Abstract

Pendulum system is one of the classical questions of study and research about non-linear control and a suitable criterion for harnessing the mechanical systems. The inverted pendulum, because of its non-linearity and instability is a useful method for testing control algorithms (PID controls, neural network, fuzzy control, genetics algorithm, etc.) 
In 1972, two researchers from the control domain succeeded, using an analogue computer, in controlling an inverted pendulum in standing position on a cart, which was stabilized by horizontal force. 
The simple inverted pendulum, the rotary inverted pendulum, double inverted pendulum, and the rotary double inverted pendulum are types of inverted pendulum in control systems. The double inverted pendulum is a non-linear, unstable and fast reaction system. This system consists of two inverted pendulums assembled on each other, as per the fig. 1, and mounted on a cart that can be controlled and stabilized through applying the force F. In stabilization of the double inverted pendulum diverse methods have been employed like using fuzzy system and the rules table [6،5], the neural-fuzzy network [9], etc. 
In this paper a controller for stabilization of a double inverted pendulum will be designed using
the feedback error learning method.