Jawad Khan
, Ma Gang, Shah Muhammad Adnan
The inverted pendulum, a classic problem in control theory, is widely used for analyzing nonlinear systems and potential energy applications. This study investigates various controller techniques classical and intelligent applied to the inverted pendulum system, providing a comprehensive review of their design, performance, and limitations through simulations and graphical analysis. Key control strategies, including PID, Linear Quadratic Regulator (LQR), Neural Networks (NN), and Fuzzy Logic Control (FLC), are implemented and evaluated for system stability, response time, and robustness under structural uncertainties and external disturbances. Simulation results reveal that classical controllers, particularly the PID and LQR, demonstrate superior performance in terms of settling time, overshoot, and steady-state error under linearized system assumptions. However, these conventional techniques struggle to handle nonlinearities and uncertainties effectively. To address these limitations, robust controllers such as the LQR are employed, minimizing actuator effort and optimizing cost functions. In contrast, intelligent controllers, including NN and FLC, exhibit adaptive capabilities, are enabling them to handle complex, nonlinear dynamics with greater accuracy and reliability. NN and FLC outperform classical controllers in terms of faster response times, improved stability, and reduced computational cost. This study underscores the advantages of NN and FLC in achieving enhanced system performance while maintaining stability and trajectory tracking for both cart position and pendulum angle. MATLAB/Simulink simulations validate the efficacy of each control strategy and highlight the potential of intelligent control techniques in addressing challenges associated with nonlinear systems and robotics technology. The findings provide critical insights into the design and application of control strategies for inverted pendulum systems, with implications for advancing feedback control in robotic systems.
Xu, C. and X. Yu, Mathematical modeling of elastic inverted pendulum control system. Journal of Control Theory and Applications, 2004. 2: p. 281-282.
2. Xiao, B., C. Xu, and L. Xu, System Model and Controller Design of an Inverted Pendulum. Intelligent Information Systems, IASTED International Conference on, 2009. 0: p. 356-359.
3. Hu, H., S. Yu, and H. Trinh, A Review of Uncertainties in Power Systems - Modelling, Impact, and Mitigation. 2023.
4. Wang, J.-J., Simulation studies of inverted pendulum based on PID controllers. Simulation Modelling Practice and Theory, 2011. 19: p. 440-449.
5. Debnath, L., Nonlinear partial differential equations for scientists and engineers: Second edition. Nonlinear Partial Differential Equations for Scientists and Engineers: Second Edition, 2005: p. 1-737.
6. Muskinja, N. and B. Tovornik, Swinging up and stabilization of a real inverted pendulum. Industrial Electronics, IEEE Transactions on, 2006. 53: p. 631-639.
7. Nersesov, S. and W. Haddad, On the Stability and Control of Nonlinear Dynamical Systems via Vector Lyapunov Functions. Automatic Control, IEEE Transactions on, 2006. 51: p. 203-215.
8. Nasir, A., Modeling and controller design for an inverted pendulum system. 2007.
9. Prasad, L., B. Tyagi, and H. Gupta, Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input. International Journal of Automation and Computing, 2014. 11: p. 661-670.
10. Lewis, J. and J. Sauro, USABILITY AND USER EXPERIENCE: DESIGN AND EVALUATION. 2021. p. 972-1015.
