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

Dariusz Pazderski, Paweł Parulski, Patryk Bartkowiak and Przemysław Herman
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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

Energies, 2022, vol. 15, issue 14, 1-23

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.

Keywords: nonlinear systems; underactuated systems; Pendubot; model transformation; quasi-velocities; stabilization methods; linear quadratic regulator (LQR); experiment (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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