Self-balancing robot: modeling and comparative analysis between PID and linear quadratic regulator

Lu Bin Lau, Nur Syazreen Ahmad, Patrick Goh


A two-wheeled self-balancing robot (TWSBR) is an underactuated system that is inherently nonlinear and unstable. While many control methods have been introduced to enhance the performance, there is no unique solution when it comes to hardware implementation as the robot’s stability is highly dependent on accuracy of sensors and robustness of the electronic control systems. In this study, a TWSBR that is controlled by an embedded NI myRIO-1900 board with LabVIEW-based control scheme is developed. We compare the performance between proportional-integral-derivative (PID) and linear quadratic regulator (LQR) schemes which are designed based on the TWSBR’s model that is constructed from Newtonian principles. A hybrid PID-LQR scheme is then proposed to compensate for the individual components’ limitations. Experimental results demonstrate the PID is more effective at regulating the tilt angle of the robot in the presence of external disturbances, but it necessitates a higher velocity to sustain its equilibrium. The LQR on the other hand outperforms PID in terms of maximum initial tilt angle. By combining both schemes, significant improvements can be observed, such as an increase in maximum initial tilt angle and a reduction in settling time.


Linear quadratic regulator; Modeling; Proportional-integral-derivative; Robot; Self-balancing

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International Journal of Reconfigurable and Embedded Systems (IJRES)
p-ISSN 2089-4864, e-ISSN 2722-2608
This journal is published by the Institute of Advanced Engineering and Science (IAES) in collaboration with Intelektual Pustaka Media Utama (IPMU).

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