This article discusses a problem of stabilization for an inverted pendulum on a cart. In this work the cart does not travel along an horizontal line, which is the case commonly considered in the literature, but along an arbitrary path in the horizontalvertical plane. The main obstacle encountered lies in the fact that the feedback controlled system becomes unstable in some ”critical regions” al...

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In this article we discuss the primliminary results of stabilising a vertically driven pendulum. Following the brief introduction on the importance of this ‘toy’ problem, we give an account of the experimental set up. We then explain the parameter extraction from the experimental data which form a cucial part of our quantitative study. We also find the stability boundary for a small range of dr...

This study presents an energy level stabilization algorithm for the pendulum on a cart system with restricted cart track length. The objective is to bring the pendulum to its unstable equilibrium. To do so the energy level of the pendulum is increased or decreased by accelerating the cart in the appropriate direction while keeping within imposed limit positions. To achieve, the equation of moti...

This paper proposes a swing-up control scheme for a cart-type single pendulum having a serial second pendulum as a parasitic part. The proposed control scheme swings up the first pendulum with controlling the motion of a cart and being robust to the parasitic part. In the swing-up, the second pendulum is swinging at the top of the first pendulum and the motion of the second pendulum works as st...

In this paper, we present Fuzzy Neural Network (FNN) structure and the back-propagation process, which tunes the weighting factors of FNN such that its output can follow the desired signal. Then they are applied to design an FNN controller to let the pole of an inverted pendulum be as vertical as possible. Simulation results show that the proposed approach produces better responses than the fuz...

Designing and analyzing controllers for underactuated systems with underactuation degree greater than one is still an open and challenging problem. In this paper, we study an unsolved problem of analyzing energy based swing-up control for a double pendulum on a cart, which has three degrees of freedom and only one control input. We present an original analysis of the convergence of the energy o...

In order to explore the essence of structural controllability, structural controllability of inverted pendulum is analyzed in this presented study and a sufficient controllability condition of a class of perturbed linear system is obtained, which is essential to prove the structural controllability for the perturbed inverted pendulum. Two different structured models of inverted pendulum are con...