Disturbances monitoring from controller states

In this paper, it is proposed to implement a given controller using observer-based structures in order to estimate or to monitor some unmeasured plant states or external disturbances. Such a monitoring can be used to perform in-line or off-line analysis (supervising controller modes, capitalizing flight data to improve disturbance modelling, ...). This observer-based structure must involve a judicious onboard model selected to be representative of the physical phenomenon one want to monitor. This principle is applied to an aircraft longitudinal flight control law to monitor wind disturbances and to estimate the angle-of-attack

Low Mach number flows, and combustion

We prove uniform existence results for the full Navier-Stokes equations for time intervals which are independent of the Mach number, the Reynolds number and the P\'eclet number. We consider general equations of state and we give an application for the low Mach number limit combustion problem introduced by Majda

Gravity capillary standing water waves

The paper deals with the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the question of the nonlinear interaction of a plane wave with its reflection off a vertical wall. The main result is the construction of small amplitude, standing (namely periodic in time and space, and not travelling) solutions of Sobolev regularity, for almost all values of the surface tension coefficient, and for a large set of time-frequencies. This is an existence result for a quasi-linear, Hamiltonian, reversible system of two autonomous pseudo-PDEs with small divisors. The proof is a combination of different techniques, such as a Nash-Moser scheme, microlocal analysis, and bifurcation analysis.Comment: 80 page

Supercritical geometric optics for nonlinear Schrodinger equations

We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local version of the modulated energy functional introduced by Y.Brenier. The system we obtain is hyperbolic symmetric, and the justification of WKB analysis follows.Comment: 29 pages. Some typos fixe

Kinematic analysis of complex gear mechanisms

This paper presents a general kinematic analysis method for complex gear mechanisms. This approach involves the null-space of the adjacency matrix associated with the graph of the mechanism weighted by complex coecients. It allows to compute the rotational speed ratios of all the links and the frequency of all the contacts in this mechanism(including roll bearings). This approach is applied to various examples including a two degrees of freedom car differential

Global solutions and asymptotic behavior for two dimensional gravity water waves

This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution, which shows that modified scattering holds. The proof is based on a bootstrap argument involving $L^2$ and $L^\infty$ estimates. The $L^2$ bounds are proved in a companion paper of this article. They rely on a normal forms paradifferential method allowing one to obtain energy estimates on the Eulerian formulation of the water waves equation. We give here the proof of the uniform bounds, interpreting the equation in a semi-classical way, and combining Klainerman vector fields with the description of the solution in terms of semi-classical lagrangian distributions. This, together with the $L^2$ estimates of the companion paper, allows us to deduce our main global existence result.Comment: 100 pages. Our previous preprint arXiv:1305.4090v1 is now splitted into two parts. This is the first one (which has the same title

The impact of local masses and inertias on the dynamic modelling of flexible manipulators

After a brief review of the recent literature dealing with flexible multi-body modelling for control design purpose, the paper first describes three different techniques used to build up the dynamic model of SECAFLEX, a 2 d.o.f. flexible in-plane manipulator driven by geared DC motors : introduction of local fictitious springs, use of a basis of assumed Euler-Bernouilli cantilever-free modes and of 5th order polynomial modes. This last technique allows to take easily into account local masses and inertias, which appear important in real-life experiments. Transformation of the state space models obtained in a common modal basis allows a quantitative comparison of the results obtained, while Bode plots of the various interesting transfer functions relating input torques to output in-joint and tip mea-surements give rather qualitative results. A parametric study of the effect of angular configuration changes and physical parameter modifications (including the effect of rotor inertia) shows that the three techniques give similar results up to the first flexible modes of each link when concentrated masses and inertias are present. From the control point of view, “pathological” cases are exhibited : uncertainty in the phase of the non-colocated transfer functions, high dependence of the free modes in the rotor inertia value. Robustness of the control to these kinds of uncertainties appears compulsory

Flexible joint control : robustness analysis of the collocated and non-collocated feedbacks

In this paper, we propose a discussion on the robustness and performance properties of a proportional-derivative controller applied to a very flexible joint. Because of the flexible mode due to in-joint compliance, the classical collocated control does not allow to obtain good rigid mode dynamics with a correct phase margin in low and high frequency, and the non-collocated control does not allow to damp correctly the rotor mode. The simultaneous analysis of discrete root loci and Nichols plots leads to a phase control law with a derivative term built from both input and output velocities. Simulations taking into account various real non-linearities and measurement imperfections are proposed to validate this improved control design