Modeling and Control of a Flexible Structure Incorporating Inertial Slip-Stick Actuators

Shape and vibration control of a linear flexible structure by means of a new type of inertial slip-stick actuator are investigated. A nonlinear model representing the interaction between the structure and a six-degree-of-freedom Stewart platform system containing six actuators is derived, and closed-loop stability and performance of the controlled systems are investigated. A linearized model is also derived for design purposes. Quasistatic alignment of a payload attached to the platform is solved simply by using a proportional controller based on a linear kinematic model. The stability of this controller is examined using a dynamic model of the complete system and is validated experimentally by introducing random thermal elongations of several structural members. Vibration control is solved using an H∞ loop-shaping controller and, although its performance is found to be less satisfactory than desired, the nonlinear model gives good predictions of the performance and stability of the closed-loop system

When is the Haar measure a Pietsch measure for nonlinear mappings?

We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed

Evaporative cooling of a small number of atoms in a single-beam microscopic dipole trap

We demonstrate experimentally the evaporative cooling of a few hundred rubidium 87 atoms in a single-beam microscopic dipole trap. Starting from 800 atoms at a temperature of 125microKelvins, we produce an unpolarized sample of 40 atoms at 110nK, within 3s. The phase-space density at the end of the evaporation reaches unity, close to quantum degeneracy. The gain in phase-space density after evaporation is 10^3. We find that the scaling laws used for much larger numbers of atoms are still valid despite the small number of atoms involved in the evaporative cooling process. We also compare our results to a simple kinetic model describing the evaporation process and find good agreement with the data.Comment: 7 pages, 5 figure