Backstepping Linear Quadratic Gaussian Controller Design for Balancing an Inverted Pendulum

Abstract

Numerous real-time implementations such as a robust balancing process, segway and hover board riding, and rocket propeller operation are done with the control principle of Inverted Pendulum (IP). Dynamically, the IP is considered as an extremely unstable, non-linear in nature, and under-actuated system. Thus, the control strategy formulation for its equilibrium is generally accepted as an initial attempt for any new control technique as a proof towards further application in the control system engineering. This paper presents a novel Backstepping Linear Quadratic Gaussian Controller (BLQGC) based on the Lyapunov function to control the cart position $x\left(t\right)$ and angular displacement $\theta \left(t\right)$ of the pendulum. The justification of enhanced control performance of BLQGC is demonstrated by comparative result analysis with optimal PID control, Linear Quadratic Gaussian (LQG) control, and other robust control techniques suggested by different authors. The simulations are carried out through MATLAB/SIMULINK environment and the results indicate comparatively better control ability of the proposed method in terms of accuracy, stability, quick damping, and robustness.

Keywords:

• Angular displacement
• Backstepping Linear Quadratic Gaussian (BLQG) control
• Cart position
• Inverted Pendulum
• LQG control
• Lyapunov function

Additional information

Notes on contributors

Akshaya Kumar Patra

Akshaya Kumar Patra is presently working as an assistant professor in the Department of EEE, ITER, S‘O’A deemed to be University, Bhubaneswar, India. He received his ME degree from Bengal Engineering and Science University, Shibpur, Howrah, India, in 2006, and PhD degree in biomedical engineering from Siksha ‘O’ Anusandhan University, Bhubaneswar, Odisha, India, in 2018. His main research includes control systems, robust control and biomedical engineering. Corresponding author. Email: [email protected]; [email protected]

Sunita Swarnamayee Biswal

Sunita Swarnamayee Biswal is presently working as an assistant professor in the Department of EEE, ITER, S‘O’A deemed to be University, Bhubaneswar, Odisha, India. She received her ME degree from Jadavpur, West Bengal, India, in 2010. Her main research includes control systems, robust control, and image processing. Email: [email protected]

Pravat Kumar Rout

Pravat Kumar Rout is a professor at the Department of EEE, ITER, S‘O’A University, Bhubaneswar, India. He received his ME degree in power system engineering from Thiagarajar College of Engineering, Madurai, Tamil Nadu, and PhD degree in power system engineering from Biju Pattanaik University of Technology, India, in 1995 and 2010, respectively. His main research area focuses on soft computing, and biomedical engineering. Email: [email protected]