Linearization and PI Controller Based Ball and Beam System with an Actuator DC motor

Hana  El saady; Farag  Hossen

doi:10.64516/n5ekfw71

Authors

Hana El saady Electrical and Electronics Engineering Department, Tobruk University, Tobruk, Libya. Author
Farag Hossen Mechanical Engineering Department, Higher Institute of Science and Technology, Tobruk, Libya Author

DOI:

https://doi.org/10.64516/n5ekfw71

Keywords:

linearization, Simulink, ball and beam system(BBS), DC motor, Proportional Integral (PI) controller

Abstract

This paper presents a revised iteration of the ball and beam system (BBS) that functions as a platform for exploring innovative control methodologies in real-time. The BBS consists of a lengthy beam with a ball situated atop, and the primary objective of the control mechanism is to maintain the ball's position on the beam by manipulating the angular location of the beam. The actuator employed in this study is a direct current (DC) motor. The mathematical model of the system was derived by applying the Newton-Euler equations. Subsequently, the resulting equations were linearized using MATLAB. The efficacy of the proposed PI controller was evaluated using the linearized model of the Ball and Beam system on the MATLAB-SIMULINK platform through careful adjustment of the controller parameters; Kp, Ki, and, Kd. The simulations conducted on SIMULINK and MATLAB demonstrate the proficient real-time performance of the designed proportional and integral (PI) controller.

References

[1] D.Colón, et al.'' NONLINEAR BALL AND BEAM CONTROL SYSTEM IDENTIFICATION'', Conference Paper in Applied Mechanics and Materials, September 2013.

[2] L.Niro,et al ''Control of a Modified Ball and Beam System Using Tracking System in Real Time with a DC Motor as an Actuator'', International Journal of Advanced Engineering Research and Science , Vol.4, No.12, pp. 99-107, Decmber2017

[3] A.A.Taifour .et al, '' Design and Implementation of Ball and Beam System using PID Controller'', Automatic Control and Information Sciences, Vol.1, 26 April 2017.

[4] M.V.Nidya. '' Stabilisation of Ball and Beam Module Using Relatively Optimal Control'', International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 2, March 2019

[5] M.Keshmiri, et al.'' Modeling and Control of Ball and Beam System using Model Based and Non-Model Based Control Approaches '', International Journal on Smart Sensing and Intelligent Systems,Vol. 5, No. 1, March 2012

[6] B. Meenakshipriya , and K.Kalpana.'' Modelling and Control of Ball and Beam System using Coefficient Diagram Method (CDM) based PID controller'', Third International Conference on a Advances in Control and Optimization of Dynamical Systems, March 13-15, 2014

[7] N.M.Tahir,et la.'' CONTROL AND STABILITY STUDIES OF BALL AND BEAM SYSTEM'', Journal of Modern Technology and Engineering Vol.4, No.2, pp.122-131, 2019

[8] H. El saady. '' Designing and implementing a Proportional Derivative-based Controllers for Ball and Beam'', International Journal of Innovative Research in Electrical, Electronics, Instrumentation and Control Engineering,Vol. 11, No. 8, August 2023.

[9] https://www3.diism.unisi.it/~control/ctm/examples/ball/ball.html#Matlab

[10] J.Hauser, et al., ''Nonlinear Control Via Approximate Input-Output Linearization: The Ball and Beam Example, IEEE TRANSACTION ON AUTOMATIC CONTROL, Vol.37,No.3, March 1992