Ters Dönmüş Bir Sarkacın Doğrusal Olmayan Konum Denetiminden En Büyük Lyapunov Üstelinin Poincare Kesitinden Elde Edilmesi

Abstract

Computing the largest Lyapunov exponent (LLE) of a 2-D planar flow through its Poincare section is shown to be possible in this study. An inverted pendulum with nonlinear position control is used as a mathematical modeL. The nonlinearity imposed on the model is caused by a dead-zone assigned to the position sensor. The dynamical system is forced to behave chaotically by tuning the system parameters; such as, the stiffness, damping, or the width of the dead-zone of the sensor.MA TLAB SIMULINK® is used as the media to build the mathematical model of the system. The goveming equations of the system are solved by using numerical integration techniques for angular position and angular velocity, which are used as the state variables in constructing the dynamical behavior of the system in the phase plane. A parallel processing algorithm working with numerical integration ofthe system' s governing equations is developed in ord er to follow the fate of a perturbation given to the states at a time. LLE of the dynamical system is generated by using this algorithm and compared with the LLE estimate computed through the Poincare section of the dynamical system.