1 979-8-3503-1576-9/23/$31.00 ©2023 IEEE Tracking Control of an Inverted Pendulum System: A Novel Radial basis function Neural Network supervisory control approach Narayan Nayak Department of EE SIT, Bhubaneswar narayan@silicon.ac.in Binayak Ghosal Department of EEE SIT, Bhubaneswar binayak5766@gmail.com Dipak Ranjan Nayak Department of EEE SIT, Bhubaneswar deepak.ranjan@silicon.ac.in Ambarish G. Mohapatra Department of EE SIT, Bhubaneswar ambarish.mahapatra@silicon.ac.in Abstract – The control of an Inverted Pendulum (IP) is one of the benchmark problems in control systems. It is very difficult to control due to its innate instability and extremely nonlinear properties. Here, a novel supervisory control method based on Radial Basis Function Neural Networks (RBFNN) approach aims to enhance the tracking performance of an IP system. The RBFNN is used as a dynamic compensator to improve the performance of the typical Proportional-Integral- Derivative (PID) controller. The network is trained to approximate the unknown nonlinear dynamics of the IP system. The corrective control signal is then produced by the trained network and added to the PID controller's output. An adaptive tuning algorithm is created to continuously update the RBFNN's parameters to achieve accurate tracking control. As a result, the system can instantly adapt to modifications in the dynamics of the plant. The effectiveness of the suggested approach in achieving reliable tracking control of the IP system is demonstrated by simulation results. When compared to the traditional PID and FUZZY-PID controller, the RBFNN supervisory control strategy significantly enhances the system's tracking performance with minimum overshoot and settling time. The method offers a promising framework for the control of complex nonlinear systems. Keywords –Inverted Pendulum(IP), PID, RBFNN, Fuzzy-PID, RBFNN-PID I. INTRODUCTION Control engineering has paid a lot of attention to the difficult task of designing and controlling an inverting pendulum(IP) system[1-2]. An IP is a pendulum system whose objective is to keep the pendulum in an inverted position, that is, upright or vertically aligned, despite outside disturbances. Engineers can learn more about the fundamentals of control theory and apply them to a variety of real-world situations by successfully designing a controller that can stabilize an IP. The pendulum, when left to itself, will naturally fall due to gravity. However, through the application of external forces or torques, The inverted pendulum concept finds numerous applications across various fields such as robotics, control system design, gyroscopic stabilization systems, transportation systems, etc. Control engineers and researchers use it to test and compare different control strategies, such as PID controllers [3],robust PID[1][4], fuzzy logic [5-9], adaptive control, and advanced optimization- based methods. The inverted pendulum provides a practical and intuitive platform for studying feedback control, state estimation, and stability analysis. Multiple PID controllers are employed to stabilize the angle of the inverted pendulum [2]. The pendulum can move in a straight line, horizontal plane as well as vertical plane. However, the results are not desirable due to the high non-linearity of the system. A fuzzy parallel distributed compensation (PDC) controller is proposed for the angle stabilization of the IP [4]. The settling time was greatly reduced with the use of these controllers. PID and fuzzy controllers are used for the stabilization and control of an IP moving on an inclined surface [7]. The angle of the pendulum and the position of the cart were controlled by using Linear Quadratic Regulator (LQR) and Pole Placement control strategy [8].Linearization of the inverted pendulum dynamics is done with the use of Taylor series approximation. RBFNN are used for the position tracking of an inverted pendulum system [10-11]. In this paper, we have proposed a control strategy for the inverted pendulum problem through the use of RBFNN along with a Proportional-Integral-Derivative (PID) controller to control the IP system. The main objective of this study is to give a thorough overview of the controller design methods for inverting pendulum systems and to discuss the advantages and disadvantages of various methods. The paper will also highlight the trade-offs between simplicity, robustness, and performance as well as the difficulties in applying these control strategies. This paper is divided into five sections. An introduction and a literature review are included in Section I. In section II, inverting pendulum systems with transfer functions and state space models were mathematically analyzed. Section III covered the various control strategies. Results and discussion were completed in section IV. Concluding remarks were provided in section V at the end. II. MATHEMATICAL ANALYSIS OF INVERTED PENDULUM SYSTEM An inverted pendulum (IP) system is a simple model for understanding the complex and dynamic systems that are available in the real world. Classical control techniques are not employed for the control of an IP system due to its nonlinear control. This is a result of having 2 degrees of freedom, namely the cart position and angle of the inverted 2023 1st International Conference on Circuits, Power and Intelligent Systems (CCPIS) | 979-8-3503-1576-9/23/$31.00 ©2023 IEEE | DOI: 10.1109/CCPIS59145.2023.10291515 Authorized licensed use limited to: Silicon Institute of Technology. Downloaded on October 30,2023 at 05:20:40 UTC from IEEE Xplore. Restrictions apply.