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Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations

Author

Listed:
  • Dariusz Pazderski

    (Institute of Automatic Control and Robotics, Poznan University of Technology, ul. Piotrowo 3a, 60-965 Poznan, Poland)

  • Paweł Parulski

    (Institute of Automatic Control and Robotics, Poznan University of Technology, ul. Piotrowo 3a, 60-965 Poznan, Poland)

  • Patryk Bartkowiak

    (Institute of Automatic Control and Robotics, Poznan University of Technology, ul. Piotrowo 3a, 60-965 Poznan, Poland)

  • Przemysław Herman

    (Institute of Automatic Control and Robotics, Poznan University of Technology, ul. Piotrowo 3a, 60-965 Poznan, Poland)

Abstract

This paper considers the issue of linear-quadratic regulator (LQR) design for nonlinear systems with the use of smooth state and input transformations. The proposed design methodology is considered in the stabilisation task of the Pendubot, which is based on the concept of feedback equivalent control systems. It turns out that it is possible to find a controller that ensures comparable dynamics of the closed-loop system in the vicinity of the set point regardless of the state-space representation adopted. In addition, the synthesis of suboptimal controllers according to the LQR strategy ensuring equal dynamics at the equilibrium point is presented. The properties of the studied controllers were investigated in a simulation environment and using experimental tests. The detailed forms of transformations and linear approximations given can be regarded as ready-made procedures that can be applied to stabilise similar mechanical systems in robotics.

Suggested Citation

  • Dariusz Pazderski & Paweł Parulski & Patryk Bartkowiak & Przemysław Herman, 2022. "Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations," Energies, MDPI, vol. 15(14), pages 1-23, July.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:14:p:5146-:d:863614
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