PID and Fuzzy Logic Control of Ball and Beam System Using Particle Swarm Optimization

In this research, we carried out the modeling of the ball and beam system (BBS) within the MATLAB/Simulink framework by applying both proportional-integral-derivative (PID) and fuzzy logic control strategies to govern the dynamics of this constructed model. The underlying non-linear dynamic equations adjusting the behavior of the BBS system are based on Newton’s second law of motion. The physical installation of the BBS, designed for potential real-time application, comprises a lengthy beam subject to movement through the action of a DC servomotor, with a ball traversing the beam in a reciprocating manner. A distance sensor is strategically placed in front of the beam to determine the exact position of the ball. In this system, an electrical control signal applied to the DC servomotor causes the beam to pivot about its horizontal axis, thereby enabling the ball to move freely along the beam's length. To avoid the risk of losing the ball equilibrium on the beam and to achieve precise system control, a mathematical model was devised and implemented within the MATLAB/Simulink environment. The use of the particle swarm optimization (PSO) algorithm was aimed at tackling the task of refining and optimizing the PID controller specifically designed for the linearized ball and beam control system. The presented system is controlled using both PID and fuzzy logic, and the use of the PSO algorithm enhances the system’s responsiveness efficiency.

Intelligent Dynamic Inversion Controller Design for Ball and Beam System

The Ball and beam system(BBS)is an attractive laboratory experimental tool because of its inherent nonlinear and open-loop unstable properties.Designing an effective ball and beam system controller is a real challenge for researchers and engineers.In this paper,the control design technique is investigated by using Intelligent Dynamic Inversion(IDI)method for this nonlinear and unstable system.The proposed control law is an enhanced version of conventional Dynamic Inversion control incorporating an intelligent control element in it.The Moore-PenroseGeneralized Inverse(MPGI)is used to invert the prescribed constraint dynamics to realize the baseline control law.A sliding mode-based intelligent control element is further augmented with the baseline control to enhance the robustness against uncertainties,nonlinearities,and external disturbances.The semi-global asymptotic stability of IDI control is guaranteed in the sense of Lyapunov.Numerical simulations and laboratory experiments are carried out on this ball and beam physical system to analyze the effectiveness of the controller.In addition to that,comparative analysis of RGDI control with classical Linear Quadratic Regulator and Fractional Order Controller are also presented on the experimental test bench.

Gravitational search algorithm–based fuzzy control for a nonlinear ball and beam system

In recent decades,fuzzy logic and its application for stabilising nonlinear systems have had a great development.In this paper,a novel optimal fuzzy controller is provided to control a ball and beam system.The fuzzy control force is calculated via a fuzzy system based on the singleton fuzzifier,the centre average defuzzifier and the product inference engine.To further improve the control performance,the Gravitational Search Algorithm is applied to optimise the controller parameters.The obtained simulation results indicate that the proposed scheme can provide a better performance in the case of convergence rate and accuracy in comparison with those of other recently published works.