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

A simplified IDA-PBC design for underactuated mechanical systems with applications
A simplified IDA-PBC design for underactuated mechanical systems with applications
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 port-controlled 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
0947-3580
1-16
Ryalat, Mutaz
0e91b18b-092b-44b1-a903-57c62f0db638
Laila, Dina Shona
41aa5cf9-3ec2-4fdf-970d-a0a349bfd90c
Ryalat, Mutaz
0e91b18b-092b-44b1-a903-57c62f0db638
Laila, Dina Shona
41aa5cf9-3ec2-4fdf-970d-a0a349bfd90c

Ryalat, Mutaz and Laila, Dina Shona (2016) A simplified IDA-PBC design for underactuated mechanical systems with applications. European Journal of Control, 27, 1-16. (doi:10.1016/j.ejcon.2015.12.001).

Record type: Article

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 (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 port-controlled 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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More information

Accepted/In Press date: 1 December 2015
e-pub ahead of print date: 17 December 2015
Published date: January 2016
Organisations: Mechatronics

Identifiers

Local EPrints ID: 382357
URI: http://eprints.soton.ac.uk/id/eprint/382357
ISSN: 0947-3580
PURE UUID: e566061e-e8fb-430a-b70b-84c4936a442b

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Date deposited: 29 Oct 2015 11:16
Last modified: 16 Dec 2019 20:13

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