Applying Approximate Entropy to Analyze the Edge of Chaos of Inverted Pendulum on a Cart
Ren Bi-chun · Control Engineering of China · 2013
Entropy is one of the approaches to measure the irregularity of a set of data.And it is one of the rare computable tests for chaos.Aiming at finding figuring out how the value of entropy varies when the motion of a mechanism become chaotic and at the edge of chaos and,the inverted pendulum on a cart,in this paper,is taken as an example in the paper.The time series of the response is extracted from the simulation of the dynamic model;approximate entropy is employed to analyzing analyze the variation of the values of entropy.It is shown that the approximate entropy undergoes a change from 0 to larger than 0 as the system changes from periodic motion to chaotic motion.And at the edge of chaos,the approximate entropy alternates between 0 and larger than 0,which means that periodic motion and chaotic motion coexist at the edge of chaos.The conclusions are proved by the phase diagrams of system.