IDA-PBC for a class of underactuated mechanical systems with application to a rotary inverted pendulum

Ryalat, Mutaz; Laila, Dina Shona

doi:10.1109/cdc.2013.6760713

Cited by 9 publications

(10 citation statements)

References 15 publications

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“…11 that the control effort is significantly increased with the increased initial angular position of the pendulum. More simulations on a different rotary inverted pendulum hardware can be found in [28].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The results have proved the effectiveness of the controller and its robustness with respect to disturbances. The theoretical results presented in this paper (together with [28]) and the experimental results can be used as the motivation to use this method in other real engineering applications. Current research is under way to extend this approach for a larger class of underactuated mechanical systems, as well as proposing an observer that facilitate the IDA-PBC methodology .…”

Section: Discussionmentioning

confidence: 99%

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A simplified IDA-PBC design for underactuated mechanical systems with applications

Ryalat

Laila

2016

European Journal of Control

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Please check your proof carefully and mark all corrections at the appropriate place in the proof (e.g., by using on-screen annotation in the PDF file) or compile them in a separate list. Note: if you opt to annotate the file with software other than Adobe Reader then please also highlight the appropriate place in the PDF file. To ensure fast publication of your paper please return your corrections within 48 hours.For correction or revision of any artwork, please consult http://www.elsevier.com/artworkinstructions.Any queries or remarks that have arisen during the processing of your manuscript are listed below and highlighted by flags in the proof. Click on the Q link to go to the location in the proof.Your article is registered as a regular item and is being processed for inclusion in a regular issue of the journal. If this is NOT correct and your article belongs to a Special Issue/Collection please contact p.atterbury@elsevier.com immediately prior to returning your corrections. Location in articleQuery / Remark: click on the Q link to go Please insert your reply or correction at the corresponding line in the proof Q1Please confirm that given names and surnames have been identified correctly and are presented in the desired order. Q2Corresponding author has not been indicated in the author group. Kindly provide the corresponding author's footnote. Q3Please provide the city of publication for Refs. [10,12,15].Thank you for your assistance. We develop a method to simplify the partial differential equations (PDEs) associated to the potential energy for interconnection and damping assignment passivity based control (IDA-PBC) of a class of underactuated mechanical systems (UMSs). Solving the PDEs, also called the matching equations, is the main difficulty in the construction and application of the IDA-PBC. We propose a simplification to the potential energy PDEs through a particular parametrization of the closed-loop inertia matrix that appears as a coupling term with the inverse of the original inertia matrix. The parametrization accounts for kinetic energy shaping, which is then used to simplify the potential energy PDEs and their solution that is used for the potential energy shaping. This energy shaping procedure results in a closed-loop UMS with a modified energy function. This approach avoids the cancellation of nonlinearities, and extends the application of this method to a larger class of systems, including separable and non-separable portcontrolled Hamiltonian (PCH) systems. Applications to the inertia wheel pendulum and the rotary inverted pendulum are presented, and some realistic simulations are presented which validate the proposed control design method and prove that global stabilization of these systems can be achieved. Experimental validation of the proposed method is demonstrated using a laboratory set-up of the rotary pendulum. The robustness of the closed-loop system with respect to external disturbances is also experimentally verified.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A simplified IDA-PBC design for underactuated mechanical systems with applications

Ryalat

Laila

2016

European Journal of Control

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“…To start with, a stabilizing controller is obtained using IDA-PBC design procedures proposed in [9]. The main objective is to provide a continuous control law to swing up the pendulum by spinning the wheel and to stabilize it at its upward position q = (0, q 2 ) for any q 2 ∈ [0, 2π].…”

Section: B Iss For Non-separable Pch Systems Using Ida-pbc Methodsmentioning

confidence: 99%

“…We briefly review the general procedure of the IDA-PBC design as has been proposed for instance in [1], [3], [9]. Given a PCH system (1), by applying the IDA-PBC design we obtain the following preserved PCH dynamics…”

Section: B Review On Ida-pbc Designmentioning

confidence: 99%

Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems

Ryalat

Laila

Torbati

2015

2015 American Control Conference (ACC)

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Interconnection and damping assignment passivity based control (IDA-PBC) is a method that has been developed to (asymptotically) stabilize nonlinear systems formulated in portcontrolled Hamiltonian (PCH) structure. This method has gained increasing popularity and has been successfully applied to a wide range of dynamical systems. However, little is known about the robustness of this method in response to the effects of uncertainty which could result from disturbances, noises, and modeling errors. This paper explores the possibility of extending the IDA-PBC method by adopting a robustness perspective, with the aim of maintaining (asymptotic) stability of the system in the presence of such perturbations which exist in any realistic problem. We propose constructive results on Robust IDA-PBC and PID-like controllers for a class of PCH systems. The results extend some existing methods and provide a new framework that allows the implementation of integral action control to underactuated PCH systems that are quite commonly found in practice. The results are applied to a Quanser inertia wheel pendulum and illustrated through numerical simulations.

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“…This approach is based on the re-parametrization of the target dynamics and has been applied to the cart and Furuta pendulums. Via a parametrization of the closed-loop inertia matrix, another simplification of the PDE equation, associated to the potential energy was proposed in [15] and has been applied to solve a global stabilization design of a rotary inverted pendulum.…”

Section: Definition and Preliminariesmentioning

confidence: 99%

Stabilization of the Inertia Wheel Inverted Pendulum by Advanced IDA-PBC Based Controllers: Comparative Study and Real-Time Experiments

Hfaiedh¹,

Chemori

Abdelkrim³

2020

2020 17th International Multi-Conference on Systems, Signals &Amp; Devices (SSD)

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IDA-PBC for a class of underactuated mechanical systems with application to a rotary inverted pendulum

Cited by 9 publications

References 15 publications

A simplified IDA-PBC design for underactuated mechanical systems with applications

A simplified IDA-PBC design for underactuated mechanical systems with applications

Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems

Stabilization of the Inertia Wheel Inverted Pendulum by Advanced IDA-PBC Based Controllers: Comparative Study and Real-Time Experiments

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