Modeling of Underactuated Ball and Beam System—A Comparative Study

Gembalczyk, Grzegorz; Domogała, Paweł; Leśniowski, Kamil

doi:10.3390/act12020059

Cited by 4 publications

(3 citation statements)

References 34 publications

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“…In the past few years, more and more new control methods have been used to control a ball and beam system, such as fuzzy logic, neural networks, robust control and backstepping [30][31][32][33]. A comparative study was conducted for models of ball and beam systems in [34]. Moreover, the λ-method matching control law was first applied to a ball and beam system, and the experimental results showed that the theoretical prediction was consistent with the experimental results in [35].…”

Section: Introductionmentioning

confidence: 86%

An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System

Liu,

Shao,

Liu

et al. 2023

Actuators

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In this paper, an adaptive technology and the interconnection and damping assignment passivity-based control method are combined to solve the stabilization problem for underactuated mechanical systems with uncertainties (including matched and unmatched). These uncertainties include unknown friction coefficients and unknown terms in kinetic energy and potential energy. A novel adaptive interconnection and damping assignment passivity-based control scheme is proposed and an adaptive stabilization controller is designed to make the closed-loop system locally stable. Verification is conducted on the ball and beam system. The locally asymptotic stability is demonstrated using the LaSalle’s invariance principle and approximate linearization. The effectiveness of the proposed control law is verified through numerical simulations.

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Section: Introductionmentioning

confidence: 86%

An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System

Liu,

Shao,

Liu

et al. 2023

Actuators

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“…In addition to UMS, many types of pendulums are often used in research, such as The Furuta pendulum or rotational inverted pendulum [29] it is a prototype underactuated nonlinear system used as a test bed for various control schemes [30], the inertia-wheel pendulum [31], the acrobat and pendubot [32], and the rotating pendulum [33], the cart pole system [34], the BBS [35], the ball and balancer system [36], the translational oscillator with a rotational actuator TORAsystem [37], and many others. Focusing on control-an observer-based nonlinear robust controller for the BBS has been successfully developed [38].…”

Section: Introductionmentioning

confidence: 99%

Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD2–PI control schemes

Zafar,

Malik,

Ali

et al. 2024

PLoS ONE

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In this paper, we propose two different control strategies for the position control of the ball of the ball and beam system (BBS). The first control strategy uses the proportional integral derivative-second derivative with a proportional integrator PIDD2-PI. The second control strategy uses the tilt integral derivative with filter (TID-F). The designed controllers employ two distinct metaheuristic computation techniques: grey wolf optimization (GWO) and whale optimization algorithm (WOA) for the parameter tuning. We evaluated the dynamic and steady-state performance of the proposed control strategies using four performance indices. In addition, to analyze the robustness of proposed control strategies, a comprehensive comparison has been performed with a variety of controllers, including tilt integral-derivative (TID), fractional order proportional integral derivative (FOPID), integral–proportional derivative (I-PD), proportional integral-derivative (PI-D), and proportional integral proportional derivative (PI-PD). By comparing different test cases, including the variation in the parameters of the BBS with disturbance, we examine step response, set point tracking, disturbance rejection analysis, and robustness of proposed control strategies. The comprehensive comparison of results shows that WOA-PIDD2-PI-ISE and GWO-TID-F- ISE perform superior. Moreover, the proposed control strategies yield oscillation-free, stable, and quick response, which confirms the robustness of the proposed control strategies to the disturbance, parameter variation of BBS, and tracking performance. The practical implementation of the proposed controllers can be in the field of under actuated mechanical systems (UMS), robotics and industrial automation. The proposed control strategies are successfully tested in MATLAB simulation.

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“…This versatility allows researchers to leverage the BnB system for designing, implementing, and testing control algorithms capable of navigating through nonlinear dynamics and stabilizing the system despite its underactuated nature. The broad spectrum of potential applications provides a valuable opportunity to assess the adaptability and transferability of control methodologies across various contexts [12].…”

Section: Introductionmentioning

confidence: 99%

Modeling and Hybrid PSO-WOA-Based Intelligent PID and State-Feedback Control for Ball and Beam Systems

Ahmad

2023

IEEE Access

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The ball and beam (BnB) system serves as a benchmark in control engineering as it provides a foundational concept applicable to addressing stabilization challenges of various underactuated nonlinear systems. This includes tasks like maintaining the balance of goods carried by mobile robots and controlling the attitude of unmanned aerial vehicles. In this study, the focus is on enhancing control optimization strategies for BnB systems that take into account inherent nonlinearities arising from actuator constraints and state measurements. The work introduces a novel intelligent control approach, termed hybrid PSO-WOA, which combines Particle Swarm Optimization (PSO) and Whale Optimization Algorithm (WOA) to automate optimal parameter search for proportional-integral-derivative (PID) and state feedback (SF) controllers. The collaborative technique between PSO and WOA is formulated to strike a balance between exploration and exploitation phases, and to mitigate premature convergence risks due to the system's complexities. Additionally, three control schemes, namely cascade PID-PID, cascade PID-SF, and cascade PID-observer are introduced, each with tailored cost functions for optimization through the hybrid PSO-WOA algorithm, accommodating both measurable and unmeasurable state scenarios. Simulation results consistently demonstrate the superior performance of the hybrid approach compared to individual PSO and WOA methods, as well as conventional PID and linear quadratic regulator approaches. Notable, the hybrid approach exhibits a significant improvement in error metrics, reducing integral-time absolute error by 18.99%, integral squared error by 35.37%, and steady-state error by 92.86%. This substantial enhancement suggests promising directions for future research in automated control parameter tuning for underactuated nonlinear systems.

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Modeling of Underactuated Ball and Beam System—A Comparative Study

Cited by 4 publications

References 34 publications

An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System

An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System

Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD2–PI control schemes

Modeling and Hybrid PSO-WOA-Based Intelligent PID and State-Feedback Control for Ball and Beam Systems

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