Abstract
In this note, we consider the same class of systems as in a previous paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the disturbance-like term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance.
Highlights
Hysteresis exists in a wide range of physical systems and devices, such as biology optics, electromagnetism, mechanical actuators, electronic relay circuits and other areas
In [1], a dynamic hysteresis model is defined to pattern a backlash-like hysteresis rather than constructing an inverse model to mitigate the effects of the hysteresis
We develop two simple backstepping adaptive control schemes for the same class of nonlinear systems as in [1], with bounded external disturbances included in our case
Summary
Hysteresis exists in a wide range of physical systems and devices, such as biology optics, electromagnetism, mechanical actuators, electronic relay circuits and other areas. Control of such systems is typically challenging. Several adaptive control schemes have recently been proposed; see, for example, [1] and [2]. In [1], the term multiplying the control and the uncertain parameters of the system must be within known intervals and the “disturbance-like” term must be bounded with known bound. To avoid possible chattering caused by the sign function, we propose an alternative smooth control law and the tracking error is still ensured to approach a prescribed bound in this case.
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