The problem of controlled excitation of oscillations in a chain of N coupled pendulums is considered. Such a problem may arise when studying different physical and mechanical systems and is also of interest for design of prospective laboratory equipment for control education. The simulation results for the chain of 50 pendulums are given. The multi-pendulum mechatronic setup from 50 computer-co...

The French Academy units of time and length — the second and the meter — are traditionally considered independent from each other. However, it is a matter of fact that a meter simple pendulum beats virtually the second in each oscillation, a 'surprising' coincidence that has no physical reason. We shortly review the steps that led to the choice of the meter as the ten millionth part of the quad...

Traditionally, the discussion about the geometrical interpretation of inertial forces is reserved for General Relativity handbooks. In these notes an analysis of the effect of such forces in a classical (newtonian) context is made, as well as a study of the relation between the precession of the Foucault pendulum and the holonomy on a surface, including some critical remarks about the common st...

The double pendulum is a classic system in the study of chaos. We have explored the double pendulum experimentally, and compared results to a numerical simulation. This comparison was done in the time it takes for the second arm of the pendulum to ”flip,” based on initial starting conditions. We also performed analyis of the vertically driven case.

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 this paper, we will propose a nonlinear passivity based controller fur a double inverted pendulum system, consisting of a two-link pendulum mounted on a pad which is moved by a linear induction motor so that the double pendulum points straight-up The proposed controller nut only can drive the double pendulum from its “natural stable hanging position” tu its “unstable upright inverted positio...

An alternative to the Iterative Newton-Euler or linked segment model was developed to compute lower extremity joint moments using the mechanics of the double pendulum. The double pendulum model equations were applied to both the swing and stance phases of locomotion. Both the Iterative Newton-Euler and double pendulum models computed virtually identical joint moment data over the entire stridec...

Reinforcement learning has been active research area not only in machine learning but also in control engineering, operation research and robotics in recent years. It is a model free learning control method that can solve Markov decision problems. Q-learning is an incremental dynamic programming procedure that determines the optimal policy in a step-by-step manner. It is an online procedure for...