Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Sabatier, Jocelyn; Poullain, Serge; Latteux, Patrick; Thomas, Jean; Oustaloup, Alain

doi:10.1007/s11071-004-3768-2

Cited by 52 publications

(26 citation statements)

References 17 publications

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“…However, for time domain analysis integer approximations of fractional powers of s, such as given in [3][4][5][6], which are not exact have to be used. On the design side, fractional order versions of classical controllers, such as fractional order PID, have been designed [7] and applied [8][9][10][11] and various results have been obtained for stability analysis [12,13]. However, the field of fractional order control systems still needs further research on many important problems.…”

Section: Open Accessmentioning

confidence: 99%

Limit Cycles in Nonlinear Systems with Fractional Order Plants

et al. 2014

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Abstract:In recent years, there has been considerable interest in the study of feedback systems containing processes whose dynamics are best described by fractional order derivatives. Various situations have been cited for describing heat flow and aspects of bioengineering, where such models are believed to be superior. In many situations these feedback systems are not linear and information on their stability and the possibility of the existence of limit cycles is required. This paper presents new results for determining limit cycles using the approximate describing function method and an exact method when the nonlinearity is a relay characteristic.

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Section: Open Accessmentioning

confidence: 99%

Limit Cycles in Nonlinear Systems with Fractional Order Plants

et al. 2014

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“…These results reveal a complex order dynamics that is a consequence of the foot-ground interaction, with several free-impact-contact-impact-free dynamical states. Complex-order dynamics have already been addressed in modelling and control [24][25][26][27].…”

Section: Transfer Function Computationmentioning

confidence: 99%

Complex-order dynamics in hexapod locomotion

2006

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This paper studies the dynamics of foot-ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear springdashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with footforce feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot-ground transfer function, which presents complex-order dynamics. r

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“…It has wide range of applications in control theory [1], viscoelasticity [2], signal processing [3] and social sciences [4]. It has been recognized that the integral derivative of a function is related only to its nearby points, while fractional derivative is related to all of the function history.…”

Section: Introductionmentioning

confidence: 99%

Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals

et al. 2017

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In this paper, we study convergence characteristics of a class of continuous time fractional-order cellular neural network containing delay. Using the method of Lyapunov and Mittag-Leffler functions, we derive sufficient condition for global Mittag-Leffler stability, which further implies global asymptotic stability of the system equilibrium. Based on the theory of fractional calculus and the generalized Gronwall inequality, we approximate the solution of the corresponding neural network model using discretization method by piecewise constant argument and obtain some easily verifiable conditions, which ensures that the discrete-time analogues preserve the convergence dynamics of the continuous-time networks. In the end, we give appropriate examples to validate the proposed results, illustrating advantages of the discrete-time analogue over continuous-time neural network for numerical simulation.

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Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Cited by 52 publications

References 17 publications

Limit Cycles in Nonlinear Systems with Fractional Order Plants

Limit Cycles in Nonlinear Systems with Fractional Order Plants

Complex-order dynamics in hexapod locomotion

Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals

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