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Performance comparison of structured H∞ based looptune and LQR for a 4-DOF robotic manipulator

Asghar, Arafat; Iqbal, Muhammad; Khaliq, Abdul; Rehman, Saif ur; Iqbal, Jamshed


Arafat Asghar

Muhammad Iqbal

Abdul Khaliq

Saif ur Rehman


We explore looptune, a MATLAB-based structured H1 synthesis technique in the context of robotics. Position control of a 4 Degree of Freedom (DOF) serial robotic manipulator developed using Simulink is the problem under consideration. Three full state feedback control systems were developed, analyzed and compared for both steady-state and transient performance using the Linear Quadratic Regulator (LQR) and looptune. Initially, a single gain feedback controller was synthesized using LQR. This system was then modified by augmenting the state feedback controller with Proportional Integral (PI) and Integral regulators, thereby creating a second and third control system respectively. In both the second and third control systems, the LQR synthesized gain and additional gains were further tuned using looptune to achieve improvement in performance. The second and third systems were also compared in terms of tracking a time-dependent trajectory. Finally, the LQR and looptune synthesized controllers were tested for robustness by simultaneously increasing the mass of each manipulator link. In comparison to LQR, the second system consisting of Single Input Single Output (SISO) PI controllers and the state feedback matrix succeeded in meeting the control objectives in terms of performance, optimality, trajectory tracking, and robustness. The third system did not improve performance in contrast to LQR, but still showed robustness under mass variation. In conclusion, our results have shown looptune to have a comparatively better performance over LQR thereby highlighting its promising potential for future emerging control system applications.


Asghar, A., Iqbal, M., Khaliq, A., Rehman, S. U., & Iqbal, J. (2022). Performance comparison of structured H∞ based looptune and LQR for a 4-DOF robotic manipulator. PLoS ONE, 17(4), Article e0266728.

Journal Article Type Article
Acceptance Date Mar 28, 2022
Online Publication Date Apr 11, 2022
Publication Date Apr 1, 2022
Deposit Date Mar 28, 2022
Publicly Available Date Oct 27, 2022
Journal PLoS ONE
Print ISSN 1932-6203
Electronic ISSN 1932-6203
Publisher Public Library of Science
Peer Reviewed Peer Reviewed
Volume 17
Issue 4
Article Number e0266728
Public URL


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Copyright Statement
Copyright: © 2022 Asghar et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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