Optimal Design of the Double Inverted Pendulum

Abstract

The inverted pendulum is a classic example commonly found in control theory. Double inverted pendulum which is a combination of inverted pendulum and double pendulum makes the control problem more challenging. The purpose of this work was to design an optimal mechanical construction of a linear double inverted pendulum on a cart. Pendulums usually have the form of a freely attached rod to the cart moving in one dimension. The presented system assumes the functionality which ensures better efficiency. The main determinant of optimal parameters is the stabilization of the pendulum in vertical position and control of the position of the cart on the guide rail. The general concept outlined at the beginning presents the key elements necessary for the proper operation of the system. In some systems available in the literature and Internet, the engine moves with the cart, increasing the inertia forces acting on it. In the designed system, it was decided to fix the motor to the base. The engine in such a system should have the precise control and a high starting torque that allows stabilization of the pendulum. The presented conception base on the most optimal selection of all components.

LQR controller design for stabilization of non-linear DIP system based on ABC algorithm

“…For control instructions or research reasons, it is cheap and easy to construct and install in laboratories. One of the non-linear problems is the inverted pendulum system, which is studied by many academicians, most of them using linearization theory control systems [1]. Controlling this system via traditional means is, in general, a difficult process.…”