Ball and Beam Control: Evaluating Type-1 and Interval Type-2 Fuzzy Techniques with Root Locus Optimization

Abstract

This study evaluates the performance of three control systems, namely the root locus method, type-1 Mamdani fuzzy logic system (FLS), and interval type-2 Mamdani FLS, in noise-free and noisy ball and beam systems. The main contribution of this study is enabling improved design and implementation of control systems in real-world applications by offering a comprehensive understanding of each control system's performance. The methodology involves conducting four tests focusing on various input types, including a 0.8-meter step input and sine wave function, and assessing the presence of noise in the system. The performance of each control system is analyzed using parameters such as rise time, setting time, and percentage overshoot, with the interval type-2 Mamdani FLS further examined by varying footprint of uncertainty values. Results from noise-free tests reveal that the root locus method has shorter rise and setting times, but a higher percentage overshoot compared to the type-1 Mamdani FLS and type-2 Mamdani FLS. In noisy environments, the type-2 Mamdani FLS with varying Footprint of Uncertainty values outperforms the type-1 Mamdani FLS with reduced rise time, setting time, and percentage overshoot. The root locus method shows a significantly higher percentage overshoot in noisy conditions compared to the other two control systems. In conclusion, the type-2 Mamdani FLS control system demonstrates superior capability under changing conditions compared to the type-1 Mamdani FLS, with its performance varying based on footprint of uncertainty values. This study highlights the importance of selecting the appropriate control system depending on specific needs and environmental factors.