Control of A Cart-Ball System Using State-Feedback Controller

Authors: M. Shakir Saat, M. Noh Ahmad, Dr, Amat Amir

Abstract:

A cart-ball system is a challenging system from the control engineering point of view. This is due to the nonlinearities, multivariable, and non-minimum phase behavior present in this system. This paper is concerned with the problem of modeling and control of such system. The objective of control strategy is to place the cart at a desired position while balancing the ball on the top of the arc-shaped track fixed on the cart. A State-Feedback Controller (SFC) with a pole-placement method will be designed in order to control the system. At first, the mathematical model of a cart-ball system in the state-space form is developed. Then, the linearization of a model will be established in order to design a SFC. The integral control strategy will be performed as to control the cart position of a system. Simulation work is then performed using MATLAB/SIMULINK software in order to study the performance of SFC when applied to the system.

Keywords: Cart-Ball System, Integral Control, Pole-PlacementMethod, State-Feedback Controller.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081013

References:

[1] Jan Jantzen, Analysis of a Pendulum Problem, Tech. Report, Technical University of Denmark, Denmark, 1999.
[2] J.J.E Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, USA, 1991.
[3] Jorgensen V., "A Ball-Balancing System For Demonstration of Basic Concepts In State Space Control Theory", Int. Journal of Elec. Eng. Edu., pp. 367-376, 1974.
[4] Norman S. Nise, Control System Engineering, Prentice Hall, USA, 2004.
[5] Mohd Shakir Md Saat, Control of a Cart-Ball System: Comparison Between Model Based and Fuzzy Logic Controllers, Master-s Thesis, Universiti Teknologi Malaysia, 2006.