Abstract
An adaptive control scheme is proposed for a class of uncertain pure-feedback nonlinear systems preceded by asymmetric hysteresis nonlinearity. The asymmetric property is described by the modified Bouc-Wen model based on the proposed asymmetric factor. State variables in the controller design are directly replaced with nonaffine functions to address the control problem caused by nonaffine appearance. Moreover, the control method can handle systems with external disturbances and guarantee the global stability of all the signals in the closed-loop system. The feasibility of the control scheme is verified by a simulation example and experimental results.
Highlights
Piezoelectric actuators have the advantages of high position resolution, maximum blocking force, high stiffness, wide bandwidth, and very short response time and play a key role in precision manufacturing and measurement [1]
The novel adaptive control scheme for pure-feedback systems is implemented through the use of nonaffine functions to replace state variables in the backstepping design
The main contributions in this paper are summarized as follows: (i) it is shown that the possibility for the proposed Bouc-Wen model as an illustration to hand asymmetric hysteresis nonlinearity; (ii) the difficulties from the nonaffine structures in pure-feedback systems are solved by a novel and simpler adaptive scheme implemented through the use of nonaffine functions to replace state variables in the backstepping design
Summary
Piezoelectric actuators have the advantages of high position resolution (nanometers or below), maximum blocking force (around hundreds of N), high stiffness, wide bandwidth, and very short response time and play a key role in precision manufacturing and measurement [1]. Adaptive neural network control schemes and fuzzy control based on the mean-value theorem have been proposed for a class of uncertain pure-feedback nonlinear systems [40,41,42,43]. The component of the hysteresis output in the proposed asymmetric Bouc-Wen model has been proven to be bounded This characteristic is essential for the controller design. The novel adaptive control scheme for pure-feedback systems is implemented through the use of nonaffine functions to replace state variables in the backstepping design. This method overcomes control problems caused by nonaffine appearance. The detailed proof of the fact that h is bounded is given in detail in Appendix A
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