Design of an eigenstructure assignment control using Genetic Algorithm applied to a Ball and Beam system
Lucas Niro1; Marcio Aurelio Furtado Montezuma1; Bruno Masaharu Shimada1; Fabian Andres Lara-Molina1; Edson Hideki Koroishi1; Lucia Valeria Ramos de Arruda1
1 Federal Technological University of Paraná
doi:10.20906/CPS/COB-2015-0668
Resumo
The present contribution aims at describing the design procedure of a ball and beam control system based on the so-called eigenstructure assignment control. The complete dynamic model of the ball and beam system was obtained by the Lagrange-Euler equations, this model was simplified to obtain a one degree of freedom system, with following assumptions: the beam dynamics was negligible and it was considered a small alignment angle of the beam. In the eigenstructure assignment controller, the states and output of the system are feedbacked. The gains of the controller depend on the imposed eigenvalues. The design procedure consists in solving a constrained nonlinear optimization problem to find the imposed eigenvalues. Therefore the optimal eigenvalues of the controlled system should minimize the settling time of the response with a constrained control input (maximum alignment angle of the beam). The optimization problem was solved by using a Genetic Algorithm. The testbed of the ball and beam system was implemented by substituting the ball by a cart, additionally it was used a linear encoder and a wireless system to measure the position of the cart along the beam. The control system was implemented with hardware-in-loop framework using Matlab / Simulink in real-time. The experimental results obtained show the improvement of the dynamic performance of the system in terms of position accuracy and the transient response.
Palavras-chave: Ball and Beam; Eigenstructure Assignment Control; Genetic Algorithm; Optimization