Pseudoinverse Fuzzy Control of Discrete-Time Time-Delay Nonlinear Systems With Butterfly Hysteresis and Its Application on BDEA-Based Motion Platform.

This article proposes a novel fuzzy approximation-based adaptive dynamic surface control scheme with a double-loop pseudoinverse compensator for a class of discrete-time (DT) nonlinear systems characterized by time-delay and butterfly hysteresis. First, a DT butterfly Krasnosel'skii-Pokrovskii (DTBKP) model is developed to accurately characterize complex hysteresis in biconical dielectric elastomer actuators (BDEAs). Then, an optimized pseudoinverse (OPI) algorithm is designed to more effectively extract the actual control signal from the designed hysteresis temporary control signal, and thereby mitigating the butterfly hysteresis with the benefit of reducing its negative impact on control performance. Furthermore, to our best knowledge, fuzzy logic system (FLS) integrated with the finite covering lemma (FCL) is skillfully combined for the first time to handle unknown DT nonlinearities and time delay, and the digital first-order low-pass filter is incorporated into the controller design to overcome the causality issue inherent in DT backstepping control method. Finally, experimental validation of the proposed control scheme on the BDEAs motion control platform demonstrates its effectiveness for high-precision actuator control.