LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation

Luis Severino; Fernando Sanhueza; Andres Peters; Francisco Vargas

doi:10.1109/CHILECON60335.2023.10418718

LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation

Luis Severino, Fernando Sanhueza, Andres Peters, Francisco Vargas

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

This work aims to explore the effects of the integral term in the discrete-time implementation of the LQI controller. To achieve this, a two-wheeled self-balancing robot system is used as a case study, and three types of numerical integration approximations are considered: Backward Euler, Forward Euler, and Tustin. Through simulations, the results obtained with each approximation are compared against the expected continuoustime design. The simulation results demonstrate that while there are no significant differences for small sampling times, the Tustin approximation exhibits notably better performance than the other alternatives as the sampling time increases.

Original language	English
Title of host publication	ChileCon 2023 - 2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350369533
DOIs	https://doi.org/10.1109/CHILECON60335.2023.10418718
State	Published - 2023
Externally published	Yes
Event	2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon 2023 - Hybrid, Valdivia, Chile Duration: 5 Dec 2023 → 7 Dec 2023

Publication series

Name	Proceedings - IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon
ISSN (Print)	2832-1529
ISSN (Electronic)	2832-1537

Conference

Conference	2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon 2023
Country/Territory	Chile
City	Hybrid, Valdivia
Period	5/12/23 → 7/12/23

Keywords

Integral Aproximation
Linear Quadratic Integral control
Self-balancing robot

Access to Document

10.1109/CHILECON60335.2023.10418718

Cite this

Severino, L., Sanhueza, F., Peters, A., & Vargas, F. (2023). LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation. In ChileCon 2023 - 2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (Proceedings - IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CHILECON60335.2023.10418718

Severino, Luis ; Sanhueza, Fernando ; Peters, Andres et al. / LQI Control of a Self Balancing Robot : A Numerical Study of the Impact of the Integral Approximation. ChileCon 2023 - 2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies. Institute of Electrical and Electronics Engineers Inc., 2023. (Proceedings - IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon).

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title = "LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation",

abstract = "This work aims to explore the effects of the integral term in the discrete-time implementation of the LQI controller. To achieve this, a two-wheeled self-balancing robot system is used as a case study, and three types of numerical integration approximations are considered: Backward Euler, Forward Euler, and Tustin. Through simulations, the results obtained with each approximation are compared against the expected continuoustime design. The simulation results demonstrate that while there are no significant differences for small sampling times, the Tustin approximation exhibits notably better performance than the other alternatives as the sampling time increases.",

keywords = "Integral Aproximation, Linear Quadratic Integral control, Self-balancing robot",

author = "Luis Severino and Fernando Sanhueza and Andres Peters and Francisco Vargas",

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language = "English",

series = "Proceedings - IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon",

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Severino, L, Sanhueza, F, Peters, A & Vargas, F 2023, LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation. in ChileCon 2023 - 2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies. Proceedings - IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon, Institute of Electrical and Electronics Engineers Inc., 2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon 2023, Hybrid, Valdivia, Chile, 5/12/23. https://doi.org/10.1109/CHILECON60335.2023.10418718

LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation. / Severino, Luis; Sanhueza, Fernando; Peters, Andres et al.
ChileCon 2023 - 2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies. Institute of Electrical and Electronics Engineers Inc., 2023. (Proceedings - IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Peters, Andres

AU - Vargas, Francisco

PY - 2023

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AB - This work aims to explore the effects of the integral term in the discrete-time implementation of the LQI controller. To achieve this, a two-wheeled self-balancing robot system is used as a case study, and three types of numerical integration approximations are considered: Backward Euler, Forward Euler, and Tustin. Through simulations, the results obtained with each approximation are compared against the expected continuoustime design. The simulation results demonstrate that while there are no significant differences for small sampling times, the Tustin approximation exhibits notably better performance than the other alternatives as the sampling time increases.

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Severino L, Sanhueza F, Peters A, Vargas F. LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation. In ChileCon 2023 - 2023 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies. Institute of Electrical and Electronics Engineers Inc. 2023. (Proceedings - IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, ChileCon). doi: 10.1109/CHILECON60335.2023.10418718

LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation

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