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.

Comparative Study of Takagi-Sugeno-Kang and Madani Algorithms in Type-1 and Interval Type-2 Fuzzy Control for Self-Balancing Wheelchairs

“…Ongoing research is also focused on evolving controller types [30]- [33], more adaptable models [34]- [39], and optimal control methods [40]- [45], particularly in the context of motors and robotic arms [46]- [49]. An example demonstrating the effectiveness of such controllers in maintaining stability can be found in the work of P. Chotikunnan et al [28], where a ball and beam system was effectively managed. In this study, a feedback system using fuzzy logic systems is developed to control the stability and movement of the electric wheelchair.…”

“…In Type-2 systems, the inclusion of a Footprint of Uncertainty (FOU) layer offers additional flexibility and nuance in control strategies [26], [27]. These controllers perform distinctly under both standard and noisy conditions, thereby adding to the broader goal of enhancing system equilibrium [28].…”

“…This research entails the development of a control system that has undergone experimental testing in real-world wheelchair systems, utilizing the TSK fuzzy logic estimation method [27]. The study specifically delves into fuzzy control systems, employing the Mamdani method [28] for estimation. Significantly, the findings of this research hold direct relevance to real-world self-balancing systems, including wheelchairs, robots, and drones.…”

Adaptive Parallel Iterative Learning Control with A Time-Varying Sign Gain Approach Empowered by Expert System

“…Additionally, fuzzy logic control (FLC) has become a popular choice [11], [12] for tuning PID gains. Furthermore, significant advancements have been made in control systems through the introduction and application of type-1 and interval Type-2 fuzzy logic systems [13]- [26]. These advancements have practical applications in controlling various systems, including motors, electric carts, robotic systems, and the inverted pendulum.…”

Altitude Control of UAV Quadrotor Using PID and Integral State Feedback

“…The proportional Integral Derivative (PID) controller has been known for its wide use in many control systems; hence, it also has been applied to control altitude in quadrotor [9] [10]. The other controller is Sliding Mode Control (SMC) [11], Linear Quadratic Regulator (LQR) [12][13], Predictive Control [14], Fuzzy Control [15] [16], Neural Network [17] [18], Fractional Order PID [19], Feedback Linearization [20], and other control techniques [21]. This research presented an application of the Integral State Feedback (ISF) controller for altitude control in quadrotor as a practical solution that enables a precise and robust control system performance.…”