Sliding Mode Control of Vibration in Single-Degree-of-Freedom Fractional Oscillators

Yuan, Jian; Zhang, Youan; Liu, Jingmao; Shi, Bao

doi:10.1115/1.4036665

Cited by 6 publications

(6 citation statements)

References 38 publications

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“…Calculating the sum of sides of inequality for l ¼ 0 to infinity, it is concluded that condition equation (17) leads to upper-boundedness of cost as…”

Section: Resultsmentioning

confidence: 99%

“…Substituting equations (21) and (22) and the candidate Lyapunov function expressed in equation (19) and then substituting the calculated expression of candidate Lyapunov function in decreased condition (equation (17)), stabilization conditions (equation 23) are derived. The inclusion of system dynamics in the term i ðk þ lÞ results in viability of control scheme for the general class of considered nonlinear multibody dynamical system.…”

Section: Resultsmentioning

confidence: 99%

“…13 Under the assumption of linearity of dynamical behavior, Li et al 14 have proposed a robust sliding control model for active suspension systems. An optimization-based control model for nonlinear viscoelastic system has been proposed by Xiong and Zhu, 15 and stabilization of viscoelastic systems by pole placement has been investigated by Skaar et al 16 Yuan et al 17 have proposed a sliding controller for single DOF fractional vibrational systems. Yaqubi et al 18,19 have proposed feed-forward schemes for multi-objective control problems in vibrational systems while ignoring robustness characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…16 Yuan et al. 17 have proposed a sliding controller for single DOF fractional vibrational systems. Yaqubi et al.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear model predictive acceleration synchronization technique for rigid-model-based tracking control of multi-DOF flexible systems

Yaqubi

Homaeinezhad

2020

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this paper, the problem of stabilization and tracking control of uncertain flexible multivariable continuum mechanism systems with additional appendage considering boundedness of undesired vibrational effects are investigated. It is proposed that rather than controlling the entire dynamical system through installation of additional actuators on appendage, it is more desirable to stabilize the core system while considering undesired vibrational effect in the appendage as optimization cost. To this end, the nonlinear programming problem corresponding to a predictive control scheme is presented based on a cost defined according to magnitude of accelerations of undesired vibrations in the appendage. Stabilization of control algorithm is conducted based on demonstration of existence of feasible Lyapunov functions. Candidate Lyapunov functions are defined based on sliding functions analysis. The associated sliding functions are defined for core subsystems which correspond to degrees of freedom of dynamical system that are associated with reference signals. Undesired vibrations caused by other degrees of freedom corresponding to appendage are considered as segments of control cost in the optimization problem. To ensure the feasibility of control model in real-time applications, the control algorithm is obtained in discrete-time basis. Based on investigation of monotonically decreasing Lyapunov functions and expression of sliding functions as a combination of dynamical terms, reference inputs and control input terms, stabilizing constraints of closed-loop system are calculated. Similarly, based on combination of sliding surfaces with considered control and vibrational constraints, additional constraints for boundedness of vibrational terms in nonlinear programming problem are obtained. Numerical comparisons with a sliding control algorithm for core mechanical system and a reaching law method indicate improvements regarding reduction of undesired vibrational effects in appendage. Furthermore, regulation of appendage dynamics is conducted without installation of additional actuators, which reduces the implementation cost in comparison with a full-control scheme for core system and appendage.

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“…Calculating the sum of sides of inequality for l ¼ 0 to infinity, it is concluded that condition equation (17) leads to upper-boundedness of cost as…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…16 Yuan et al. 17 have proposed a sliding controller for single DOF fractional vibrational systems. Yaqubi et al.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear model predictive acceleration synchronization technique for rigid-model-based tracking control of multi-DOF flexible systems

Yaqubi

Homaeinezhad

2020

Proceedings of the Institution of Mechanical Engineers, Part K:

View full text Add to dashboard Cite

show abstract

“…Based on the energy storage and dissipation properties of the Caputo fractionalorder derivatives, the expression of mechanical energy in single-degree-of-freedom fractional oscillators has been determined and energy regeneration and dissipation during the vibratory motion have been obtained in [22]. Vibration controls have been designed using sliding mode control technique and adaptive control technique for single-degree-of-freedom fractional oscillators, multi-degree-of-freedom fractional oscillators, and fractional Duffing oscillators in [23,24].…”

Section: Introductionmentioning

confidence: 99%

Hereditary effects of exponentially damped oscillators with past histories

Yuan¹,

Xiu²,

Shi³

et al. 2018

Preprint

Self Cite

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Hereditary effects of exponentially damped oscillators with past histories are considered in this paper. Nonviscously damped oscillators involve hereditary damping forces which depend on time-histories of vibrating motions via convolution integrals over exponentially decaying functions. As a result, this kind of oscillators are said to have memory. In this work, initialization for nonviscously damped oscillators is firstly proposed. Unlike the classical viscously damped ones, information of the past history of response velocity is necessary to fully determine the dynamic behaviors of nonviscously damped oscillators. Then, initialization response of exponentially damped oscillators is obtained to characterize the hereditary effects on the dynamic response. At last, stability of initialization response is proved and the hereditary effects are shown to gradually recede with increasing of time.

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Control of MIMO mechanical systems interacting with actuators through viscoelastic linkages

Homaeinezhad

Yaqubi

Gholyan

2020

Mechanism and Machine Theory

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Sliding Mode Control of Vibration in Single-Degree-of-Freedom Fractional Oscillators

Cited by 6 publications

References 38 publications

Nonlinear model predictive acceleration synchronization technique for rigid-model-based tracking control of multi-DOF flexible systems

Nonlinear model predictive acceleration synchronization technique for rigid-model-based tracking control of multi-DOF flexible systems

Hereditary effects of exponentially damped oscillators with past histories

Control of MIMO mechanical systems interacting with actuators through viscoelastic linkages

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