Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm

Bharti Panjwani; Vipul Kumar; Jyoti Yadav; Vijay Mohan

doi:10.1007/978-981-99-0969-8_31

Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm

Bharti Panjwani, Vipul Kumar, Jyoti Yadav, Vijay Mohan

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

Abstract

In this work, a Linear-Quadratic Regulator (LQR)-based control scheme is designed for a highly nonlinear and unstable inverted pendulum system. The system is linearised about its vertical position based on certain assumptions. Initially, weight matrices of the LQR controller are selected based on a trial and error method. These matrices are then optimised using a multi-objective genetic algorithm (GA) and whale optimization algorithm (WOA). The robustness of designed controllers is tested by reference tracking and parametric uncertainty analysis. The results reveal that optimisation of LQR by WOA provides superior performance compared to GA.

Original language	English
Title of host publication	Signals, Machines and Automation - Select Proceedings of SIGMA 2022
Editors	Asha Rani, Bhavnesh Kumar, Vivek Shrivastava, Ramesh C. Bansal, Ramesh C. Bansal
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	307-315
Number of pages	9
ISBN (Print)	9789819909681
DOIs	https://doi.org/10.1007/978-981-99-0969-8_31
Publication status	Published - 2023
Event	2nd International Conference on Signals, machines, and Automation, SIGMA 2022 - Delhi, India Duration: 05-08-2022 → 06-08-2022

Publication series

Name	Lecture Notes in Electrical Engineering
Volume	1023 LNEE
ISSN (Print)	1876-1100
ISSN (Electronic)	1876-1119

Conference

Conference	2nd International Conference on Signals, machines, and Automation, SIGMA 2022
Country/Territory	India
City	Delhi
Period	05-08-22 → 06-08-22

All Science Journal Classification (ASJC) codes

Industrial and Manufacturing Engineering

Access to Document

10.1007/978-981-99-0969-8_31

Cite this

Panjwani, B., Kumar, V., Yadav, J., & Mohan, V. (2023). Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm. In A. Rani, B. Kumar, V. Shrivastava, R. C. Bansal, & R. C. Bansal (Eds.), Signals, Machines and Automation - Select Proceedings of SIGMA 2022 (pp. 307-315). (Lecture Notes in Electrical Engineering; Vol. 1023 LNEE). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-981-99-0969-8_31

Panjwani, Bharti ; Kumar, Vipul ; Yadav, Jyoti et al. / Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm. Signals, Machines and Automation - Select Proceedings of SIGMA 2022. editor / Asha Rani ; Bhavnesh Kumar ; Vivek Shrivastava ; Ramesh C. Bansal ; Ramesh C. Bansal. Springer Science and Business Media Deutschland GmbH, 2023. pp. 307-315 (Lecture Notes in Electrical Engineering).

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title = "Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm",

abstract = "In this work, a Linear-Quadratic Regulator (LQR)-based control scheme is designed for a highly nonlinear and unstable inverted pendulum system. The system is linearised about its vertical position based on certain assumptions. Initially, weight matrices of the LQR controller are selected based on a trial and error method. These matrices are then optimised using a multi-objective genetic algorithm (GA) and whale optimization algorithm (WOA). The robustness of designed controllers is tested by reference tracking and parametric uncertainty analysis. The results reveal that optimisation of LQR by WOA provides superior performance compared to GA.",

author = "Bharti Panjwani and Vipul Kumar and Jyoti Yadav and Vijay Mohan",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.; 2nd International Conference on Signals, machines, and Automation, SIGMA 2022 ; Conference date: 05-08-2022 Through 06-08-2022",

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Panjwani, B, Kumar, V, Yadav, J & Mohan, V 2023, Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm. in A Rani, B Kumar, V Shrivastava, RC Bansal & RC Bansal (eds), Signals, Machines and Automation - Select Proceedings of SIGMA 2022. Lecture Notes in Electrical Engineering, vol. 1023 LNEE, Springer Science and Business Media Deutschland GmbH, pp. 307-315, 2nd International Conference on Signals, machines, and Automation, SIGMA 2022, Delhi, India, 05-08-22. https://doi.org/10.1007/978-981-99-0969-8_31

Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm. / Panjwani, Bharti; Kumar, Vipul; Yadav, Jyoti et al.
Signals, Machines and Automation - Select Proceedings of SIGMA 2022. ed. / Asha Rani; Bhavnesh Kumar; Vivek Shrivastava; Ramesh C. Bansal; Ramesh C. Bansal. Springer Science and Business Media Deutschland GmbH, 2023. p. 307-315 (Lecture Notes in Electrical Engineering; Vol. 1023 LNEE).

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

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AB - In this work, a Linear-Quadratic Regulator (LQR)-based control scheme is designed for a highly nonlinear and unstable inverted pendulum system. The system is linearised about its vertical position based on certain assumptions. Initially, weight matrices of the LQR controller are selected based on a trial and error method. These matrices are then optimised using a multi-objective genetic algorithm (GA) and whale optimization algorithm (WOA). The robustness of designed controllers is tested by reference tracking and parametric uncertainty analysis. The results reveal that optimisation of LQR by WOA provides superior performance compared to GA.

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Panjwani B, Kumar V, Yadav J, Mohan V. Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm. In Rani A, Kumar B, Shrivastava V, Bansal RC, Bansal RC, editors, Signals, Machines and Automation - Select Proceedings of SIGMA 2022. Springer Science and Business Media Deutschland GmbH. 2023. p. 307-315. (Lecture Notes in Electrical Engineering). doi: 10.1007/978-981-99-0969-8_31

Optimum LQR Controller for Inverted Pendulum Using Whale Optimization Algorithm

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