaptive state-estimation filter and a modified hysteretic quantizer. The former facilitates state approximation by incorporating feedback information, while the latter regulates the communication rate. With the proposed EIC-FPAQC scheme, the closed-loop systems achieve semiglobal practical finite-time stability, and the tracking error can be guaranteed within a predefined accuracy. Experimental results on a piezoelectric-driven micropositioning stage demonstrate the effectiveness of the proposed method.