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Energy shaping dynamic tube-MPC for underactuated mechanical systems

Nonlinear Dynamics volume 106, pages 359–380 (2021)Cite this article

Abstract

This work investigates the tracking control problem for underactuated mechanical systems. To this end, we develop an extension of the dynamic tube Model Predictive Control (MPC) approach by combining an MPC design, an ancillary energy shaping controller constructed with the Interconnection and Damping Assignment Passivity-Based Control methodology, and an analytical expression of the dynamic tube. In addition, we extend the proposed approach by including the adaptive compensation of a class of unknown disturbances. The stability analysis is presented by employing a Lyapunov approach. The effectiveness of the proposed controller is demonstrated with simulations on two underactuated systems: a two-mass-spring-damper system with uncertain damping and either linear or nonlinear spring; an inertia-wheel-pendulum with unmodeled disturbances.

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Acknowledgements

The first author thanks the “Fundação de Amparo à Ciência e Tecnologia de Pernambuco” for the research support in Pernambuco (Brazil) through the project APQ-1226-3.05/15. The second author was supported by the UK Engineering and Physical Sciences Research Council (Grant Number EP/R009708/1 and EP/R511547/1).

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Authors and Affiliations

  1. Mechanical Engineering Department, Federal University of Pernambuco, Av. Prof. Moraes Rego 1235, Recife-PE, 50670-901, Brazil

    Guaraci Bastos Jr.

  2. Mechatronics in Medicine Laboratory, Mechanical Engineering Department, Imperial College London, Exhibition Road, London, SW7 2AZ, UK

    Enrico Franco

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  1. Guaraci Bastos Jr.
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  2. Enrico Franco
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Correspondence to Guaraci Bastos Jr..

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Bastos, G., Franco, E. Energy shaping dynamic tube-MPC for underactuated mechanical systems. Nonlinear Dyn 106, 359–380 (2021). https://doi.org/10.1007/s11071-021-06863-9

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Keywords

  • Underactuated systems
  • Port-Hamiltonian systems
  • Robust control
  • IDA-PBC
  • Dynamic tube-MPC