Adaptive control with hysteresis estimation and compensation using RFNN for piezo-actuator

Nonlinear Dynamics and Performance Analysis of a Buck Converter with Hysteresis Control

This paper presents the mathematical modeling and experimental implementation of a Buck converter with hysteresis control. The system is described using a state-space model. Theoretical and simulation studies show that the zero hysteresis control leads to an equilibrium point with the implication of an infinite commutation frequency, while the use of a constant hysteresis band induces a limit cycle with a finite switching frequency. There exists a tradeoff between voltage output ripple and transistor switching frequency. An experimental prototype for the Buck power converter is built, and theoretical results are verified experimentally. In general terms, the Buck converter with the hysteresis control shows a robust control with respect to load variations, with undesired high switching frequency taking place for a very narrow hysteresis band, which is solved by tuning the hysteresis band properly.

Globally exponential continuous controller/observer for position tracking in robot manipulators with hysteretic joint friction

In this work, we present a continuous observer and continuous controller for a multiple degree of freedom robot manipulator with hysteretic joint friction. The fictitious hysteresis state is of course unknown to the controller and must be estimated. The joint velocities are assumed measured here. For this considered plant, we propose and present a continuous observer/controller that estimates or observes the hysteresis state and drives the position tracking error to zero. We prove that the combined tracking error and observer error converges to zero globally exponentially.

An adaptive recurrent radial basis function network tracking controller for a two-dimensional piezo-positioning stage

An adaptive recurrent radial basis function network (ARRBFN) tracking controller for a two-dimensional piezo-positioning stage is proposed in this study. First, a mathematical model that represents the dynamics of the two-dimensional piezo-positioning stage is proposed. In this model, a hysteresis friction force that describes the hysteresis behavior of one-dimensional motion is used; and a nonconstant stiffness with the cross-coupling dynamic due to the effect of bending of a lever mechanism in x and y axes also is included. Then, according to the proposed mathematical model, an ARRBFN tracking controller is proposed. In the proposed ARRBFN control system, a recurrent radial basis function network (RRBFN) with accurate approximation capability is used to approximate an unknown dynamic function. The adaptive learning algorithms that can learn the parameters of the RRBFN on line are derived using Lyapunov stability theorem. Moreover, a robust compensator is proposed to confront the uncertainties, including approximation error, optimal parameter vectors, higher-order terms in Taylor series. To relax the requirement of the value of the lumped uncertainty in the robust compensator, an adaptive law is investigated to estimate the lumped uncertainty. Using the proposed control scheme, the position tracking performance is substantially improved and the robustness to uncertainties, including hysteresis friction force and cross-coupling stiffness, can be obtained as well. The tracking performance and the robustness to external load of the proposed ARRBFN control system are illustrated by some experimental results.