Eventos Anais de eventos
COBEM 2017
24th ABCM International Congress of Mechanical Engineering
Dynamical Analysis and Control of a Parametrically Excited Elastic Pendulum
Submission Author:
José Manoel Balthazar , SP , Brazil
Co-Authors:
Thiago Cesar Lousada Marsola, Mateus de Freitas Virgílio Pereira, Angelo Marcelo Tusset, José Manoel Balthazar
Presenter: Thiago Cesar Lousada Marsola
doi://10.26678/ABCM.COBEM2017.COB17-0733
Abstract
This work presents the modeling and a numerical method that enables the stability analysis and control of a periodic dynamic system, a parametrically excited elastic pendulum, with vertical excitation and variable length. First, the system is modeled through the Lagrangian method in order to obtain the movement equations. With this, it is designed a nonlinear SDRE (State-Dependent Riccati Equation) control to take the system to an equilibrium point and to an equilibrium periodic orbit. Then, a stability analysis of the nonlinear system is done through a stability diagram, which is possible to verify the occurrence of bifurcations for given parameter values. This method is based on L-F (LyapunovFloquet) transformation and uses the Chebyshev polynomial expansion to approximate the periodical term and to prevent an ill-conditioning problem. The Picard iterative method is also used to calculate the state transition matrix (STM). If the system is proved to have bifurcations for a certain parameter value, a feedback and feedforward linear control based on Sinha’s method is also designed to try to control the system. The stability analysis and control results are verified in numeric and symbolic simulations with Matlab.
Keywords
Lyapunov-Floquet transformation, Chebyshev Polynomials, Picard iteration, periodic system, Chaos Control
