Une étude sur les spécificités de la commande dans le micromonde.

National audienceThe development of micro and nanotechnologies requires the design of microrobots and Microsystems able to handle submillimetric objects. Many micromanipulation systems have been built. However, improvement of the performances requires the use of advanced control methods. In this paper, we present the main characteristics of the microworld from a control point of view and some control strategies adapted to the microsystems

Force control in piezoelectric microactuators using self scheduled H∞ technique.

International audienceIn micromanipulation and microassembly tasks, the manipulated micro-objects do not always have the same characteristics, such as compliance. Thus, both the static and dynamic models representing the force behavior respect to input sollicitations depend on the characteristics of of the manipulated micro-object. As a result, it is hard to synthesize a single controller able to ensure desired performances for all set of micro-objects, especially when their compliance range is very large. In this paper, we propose to model and control the manipulation force applied by piezoelectric microactuators by using a parameter dependent approach such that desired performances are ensured for all kind of manipulated objects. The resulting controller is said self-scheduled and easy to implement from numerical point of view. First, we derive a model that is dependent on the characteristics of the manipulated micro-object. The strong hysteresis nonlinearity of the piezoelectric microactuator was compensated and the derived model is therefore linear. Afterwards, we design a self-scheduled controller using H technique. In order to ensure the desired performances (micrometric accuracy, tens of millisecon∞d of settling time) for any manipulated micro-objects, a parameter dependent controller is designed respect to the continuum of models. Finally, the efficiency of the proposed design procedure will be illustrated from experimental results

Matrix-valued Impedances with Fractional Derivatives and Integrals in Boundary Feedback Control: a port-Hamiltonian approach

This paper discusses the passivity of the port-Hamiltonian formulation of a multivariable impedance matching boundary feedback of fractional order, expressed through diffusive representation. It is first shown in the 1D-wave equation case that the impedance matching boundary feedback can be written as a passive feedback on the boundary port variables. In the Euler-Bernoulli case, the impedance matching feedback matrix involves fractional derivatives and integrals. It is shown that the usual diffusive representation of such feedback is not formally a dissipative port-Hamiltonian system, even if from a frequency point of view this feedback proves passive

Exponential stability of a class of boundary control systems

We study a class of partial differential equations (with variable coefficients) on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we provide simple tools to check exponential stability. This class is general enough to include models of flexible structures, traveling waves, heat exchangers, and bioreactors among others. The result is based on the use of a generating function (the energy for physical systems) and an inequality condition at the boundary. Furthermore, based on the port Hamiltonian approach, we give a constructive method to reduce this inequality to a simple matrix inequality

Controller parametric robustification using observer based formulation and multimodel design technique

This paper deals with equivalent observer based structure and controller robustification. The purpose of the method is to improve the parametric robustness of an initial controller, synthesized, for example, by using H∞ or μ technics. The method is based on equivalent Luenberger observer formulation and multimodel design procedure for the parametric robustification. Matrices of the equivalent ”feedforward+observer +feedback” controller are synthesized to guarantee the same closed loop eigenstructure and input/output transfert as the initial controller (without any restriction on the initial controller order). Afterwards, they are used to initialize an iterative design procedure aiming at improving the parametric robustness. This procedure is based on real-μ analysis and multimodel eigenstructure assignment (using the observer based formulation). Due to the observer structure, improvement of the parametric robustness of the initial controller without paying attention to the closed loop poles coming from the controller dynamic is obtained. Another advantage of the equivalent observer based formulation lies in the fact that it would directly be used to schedule the controller (dynamic and feedback parts). Finally the global method (equivalent observer plus robustification) is applied on the robust control of the space shuttle described in μ-analysis and synthesis toolbox

Boundary port Hamiltonian control of a class of nanotweezers.

International audienceBoundary controlled-port Hamiltonian systems have proven to be of great use for the analysis and control of a large class of systems described by partial differential equations. The use of semi-group theory, combined with the underlying physics of Hamiltonian systems permits to prove existence, well-possessedness and stability of solutions using constructive techniques. On other hand, the differential geometric representation of these systems has lead to finite dimension approximation methods that conserves physical properties such as the interconnection structure and the energy. These results are applied to the modelling and control of a class of nanotweezers used for DNA-manipulation. The Nanotweezer may be modelled as a flexible beam interconnected with a finite dimensional dynamical system representing the manipulated object. A boundary controlled-port Hamiltonian model for the ensemble and an exponentially stabilizing controller are proposed. A geometric approximation scheme is used to reduce the infinite dimensional system and numerical simulations of the closed-loop system presented

Exponential stability of a class of PDE's with dynamic boundary control.

International audienceWe show that a finite dimensional strictly passive linear controller exponentially stabilizes a large class of partial differential equations which are actuated through its boundaries on a one dimensional spatial domain. This is achieved by extending existing results on exponential stability of boundary control system with static boundary control to the case with dynamic boundary control. The approach is illustrated on a physical example

Port hamiltonian modeling of MSMA based actuator: toward a thermodynamically consistent formulation.

International audienceThis paper presents a thermodynamically consistent model of MSMA (Magnetic Shape Memory Alloys) under port Hamiltonian framework. It is based on previous works on MSMA proposed in (Gauthier et al., 2008; Calchand et al., 2011). The main di erence lies in the choice of the state variables and manipulated thermodynamic forces. Furthermore in (Gauthier et al., 2008), subsequent experiments revealed a highly hysteretic behavior of these materials. Here, the simpli ed hysteretic behavior is incorporated into the port-hamiltonian model to obtain a ner and more precise model. Such modeling will allow the use of a wide range of energy based methods to design the associated control system. The paper ends with some extensions to more complex hysterestic phenomena by using Preisach like model. First ideas are proposed to extend the previous physical model to systems with internal hysteretic loops

Robust Control of a Pressure Swing Adsorption Process.

International audienceThis paper presents the H1 control of a pressure swing adsorption process. This separation process is characterized by periodic operations. The objective of the control is to assign the trajectory of the output system purity and to reject the perturbation on the inlet composition. The control design is synthetized from some Hammerstein model that approximates the cyclic process. The control scheme is designed using H1 optimization method. J-spectral factorization is applied to derive the controller. The controller is then validated both on the Hammerstein and complete models. Simulation results are given. Comparison with PI controller is provided

Using System Theory to prove Existence of Non-Linear PDE's.

International audienceIn this discussion paper we present an idea of using techniques known from systems theory to show existence for a class of non-linear partial differential equations (pde's). At the end of the paper a list of research questions and possible approaches is given