Published by De Gruyter (O) July 2, 2022

Stepping quantum genetic algorithm-based LQR control strategy for lateral vibration of high-speed elevator

Schrittweise quanten-genetischer Algorithmus-basierte LQR-Steuerungsstrategie für laterale Schwingungen von Hochgeschwindigkeitsaufzügen

Li Li

Li Li received the B.Ṡ. degree in Mechanical design, manufacturing and automation from University of Science and Technology Liaoning, Anshan, in 2004, the M. S. degree in Mechanical design and theory from University of Science and Technology Liaoning, Anshan, in 2007.Since 2009, she has been a Lecturer in School of Mechanical and Electrical Engineering, Shandong Jianzhu University, Jinan. She is the author of four books and six articles. Her research interests include mechanical innovative design and mechanical control theory.
, Tian Qiu

Tian Qiu was born in Heze, China. He received the B. S. degree in Electronic and Information Engineering from Electrical and Electronic Engineering College, Shandong University of Technology, Zibo, in 2017. He is currently pursuing the M. S. degree with School of Mechanical and Electrical Engineering, Shandong Jianzhu University, Jinan.His current research interests include optimal control, adaptive control and intelligent control.
, Tichang Jia

Tichang Jia was born in Liaocheng, China. He received the B. S. degree in mechanical engineering from Shandong Jianzhu University, Jinan, in 2017, the M. S. degree in mechanical engineering from Shandong Jianzhu University in 2020. He is currently pursuing the Ph. D. degree in mechanical engineering from Northeastern University, Shenyang.His research interests include model predictive control, intelligent control and mechanical precision machining.
and Chen Chen

Chen Chen was born in Zaozhuang, China. She received the B. S. degree in mechanical engineering from ShanDong JiaoTong University, Jinan, in 2018, the M. S. degree in mechanical engineering from Shandong Jianzhu University in 2020. She is currently pursuing the Ph. D. degree in mechanical engineering from Northeastern University, Shenyang.Her research interests include robust control and intelligent control.

From the journal at - Automatisierungstechnik

https://doi.org/10.1515/auto-2021-0154

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Abstract

To effectively restrain the lateral vibration caused by the guide rail excitation and improve the ride comfort of the car system, a state-weighted linear quadratic regulator (LQR) control strategy is proposed. Firstly, based on the active control model of the 4-DOF car system with actuators distributed diagonally along the center of the car frame, an LQR controller for lateral vibration of high-speed elevator car systems is designed. Furthermore, in view of the tedious and time-consuming of the empirical method to choose state-weighted matrix Q, stepping quantum genetic algorithm (SQGA) is proposed to improve the performance of the controller. Finally, the time-frequency characteristic curves of the lateral vibration acceleration and the vibration displacement of the car system are compared and analyzed by MATLAB to verify the effectiveness of the proposed controller.

Zusammenfassung

Um die durch die Führungsschienenanregung verursachten seitlichen Vibrationen effektiv zu begrenzen und den Fahrkomfort des Fahrzeugsystems zu verbessern, wird eine zustandsgewichtete lineare quadratische Reglerstrategie (LQR) vorgeschlagen. Zunächst wird basierend auf dem aktiven Steuerungsmodell des 4-DOF-Fahrzeugsystems mit diagonal entlang der Mitte des Fahrzeugrahmens verteilten Aktoren ein LQR-Controller für seitliche Vibrationen von Hochgeschwindigkeitsaufzugsystemen entworfen. Darüber hinaus wird angesichts der aufwändigen empirischen Methode zur Auswahl der zustandsgewichteten Matrix Q ein schrittweiser quanten-genetischer Algorithmus (SQGA) vorgeschlagen, um die Leistung des Reglers zu verbessern. Schließlich werden die Zeit-Frequenz-Kennlinien der seitlichen Schwingungsbeschleunigung und der Schwingungsverschiebung des Fahrzeugsystems mit MATLAB verglichen und analysiert, um die Wirksamkeit des vorgeschlagenen Reglers zu überprüfen.

Keywords: high-speed elevator; active damping; LQR controller; stepping quantum genetic algorithm

Schlagwörter: Hochgeschwindigkeitsaufzug; aktive Dämpfung; LQR-Controller; Schrittquanten-genetischer Algorithmus

Funding statement: This study was funded by the horizontal project of school enterprise cooperation, China (H21097E).

About the authors

Li Li

Li Li received the B.Ṡ. degree in Mechanical design, manufacturing and automation from University of Science and Technology Liaoning, Anshan, in 2004, the M. S. degree in Mechanical design and theory from University of Science and Technology Liaoning, Anshan, in 2007.Since 2009, she has been a Lecturer in School of Mechanical and Electrical Engineering, Shandong Jianzhu University, Jinan. She is the author of four books and six articles. Her research interests include mechanical innovative design and mechanical control theory.

Tian Qiu

Tian Qiu was born in Heze, China. He received the B. S. degree in Electronic and Information Engineering from Electrical and Electronic Engineering College, Shandong University of Technology, Zibo, in 2017. He is currently pursuing the M. S. degree with School of Mechanical and Electrical Engineering, Shandong Jianzhu University, Jinan.His current research interests include optimal control, adaptive control and intelligent control.

Tichang Jia

Tichang Jia was born in Liaocheng, China. He received the B. S. degree in mechanical engineering from Shandong Jianzhu University, Jinan, in 2017, the M. S. degree in mechanical engineering from Shandong Jianzhu University in 2020. He is currently pursuing the Ph. D. degree in mechanical engineering from Northeastern University, Shenyang.His research interests include model predictive control, intelligent control and mechanical precision machining.

Chen Chen

Chen Chen was born in Zaozhuang, China. She received the B. S. degree in mechanical engineering from ShanDong JiaoTong University, Jinan, in 2018, the M. S. degree in mechanical engineering from Shandong Jianzhu University in 2020. She is currently pursuing the Ph. D. degree in mechanical engineering from Northeastern University, Shenyang.Her research interests include robust control and intelligent control.

Acknowledgment

The authors are grateful for the equipment support provided by Shandong Fuji Zhiyu Elevator Co., Ltd. The authors sincerely thank the editors and reviewers for their insights and comments to further improve the quality of the manuscript.

Conflict of interest: Authors declare no competing financial interests or personal relationships that could have appeared to influence the study presented in this paper.

Appendix

A = A 11 A 12 A 21 A 22 , C = C 11 C 12 A 11 = 0 1 0 0 − 4 ( k 1 + k 2 ) m f − 4 c 1 m f 2 [ k 1 ( L 1 − L 2 ) + k 2 ( L 1 − L 2 ) ] m f 2 c 1 ( L 1 − L 2 ) m f 0 0 0 1 2 k 1 [ ( L 1 − L 2 ) − k 2 ( L 5 − L 6 ) ] I f 2 ( L 1 − L 2 ) c 1 I f − 2 [ k 1 ( L 1 2 + L 2 2 ) + k 2 ( L 5 2 + L 6 2 ) ] I f − 2 c 1 ( L 1 2 + L 2 2 ) I f A 12 = 0 0 0 0 4 k 2 m f 4 c 2 m f 2 k 2 ( L 4 − L 3 ) m f 2 k 2 ( L 4 − L 3 ) m f 0 0 0 0 2 k 2 ( L 6 − L 5 ) I f 2 c 2 ( L 6 − L 5 ) I f 2 k 2 ( L 5 L 3 + L 6 L 4 ) I f 2 c 2 ( L 5 L 3 + L 6 L 4 ) I f A 21 = 0 0 0 0 4 k 2 m c 4 c 2 m c 2 k 2 ( L 6 − L 5 ) m c 2 c 2 ( L 6 − L 5 ) m c 0 0 0 0 2 ( L 4 − L 3 ) k 2 I c 2 ( L 4 − L 3 ) c 2 I c 2 ( L 3 L 5 + L 4 L 6 ) k 2 I c 2 ( L 3 L 5 + L 4 L 6 ) c 2 I c A 22 = 0 1 0 0 − 4 k 2 m c − 4 c 2 m c 2 k 2 ( L 3 − L 4 ) m c 2 c 2 ( L 3 − L 4 ) m c 0 0 0 1 − 2 ( L 4 − L 3 ) k 2 I c − 2 ( L 4 − L 3 ) c 2 I c − 2 ( L 3 2 + L 4 2 ) k 2 I c − 2 ( L 3 2 + L 4 2 ) c 2 I c C 11 = − 4 ( k 1 + k 2 ) m f − 4 c 1 m f 2 [ k 1 ( L 1 − L 2 ) + k 2 ( L 1 − L 2 ) ] m f 2 c 1 ( L 1 − L 2 ) m f 2 k 1 [ ( L 1 − L 2 ) − k 2 ( L 5 − L 6 ) ] I f 2 ( L 1 − L 2 ) c 1 I f − 2 [ k 1 ( L 1 2 + L 2 2 ) + k 2 ( L 5 2 + L 6 2 ) ] I f − 2 c 1 ( L 1 2 + L 2 2 ) I f 4 k 2 m c 4 c 2 m c 2 k 2 ( L 6 − L 5 ) m c 2 c 2 ( L 6 − L 5 ) m c 2 ( L 4 − L 3 ) k 2 I c 2 ( L 4 − L 3 ) c 2 I c 2 ( L 3 L 5 + L 4 L 6 ) k 2 I c 2 ( L 3 L 5 + L 4 L 6 ) c 2 I c C 12 = 4 k 2 m f 4 c 2 m f 2 k 2 ( L 4 − L 3 ) m f 2 k 2 ( L 4 − L 3 ) m f 2 k 2 ( L 6 − L 5 ) I f 2 c 2 ( L 6 − L 5 ) I f 2 k 2 ( L 5 L 3 + L 6 L 4 ) I f 2 c 2 ( L 5 L 3 + L 6 L 4 ) I f − 4 k 2 m c − 4 c 2 m c 2 k 2 ( L 3 − L 4 ) m c 2 c 2 ( L 3 − L 4 ) m c − 2 ( L 4 − L 3 ) k 2 I c − 2 ( L 4 − L 3 ) c 2 I c − 2 ( L 3 2 + L 4 2 ) k 2 I c − 2 ( L 3 2 + L 4 2 ) c 2 I c B = 0 0 0 0 1 1 1 1 0 0 0 0 L 1 I f − L 2 I f L 1 I f − L 2 I f 0 0 0 0 0 0 1 m c 1 m c 0 0 0 0 0 0 − L 3 I c L 4 I c B 1 = 0 0 0 0 0 0 0 0 k 1 m f k 1 m f k 1 m f k 1 m f c 1 m f c 1 m f c 1 m f c 1 m f 0 0 0 0 0 0 0 0 − L 1 k 1 I f − L 1 c 1 I f − L 1 k 1 I f − L 1 c 1 I f L 2 k 1 I f L 2 c 1 I f L 2 k 1 I f L 2 c 1 I f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 D = 1 m f + m c 1 m f + m c 1 m f + m c 1 m f + m c 0 0 − L 1 I f − L 1 I f L 2 I f L 2 I f 0 0 0 0 0 0 1 m c 1 m c 0 0 0 0 − L 3 I c L 4 I c .

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Received: 2021-10-28

Accepted: 2022-04-19

Published Online: 2022-07-02

Published in Print: 2022-07-26