<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, a nonlinear balancing cube system is considered, the concept for which is based on an inverted pendulum. The main purpose of this work was the modelling and construction of a balancing cube with the synthesis of the control system. The control objectives included swing-up and stabilization of the cube on its vertex at an unstable equilibrium. Execution of the intended purpose required, first, deriving a cognitive mathematical model. It was based on the Lagrange method. Next, a mathematical model for control purposes was derived. The project of the physical model of the balancing cube was presented. A stabilization system based on a linear quadratic regulator (LQR) was developed. Moreover, a swing-up mechanism was used to bring the cube close to the upper equilibrium point. The algorithm switching condition was important to enable the correct functioning of the system. The developed control system was verified in the Matlab environment. Finally, verifying experiments and comparisons among models (mathematical and physical) were performed.</p>
</abstract>

In this paper, a nonlinear balancing cube system is considered, the concept for which is based on an inverted pendulum. The main purpose of this work was the modelling and construction of a balancing cube with the synthesis of the control system. The control objectives included swing-up and stabilization of the cube on its vertex at an unstable equilibrium. Execution of the intended purpose required, first, deriving a cognitive mathematical model. It was based on the Lagrange method. Next, a mathematical model for control purposes was derived. The project of the physical model of the balancing cube was presented. A stabilization system based on a linear quadratic regulator (LQR) was developed. Moreover, a swing-up mechanism was used to bring the cube close to the upper equilibrium point. The algorithm switching condition was important to enable the correct functioning of the system. The developed control system was verified in the Matlab environment. Finally, verifying experiments and comparisons among models (mathematical and physical) were performed.

Optimal State Feedback Controller For Balancing Cube

Journal of Automation, Mobile Robotics and Intelligent Systems

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Optimal State Feedback Controller For Balancing Cube"}

In this paper, a nonlinear balancing cube system is considered, the concept for which is based on an inverted pendulum. The main purpose of this work was the...

Optimal State Feedback Controller For Balancing Cube

Online veröffentlicht: 06. Sept. 2023

Seitenbereich: 3 - 12

Eingereicht: 11. Apr. 2022

Akzeptiert: 23. Mai 2022

DOI: https://doi.org/10.14313/jamris/3-2022/19

Schlüsselwörter
balancing cube, control systems, linear quadratic regulator, mathematical model, physical model

© 2022 Adam Kowalczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Optimal State Feedback Controller For Balancing Cube

Online veröffentlicht: 06. Sept. 2023

Seitenbereich: 3 - 12

Eingereicht: 11. Apr. 2022

Akzeptiert: 23. Mai 2022

DOI: https://doi.org/10.14313/jamris/3-2022/19

Schlüsselwörterbalancing cube, control systems, linear quadratic regulator, mathematical model, physical model

© 2022 Adam Kowalczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
balancing cube, control systems, linear quadratic regulator, mathematical model, physical model