Marc Rouff

Computation of feedback laws for static linearization of nonlinear dynamical systems

Abstract This article gives the algorithm for computing the feedback laws of the static state linearization method. An example is given, and the program, written in Reduce, is given in the Appendix. The case of dynamical state feedback is also considered.

Dynamical and thermal modelling of creep and relaxation for force and weight sensors

We present in this article analytic formulations of creep and relaxation processes, including thermal variation, for force and weight mechatronic sensors. We found that these phenomena can be modelled by a two timescales process for the dynamical behaviour of creep and relaxation, and that under a quasi static assumption of the temperature evolution thermal variation can be given, under usual range of temperature, by a polynomial representation of low order.

Control of mechanical oscillators and their application to weight and force measurement

Abstract We present the problem of the control of a new low cost and robust technology of mechatronic sensors composed of a double metallic multi-layered tuning-fork resonator, and controlled by two bimorphic piezoelectric ceramic transducers. The problem of the stability of the eigenfrequency is considered and the performance of our first prototype is given.

Study of invariance properties in robotic systems: a Lagrangian formulation approach

We present here some interesting properties of regularity regarding firstly the flexural deformation spectra and secondly the flexural and torsional spectra of mechanical loaded bodies which can be useful for the finite control of these systems. In these two cases, two main cases are studied: the non compliant and non dissipative case, and the compliant and non dissipative case. By studying flexural spectra of general deformable bodies versus the load, we found a noteworthy invariance property of the eigenfrequencies versus the system load. Roughly we found that under a preload condition the eigenfrequencies of deformation of the system are invariant versus loads, i.e. on a diagram eigenfrequencies versus loads, the curves are horizontal lines. As shown by our curves, these behaviors are not very distant from the asymptotic behaviors but occur for very small values of loads and frequencies, allowing the implementation of this property to real technological devices. For loaded flexural and torsional deformable bodies, we found that under a preload condition, each eigenfrequency is invariant versus the load mN. For the mode 7 and beyond, the preload conditions are less than mN=1, and the seven first modes (from 0 to 6) can be easily modelled by polynomial functions of mN in the neighborhood of useful mN

Eigenfrequencies Invariance Properties in Deformable Flexion-Torsion Loaded Bodies -1- General Properties

We present here, in the framework of resonnant behaviours, an eigenfrequency invariance properties for loaded flexural and torsional deformable bodies. We found that under a preload condition each eigenfrequency is invariant versus the load mN . For the mode 7 and beyond the preload conditions are less than mN = 1, and the seven first modes (form 0 to 6) can be easily modelled by polynomial functions of mN in the neighbourhood of useful mN . These properties open the way to new finite dimension controllers.

Decoupling Partially Unknown Dynamical Systems by State Feedback Equations

One problem for efficient control of complex systems is to take into account the influence of unknown dynamics in interaction with a fixed defined one by a set of defined time varying parameters behaviour coming from coupling partially unknown dynamics. Under the assumption of robust model, nonlinear state feedback decoupling methods can be used for the control of such systems. We show in our paper, that if these parameters are slowly varying in time before the main dynamics (the exact mathematical meaning of this notion is given in the article), the classical decoupling methods remain valid with parameterized laws, but if parameters dynamic are non negligible before the main dynamic, we are in the fast varying parameters case, and we show that in this case decoupling methods operators must be changed in order to include these dynamical effects. We show also that in this case the use of classical decoupling methods, leads to non effcient control and multiple spurious effects. The computation of the static and dynamic feedback laws, in case of fast varying parameters, are given, for nonlinear decoupling methods, linearization and rejection of perturbations, as the research of the functional invariants of the output. A robust example in robotics is given, and the contribution of parameters dynamic is shown.

Robust control of intelligent robots by parametrized state feedback methods

Intelligent robots must be able to be faced to many new difficult tasks. This implies the use of many parameters in the control laws. We show that if these parameters are slowly varying before the dynamics of the grand motion axes, the classical decoupling methods remain valid with parametrized laws, but if parameters dynamic are non negligible before the decoupling dynamic, we are in the fast varying parameters case, and we show in this case that decoupling methods operators must be changed in order to include these dynamical effects, which lead by using the classical decoupling methods, to non-efficient control. The computation of the static and dynamic feedback laws are given in the case of nonlinear decoupling, linearization and rejection of perturbations. A robust example in robotics is given, and the contribution of the parameters dynamic is shown. We show also that this kind of robust robot model can be treated by differential flatness methods. An N link robot manipulator is considered in this way and the same operators appear. Finally, an application to the pseudo differential flatness of these models are presented by a closed loop approach.

A new approach of modelling vibrations for intelligent robotized structures

Intelligent precise and fast robotized systems must take into account the flexible and torsional nature of their structure. This leads to theoretical infinite dimensional controllers. We present in the framework of resonant behaviors an eigenfrequency invariance property for loaded flexural and torsional deformable bodies which is very suitable for modelling these new robots as the resulting model is finite dimensional of low order and can be determined by an a priori precision given by the designer. We found that under a preload condition each eigenfrequency is invariant versus the tipload. To further improve this result, the role of passive system parameters has been studied. We show that compliant behaviors at mechanical joints create a new order on the system which leads to a large invariance property. A compliant mechanical joint diminishes drastically the preload condition.