Optimal time control to swing-up the inverted pendulum-cart in open-loop form

National audienceThis work deals with simulation on an Inverted Pendulum (IP). The control strategy of an IP is split into two main control phases: (i) swing-up control to bring back the pendulum from the downward position to the upward one, and (ii) upright stabilization control to maintain the pendulum to the upright vertical position. In the case (ii), a feedback or a neuro-fuzzy controller is used to stabilize the pendulum cart, while in the first case (i), a non-linear controller based on the energy of the pendulum is used in order to reach the desired performance with a minimum number of swings. Our contribution is to present a simulation using MatLab of time-optimal control system for swinging-up the pendulum, with a single control law in an open-loop form. From the bang-bang structure of the time-optimal control resulting from the necessary condition of the Pontryagin Maximum Principle, the solution obtained from direct discretization method is adjusted by using Newton based method

A family of smooth controllers for swinging up a pendulum

Es el primer envío que hago. Le agradeceré si me confirma que es todo correcto, especialmente el cumplimiento de los derechos de propiedad de la editorial. Mi email es [email protected] paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach.MCyT-FEDER DPI2006-0733

Rapid inversion: running animals and robots swing like a pendulum under ledges.

Escaping from predators often demands that animals rapidly negotiate complex environments. The smallest animals attain relatively fast speeds with high frequency leg cycling, wing flapping or body undulations, but absolute speeds are slow compared to larger animals. Instead, small animals benefit from the advantages of enhanced maneuverability in part due to scaling. Here, we report a novel behavior in small, legged runners that may facilitate their escape by disappearance from predators. We video recorded cockroaches and geckos rapidly running up an incline toward a ledge, digitized their motion and created a simple model to generalize the behavior. Both species ran rapidly at 12-15 body lengths-per-second toward the ledge without braking, dove off the ledge, attached their feet by claws like a grappling hook, and used a pendulum-like motion that can exceed one meter-per-second to swing around to an inverted position under the ledge, out of sight. We discovered geckos in Southeast Asia can execute this escape behavior in the field. Quantification of these acrobatic behaviors provides biological inspiration toward the design of small, highly mobile search-and-rescue robots that can assist us during natural and human-made disasters. We report the first steps toward this new capability in a small, hexapedal robot

A quasi-complete mechanical model for a double torsion pendulum

We present a dynamical model for the double torsion pendulum nicknamed PETER, where one torsion pendulum hangs in cascade, but off-axis, from the other. The dynamics of interest in these devices lies around the torsional resonance, that is at very low frequencies (mHz). However, we find that, in order to properly describe the forced motion of the pendulums, also other modes must be considered, namely swinging and bouncing oscillations of the two suspended masses, that resonate at higher frequencies (Hz). Although the system has obviously 6+6 Degrees of Freedom, we find that 8 are sufficient for an accurate description of the observed motion. This model produces reliable estimates of the response to generic external disturbances and actuating forces or torques. In particular, we compute the effect of seismic floor motion (tilt noise) on the low frequency part of the signal spectra and show that it properly accounts for most of the measured low frequency noise.Comment: 15 pages, 6 figure

Swinging Atwood's Machine: Experimental and Theoretical Studies

A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have non-negligible radii and masses. Equations of motion must therefore take into account the inertial momentum of the pulleys, as well as the winding of the rope around them. Their influence is compared to previous studies. A preliminary discussion of the role of dissipation is included. The theoretical behaviour of the system with pulleys is illustrated numerically, and the relevance of different parameters is highlighted. Finally, the integrability of the dynamic system is studied, the main result being that the Machine with pulleys is non-integrable. The status of the results on integrability of the pulley-less Machine is also recalled.Comment: 37 page

Exploratory electromagnetic thruster research, phase 3, 23 June - 23 December 1969

Performance evaluation of MPD arc jets operating in quasi-steady mode