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

M. Ryalat, Dina Shona Laila

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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.
Original languageEnglish
Pages (from-to)1-16
JournalEuropean Journal of Control
Volume27
DOIs
Publication statusPublished - 17 Dec 2015

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Potential energy
Partial differential equations
Pendulums
Damping
Hamiltonians
Closed loop systems
Kinetic energy
Wheels
Stabilization

Bibliographical note

CC-BY-NC-ND user license

Keywords

  • Hamiltonian systems
  • Inertia wheel pendulum
  • Nonlinear control
  • Passivity-based control
  • Rotary inverted pendulum
  • Underactuated systems

Cite this

A simplified IDA-PBC design for underactuated mechanical systems with applications. / Ryalat, M.; Laila, Dina Shona.

In: European Journal of Control, Vol. 27, 17.12.2015, p. 1-16.

Research output: Contribution to journalArticle

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