Elastic inverted pendulum with backlash in suspension: stabilization problem

Abstract

In this paper, we investigate the elastic inverted pendulum with hysteretic nonlinearity (a backlash) in the suspension point. Namely, the problems of stabilization and optimization of such a system are considered. The algorithm (based on the bionic model) which provides the effective procedure for finding of optimal parameters is presented and applied to considered system. The results of numerical simulations, namely the phase portraits and the dynamics of Lyapunov function, are also presented and discussed.

Broadband frequency response of a nonlinear resonator with clearance for energy harvesting

“…We continue these studies on an inverted elastic pendulum by investigating capability of impacts for energy conversion. In our dynamical system the contact between amplitude limiters and the pendulum is defined in a different way (comparing to earlier proposals [17,18]). …”

“…Later, Semenov at al. [17,18] also the horizontal excitation in the proposed system with a hysteretic coupling between the excitation frame and the inverted pendulum. We continue these studies on an inverted elastic pendulum by investigating capability of impacts for energy conversion.…”

State-feedback Control Principles for Inverted Pendulum with Hysteresis in Suspension

“…The backlashes appear in such systems during its long operation due to the "aging" of the materials. As was mentioned above such backlashes are of hysteretic nature and the analysis of such nonlinearities is quiet important and actual problem [16,17]. In this paper we investigate the problem of the state feedback control of the inverted pendulum with the hysteretic nonlinearity in the form of backlash.…”

Resonance Phenomena in Systems With Hysteretic Nonlinearities

“…Appearance of mathematical models of hysteretic phenomena is connected with the wide set of applied problems, generally in the theory of automatic control (see, e.g., [1,2,3] and related references). In these systems the sources with hysteretic properties can not be considered separately, but should be considered as a part of some complex system [1,4].…”

“…Krasnoselskii and A.V. Pokrovskii [3] where the hysteretic phenomena are considered in the frame of the system's theory. Namely, the hysteretic converters are treated as operators (such operators parametrically depend on its initial state) defined on a sufficiently rich functional space (for example, in the space of continuous functions).…”