arXiv subjects

Philippe Martin

Publications and source records attributed to Philippe Martin.

30 records · Page 2Linked to original sources

arXiv2014

Velocity-aided Attitude Estimation for Accelerated Rigid Bodies

Two nonlinear observers for velocity-aided attitude estimation, relying on gyrometers, accelerometers, magnetometers, and velocity measured in the body-fixed frame, are proposed. As opposed to state-of-the-art body-fixed velocity-aided attitude observers endowed with local properties, both observers are (almost) globally asymptotically stable, with very simple and flexible tuning. Moreover, the roll and pitch estimates are globally decoupled from magnetometer measurements.

math.OC↗

arXiv2014

Controllability of the 1D Schrodinger equation by the flatness approach

We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control input achieving the exact controllability in the energy space. As an application, we derive an explicit pair of control inputs achieving the exact steering to zero for a simply-supported beam.

math.OC↗

arXiv2014

Energy-based modeling of electric motors

We propose a new approach to model electrical machines based on energy considerations and construction symmetries of the motor. We detail the approach on the Permanent-Magnet Synchronous Motor and show that it can be extended to Synchronous Reluctance Motor and Induction Motor. Thanks to this approach we recover the usual models without any tedious computation. We also consider effects due to non-sinusoidal windings or saturation and provide experimental data.

math.OC↗

arXiv2013

Null controllability of the heat equation using flatness

We derive in a direct and rather straightforward way the null controllability of the N-dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This yields an explicit control law achieving the exact steering to zero. Replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds. Numerical experiments demonstrate the relevance of the approach.

math.OC↗

arXiv2013

Null Controllability of the 2D Heat Equation Using Flatness

We derive in a direct and rather straightforward way the null controllability of a 2-D heat equation with boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. Numerical experiments demonstrate the relevance of the approach.

math.OC↗

arXiv2013

Null controllability of the 1D heat equation using flatness

We derive in a straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em flatness approach}, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. We also give accurate error estimates when the various series involved are replaced by their partial sums, which is paramount for an actual numerical scheme. Numerical experiments demonstrate the relevance of the approach.

math.OC↗

arXiv2012

Sensorless position estimation of Permanent-Magnet Synchronous Motors using a saturation model

Sensorless control of Permanent-Magnet Synchronous Motors (PMSM) at low velocity remains a challenging task. A now well-established method consists in injecting a high-frequency signal and use the rotor saliency, both geometric and magnetic-saturation induced. This paper proposes a clear and original analysis based on second-order averaging of how to recover the position information from signal injection; this analysis blends well with a general model of magnetic saturation. It also proposes a simple parametric model of the saturated PMSM, based on an energy function which simply encompasses saturation and cross-saturation effects. Experimental results on a surface-mounted PMSM and an interior magnet PMSM illustrate the relevance of the approach.

math.OC↗

arXiv2012

Signal injection and averaging for position estimation of Permanent-Magnet Synchronous Motors

Sensorless control of Permanent-Magnet Synchronous Motors at low velocity remains a challenging task. A now well-established method consists in injecting a high-frequency signal and use the rotor saliency, both geometric and magnetic-saturation induced. This paper proposes a clear and original analysis based on second-order averaging of how to recover the position information from signal injection; this analysis blends well with a general model of magnetic saturation. It also experimentally demonstrates the relevance for position estimation of a simple parametric saturation model recently introduced by the authors.

math.OC↗

arXiv2011

Null controllability of the structurally damped wave equation with moving point control

We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove that the null controllability holds in some suitable Sobolev space and after a fixed positive time independent of the initial conditions.

math.OC↗

arXiv2011

Estimation of Saturation of Permanent-Magnet Synchronous Motors Through an Energy-Based Model

We propose a parametric model of the saturated Permanent-Magnet Synchronous Motor (PMSM) together with an estimation method of the magnetic parameters. The model is based on an energy function which simply encompasses the saturation effects. Injection of fast-varying pulsating voltages and measurements of the resulting current ripples then permit to identify the magnetic parameters by linear least squares. Experimental results on a surface-mounted PMSM and an interoir magnet PMSM illustrate the relevance of the approach.

math.OC↗

arXiv2010

A Separation Principle on Lie Groups

For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local separation principle holds around steady-states, as the linearized system is time-invariant. This paper addresses the issue of a non-linear separation principle on Lie groups. For invariant systems on Lie groups, we prove there exists a large set of (time-varying) trajectories around which the linearized observer-controler system is time-invariant, as soon as a symmetry-preserving observer is used. Thus a separation principle holds around those trajectories. The theory is illustrated by a mobile robot example, and the developed ideas are then extended to a class of Lagrangian mechanical systems on Lie groups described by Euler-Poincare equations.

math.OC↗

arXiv2007

Design of a Virtual Component Neutral Network-on-Chip Transaction Layer

Research studies have demonstrated the feasibility and advantages of Network-on-Chip (NoC) over traditional bus-based architectures but have not focused on compatibility communication standards. This paper describes a number of issues faced when designing a VC-neutral NoC, i.e. compatible with standards such as AHB 2.0, AXI, VCI, OCP, and various other proprietary protocols, and how a layered approach to communication helps solve these issues.

cs.AR↗