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

M. Ryalat; Dina Shona Laila

doi:10.1109/CDC.2013.6760713

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

M. Ryalat, Dina Shona Laila

Research output: Contribution to conference › Paper

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages	5240-5245
DOIs	https://doi.org/10.1109/CDC.2013.6760713
Publication status	Published - 10 Mar 2014
Event	IEEE Conference on Decision and Control - Florence, Italy Duration: 10 Dec 2013 → 13 Dec 2013

Conference

Conference	IEEE Conference on Decision and Control
Country/Territory	Italy
City	Florence
Period	10/12/13 → 13/12/13

Bibliographical note

The full text is currently unavailable on the repository.

Keywords

Potential energy
Mechanical systems
Damping
Kinetic energy
Equations
Mathematical model
stability
closed loop systems
control system synthesis
matrix algebra
nonlinear control systems
partial differential equations
pendulums
Quanser rotary inverted pendulum
IDA-PBC design
interconnection and damping assignment passivity based control
underactuated mechanical systems
matching equations
closed-loop inertia matrix
potential energy PDE
coupling term
numerical simulations
underactuated systems
Hamiltonian systems
passivity-based control
rotary inverted pendulum

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10.1109/CDC.2013.6760713

Cite this

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

abstract = "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.",

keywords = "Potential energy, Mechanical systems, Damping, Kinetic energy, Equations, Mathematical model, stability, closed loop systems, control system synthesis, matrix algebra, nonlinear control systems, partial differential equations, pendulums, Quanser rotary inverted pendulum, IDA-PBC design, interconnection and damping assignment passivity based control, underactuated mechanical systems, matching equations, closed-loop inertia matrix, potential energy PDE, coupling term, numerical simulations, underactuated systems, Hamiltonian systems, passivity-based control, rotary inverted pendulum",

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AU - Ryalat, M.

AU - Laila, Dina Shona

N1 - The full text is currently unavailable on the repository.

PY - 2014/3/10

Y1 - 2014/3/10

N2 - 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.

AB - 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.

KW - Potential energy

KW - Mechanical systems

KW - Damping

KW - Kinetic energy

KW - Equations

KW - Mathematical model

KW - stability

KW - closed loop systems

KW - control system synthesis

KW - matrix algebra

KW - nonlinear control systems

KW - partial differential equations

KW - pendulums

KW - Quanser rotary inverted pendulum

KW - IDA-PBC design

KW - interconnection and damping assignment passivity based control

KW - underactuated mechanical systems

KW - matching equations

KW - closed-loop inertia matrix

KW - potential energy PDE

KW - coupling term

KW - numerical simulations

KW - underactuated systems

KW - Hamiltonian systems

KW - passivity-based control

KW - rotary inverted pendulum

U2 - 10.1109/CDC.2013.6760713

DO - 10.1109/CDC.2013.6760713

M3 - Paper

SP - 5240

EP - 5245

T2 - IEEE Conference on Decision and Control

Y2 - 10 December 2013 through 13 December 2013

ER -

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

Abstract

Conference

Bibliographical note

Keywords

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