Interconnection and Damping Assignment Passivity—Based Control of the Pendubot

Sandoval, Jesús; Kelly, Rafael

doi:10.3182/20080706-5-kr-1001.01302

Cited by 16 publications

(11 citation statements)

References 3 publications

(1 reference statement)

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“…2) Damping assignment: The damping injection controller follows the construction (11). Given M d that has been obtained when reshaping the total energy, we have…”

Section: B Controller Designmentioning

confidence: 99%

“…In [8], a pasivity and energy based technique has been proposed for general underactuated mechanical systems by applying partial feedback linearization. PBC methods have been developed for various underactuated systems, such as pendulum on a cart [9], inertia wheel and ball on beam [10], Pendubot [11] and Acrobot [12]. Other nonlinear control designs have been reported in [7].…”

Section: Introductionmentioning

confidence: 99%

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

Ryalat

Laila

2013

52nd IEEE Conference on Decision and Control

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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. Solving the PDEs, also called the matching equations, is the main difficulty in the construction and application of the IDA-PBC. With the proposed method, a simplification to the potential energy PDE is achieved through a particular parametrization of the closed-loop inertia matrix that appears as a coupling term with the inverse of original inertia matrix. The results are applied to the Quanser rotary inverted pendulum and illustrated through numerical simulations.Index Terms-Hamiltonian systems, passivity-based control, rotary inverted pendulum, underactuated systems.

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“…2) Damping assignment: The damping injection controller follows the construction (11). Given M d that has been obtained when reshaping the total energy, we have…”

Section: B Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ryalat

Laila

2013

52nd IEEE Conference on Decision and Control

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“…The potential energy shaping is then achieved by using the fixed M d and by imposing that M d and V d are both functions of one and the same actuated coordinate. Inspired by the work of [2], several IDA-PBC controllers have been proposed in [35,29,20,38], for various UMSs.…”

Section: The Matching Equationsmentioning

confidence: 99%

“…A number of constructive approaches to solve or simplify these PDEs for different classes of UMSs have been recently proposed in [2,7,14,20,25,38] and references therein. Also, IDA-PBC has been applied to various underactuated systems, such as pendulum on a cart [35], inertia wheel and ball and beam systems [25], Pendubot [29] and Acrobot [20].…”

Section: Introductionmentioning

confidence: 99%

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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“…Assumption A1 includes a class of underactuated mechanical systems where the vector of desired positions q * in the closed-loop system belongs to the set of critical points of the open-loop system, such that ∇ q V (q)| q=q * = 0. Some examples are the inertial wheel pendulum and the ball and beam systems shown in [7], the cart-pole system [18], the acrobot [19], the Furuta pendulum [20], and the pendubot [21].…”

Section: Remarkmentioning

confidence: 99%

Interconnection and damping assignment passivity‐based control of a class of underactuated mechanical systems with dynamic friction

Sandoval

Kelly

Santibáñez

2011

Intl J Robust & Nonlinear

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SUMMARYThis paper considers the extension of the interconnection and damping assignment passivity-based control methodology for a class of underactuated mechanical systems with dynamic friction. We present a new damping assignment approach to compensate friction by means of a nonlinear observer. Friction at the actuated joints is assumed to be captured by a bristle deflection model: the Dahl model. Based on the Lyapunov direct method we show that, under some conditions, the overall closed-loop system is stable and, by invoking the theorem of Barbashin-Krasovskii, we arrive to asymptotic stability conditions. Experiments with an underactuated mechanical system, the Furuta pendulum, show the effectiveness of the proposed scheme when friction is compensated.

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Interconnection and Damping Assignment Passivity—Based Control of the Pendubot

Cited by 16 publications

References 3 publications

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

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

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

Interconnection and damping assignment passivity‐based control of a class of underactuated mechanical systems with dynamic friction

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