Inverted pendulum under hysteretic control: stability zones and periodic solutions

Семенов, Михаил Е.; Shevlyakova, Darya V.; Meleshenko, Peter A.

doi:10.1007/s11071-013-1062-x

Cited by 26 publications

(15 citation statements)

References 30 publications

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“…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.…”

Section: Introductionmentioning

confidence: 97%

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

Abbas¹,

Kanishcheva²,

Семенов³

et al. 2016

J. Sib. Fed. Univ., Math. phys.

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In this paper we consider the mathematical model of the inverted pendulum with the hysteretic nonlinearity (in the form of a backlash) under state feedback control. The analytic results for the stability criteria as well as for the solution of the linearized equation are observed and analyzed. The theorems that determine the stabilization of the considered system are formulated and discussed. The question on the optimal control of the system under consideration is also discussed and the corresponding theorem is considered.

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Section: Introductionmentioning

confidence: 97%

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

Abbas¹,

Kanishcheva²,

Семенов³

et al. 2016

J. Sib. Fed. Univ., Math. phys.

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“…Moreover, such a mechanical system can be applied in various fields. Namely, the model of inverted pendulum (especially, under various kinds of control of the suspension point motion) is widely used in physics [32], applied mathematics [38], engineering science [21,31,33], neuroscience [39], economics [30], etc.…”

Section: Introductionmentioning

confidence: 99%

Elastic inverted pendulum with backlash in suspension: stabilization problem

2015

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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.

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“…In general, the problem of inverted pendulum is of more than one hundred years history and it still relevant even in the present days (see, e.g., [8,9,10,11] and related references).…”

Section: Introductionmentioning

confidence: 99%

Elastic Inverted Pendulum Under Hysteretic Nonlinearity in Suspension: Stabilization and Optimal Control

Семенов¹,

Solovyov²,

Semenov³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This paper is dedicated to investigation of the elastic inverted pendulum with hysteretic nonlinearity in the suspension point. We consider the problem of stabilization and optimal control of such a system. In the frame of the bionic model we present an algorithm which provides an effective procedure for finding of optimal control parameters together with application of this algorithm to the system under consideration. The results of numerical simulations, namely, the phase portraits and the dynamics of Lyapunov function are presented and discussed.

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Inverted pendulum under hysteretic control: stability zones and periodic solutions

Cited by 26 publications

References 30 publications

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

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

Elastic inverted pendulum with backlash in suspension: stabilization problem

Elastic Inverted Pendulum Under Hysteretic Nonlinearity in Suspension: Stabilization and Optimal Control

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