Classification of two‐degree‐of‐freedom underactuated mechanical systems

Maalouf, Divine; Moog, Claude H.; Aoustin, Yannick; Li, Shunjie

doi:10.1049/iet-cta.2014.0280

Cited by 13 publications

(4 citation statements)

References 25 publications

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“…In the case of underactuated systems with two degrees of freedom, three classes are defined, namely, Class I, Class II, and Class III associated with strict feedback, nontriangular quadratic, and feedforward forms, respectively. Some efforts of classification of the underactuated mechanical systems were carried out, in particular in [58,59] where the classification is based on certain characteristics of the model of the studied system.…”

Section: Classification Of Underactuated Mechanical Systemsmentioning

confidence: 99%

A Review on the Control of Second Order Underactuated Mechanical Systems

2018

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This paper describes some important classes of two degrees of freedom of underactuated mechanical system and also surveys review of the recent state-of-the-art concerning the mathematical modeling of these systems, their classification, and all the control strategies (linear, nonlinear, and intelligent) that have been made so far (i.e., from the year 2000 to date) to control these systems. Future research and challenges concerning the improvement, the effectiveness, and robustness of the proposed controllers for underactuated mechanical systems are presented.

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Section: Classification Of Underactuated Mechanical Systemsmentioning

confidence: 99%

A Review on the Control of Second Order Underactuated Mechanical Systems

2018

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Section: Introductionmentioning

confidence: 99%

“…In the first case, the systems will be called of class (1,1) and in the second case, of class (1,2), where the first component being 1 refers to the linearizability defect equal 1 and the second component being 1 or 2 refers to the number of independent maximally part-linearizing outputs being, respectively, 1 or 2. Early attempts for such a classification can be found in the works of Olfati-Saber 3,4 and Maalouf et al 5 The main contributions of this paper are as follows. We propose a classification of nonlinear single-input control-affine systems in terms of the linearizability defect and of the number of independent partially linearizing outputs.…”

Section: Introductionmentioning

confidence: 99%

Maximal feedback linearization and its internal dynamics with applications to mechanical systems on

Moog

Respondek

2019

Intl J Robust & Nonlinear

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Summary For systems that are not feedback linearizable, a natural question is: how to find the largest feedback linearizable subsystem and, if the partial linearization is not unique, what are the control‐theoretic properties of various partial linearizations. In this paper, we will consider the problem of how to choose a partially linearizing output that renders the zero dynamics asymptotically stable and when such an output exists. We will state general results solving completely the problem for systems whose linearizability defect is one by identifying and describing two classes of systems. For the first class, all maximal partial linearizations lead to the same zero dynamics. For the second class, any asymptotic behavior of the zero dynamics can be achieved by a suitable choice of a partially linearizing output. In the second part, we apply our results to mechanical systems with two‐degrees‐of‐freedom and provide a detailed study of their partial linearizations. We illustrate the obtained results by examples of Acrobot (which belongs to the second class) and Pendubot (which belongs to the first class).

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“…Depending on the class of the underactuated mechanical system under consideration and the proposed output function, the closed-loop system may be composed of an internal dynamics which must be stable in order to accomplish the control task. 33 The previous literature review shows that only a few works have addressed the problem of tracking control of periodic oscillatory trajectories of the Furuta pendulum.…”

Section: Introductionmentioning

confidence: 99%

Tracking of periodic oscillations in an underactuated system via adaptive neural networks

Puga-Guzmán

Aguilar-Avelar

Moreno–Valenzuela

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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In this paper, the tracking control of periodic oscillations in an underactuated mechanical system is discussed. The proposed scheme is derived from the feedback linearization control technique and adaptive neural networks are used to estimate the unknown dynamics and to compensate uncertainties. The proposed neural network-based controller is applied to the Furuta pendulum, which is a nonlinear and nonminimum phase underactuated mechanical system with two degrees of freedom. The new neural network-based controller is experimentally compared with respect to its modelbased version. Results indicated that the proposed neural algorithm performs better than the model-based controller, showing that the real-time adaptation of the neural network weights successfully estimates the unknown dynamics and compensates uncertainties in the experimental platform.

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Classification of two‐degree‐of‐freedom underactuated mechanical systems

Cited by 13 publications

References 25 publications

A Review on the Control of Second Order Underactuated Mechanical Systems

A Review on the Control of Second Order Underactuated Mechanical Systems

Maximal feedback linearization and its internal dynamics with applications to mechanical systems on

Tracking of periodic oscillations in an underactuated system via adaptive neural networks

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