Discrete Dynamics-Based Parameter Analysis and Optimization of Fuzzy Controller for Inverted Pendulum Systems Based on Chaos Algorithm

Table 1

Introduction of symbols used in the double inverted pendulum system [17].

Parameters	Values	Significance
	m	Displacements of a cart
	rad	The angle between the inverted pendulum 1 and the vertical direction
	rad	The angle between the inverted pendulum 2 and the vertical direction
	1.096 kg	Equivalent mass of the cart
	0.13 kg	The quality of the inverted pendulum 1
	0.05 kg	The quality of the inverted pendulum 2
	0.0002 kg·m·m	The moment of inertia of an inverted pendulum 1
	0.0034 kg·m·m	The moment of inertia of an inverted pendulum 2
	0.0775 m	The half length of the inverted pendulum 1
	0.25 m	The half length of the inverted pendulum 2
	0.155 m	The length of the inverted pendulum 1
	10.1403 N·m/s	Friction coefficient of the cart
	0.003415 N·m/s	Friction coefficient of the inverted pendulum 1
	0.003224 N·m/s	Friction coefficient of the inverted pendulum 2
	9.8 m/	Gravitational acceleration