Yann Le Gorrec

Bouc–Wen Modeling and Feedforward Control of Multivariable Hysteresis in Piezoelectric Systems: Application to a 3-DoF Piezotube Scanner

This paper is concerned with multivariable coupled hysteretic systems. The traditional Bouc-Wen monovariable hysteresis model devoted to 1 degree of freedom (DoF) actuated systems is extended to model the hysteresis in systems with multiple DoF, which typify strong cross-couplings. The proposed approach is able to model and to compensate for known hysteresis nonlinearities that affect smart materials. First, after presenting the new multivariable hysteresis Bouc-Wen model, a procedure of identification of its parameters is proposed. Then, we propose a multivariable compensator for the hysteresis. The compensator is based on the combination of the inverse multiplicative structure with the model, which permits to avoid additional calculation of its parameters. Such advantage is essential when the number of DoF is high. All along this paper, the cases of underactuated, overactuated, and fully actuated hysteretic systems are discussed. Finally, the proposed method is used to model and to compensate for the hysteresis in a 3-DoF piezoelectric tube actuator. The experimental results demonstrate its efficiency to linearize the hysteresis in the direct transfers and to minimize the hysteresis of the cross-couplings.

Modal Multimodel Control Design Approach Applied to Aircraft Autopilot Design

Modal approaches like eigen- structure assignment have shown them- selves to be efficient for flight control design. Performance requirements are easily met using this approach. How- ever, generally, robustness is not satisfac- tory. This paper presents a technique that can be viewed as an improvement over traditional eigenstructure assignment as it produces systems wich meet robust- ness requirements (multimodel approach). The proposed technique reduces to solv- ing a quadratic problem under linear con- straints. The application treated concerns the landing phase of a large transport air- craft. It is shown that standard gain scheduling can be replaced by a single low dimensional dynamic feedback.

Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems With Dynamic Feedback

It is shown that a strictly-input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain. This follows since the controller imposes exponential dissipation of the total energy. The result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled PDEs and ODEs. The result is specialized to port-Hamiltonian control systems and a simplified DNA-manipulation process is used to illustrate the result.

On the passivity based control of irreversible processes

Irreversible port-Hamiltonian systems (IPHS) have recently been proposed for the modelling of irreversible thermodynamic systems. On the other hand, a classical result on the use of the second law of thermodynamics for the stabilization of irreversible processes is the celebrated thermodynamic availability function. These frameworks are combined to propose a class of Passivity Based Controller (PBC) for irreversible processes. An alternative formulation of the availability function in terms of internal energy is proposed. Using IPHS a matching-condition, which is interpreted in terms of energy-shaping, is derived and a specific solution that permits to assign a desired closed-loop structure and entropy rate is proposed. The approach can be compared with Interconnection and Damping Assignment-PBC, this method however leads in general to thermodynamically non-coherent closed-loop systems. In this paper a system theoretic approach is employed to derive a constructive method for the control design. The closed-loop system is in IPHS form, hence it can be identified with a thermodynamic system and the control parameters related with thermodynamic variables, such as the reaction rates in the case of chemical reactions. A generic non-linear non-isothermal continuous stirred tank reactor is used to illustrate the approach.

On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems

This paper is concerned with the energy shaping of 1-D linear boundary controlled port-Hamiltonian systems. The energy-Casimir method is first proposed to deal with power preserving systems. It is shown how to use finite dimensional dynamic boundary controllers and closed-loop structural invariants to partially shape the closed-loop energy function and how such controller finally reduces to a state feedback. When dissipative port-Hamiltonian systems are considered, the Casimir functions do not exist anymore (dissipation obstacle) and the immersion (via a dynamic controller)/reduction (through invariants) method cannot be applied. The main contribution of this paper is to show how to use the same ideas and state functions to shape the closed-loop energy function of dissipative systems through direct state feedback i.e. without relying on a dynamic controller and a reduction step. In both cases, the existence of solution and the asymptotic stability (by additional damping injection) of the closed-loop system are proven. The general theory and achievable closed-loop performances are illustrated with the help of a concluding example, the boundary stabilization of a longitudinal beam vibrations.

From Brayton-Moser formulation to Port Hamiltonian representation: the CSTR case study

Abstract This paper shows that any thermodynamic potential fulfilling some thermodynamic stability criterion (e.g. the chemical affinity or the ectropy) can be used as a potential function for the dissipative (pseudo) Port Hamiltonian formulation of the non isothermal Continuous Stirred Tank Reactor (CSTR) model. Besides Brayton-Moser formulation is used to obtain some dissipative Port Hamiltonian representation.

Improvement of Silicon Nanotweezers Sensitivity for Mechanical Characterization of Biomolecules Using Closed-Loop Control

In this paper, we show that closed-loop control can be advantageously used for the characterization of mechanical properties of biomolecules using silicon nanotweezers (SNT). SNT have already been used in open-loop mode for the characterization of mechanical properties of DNA molecules. Up to now, such an approach allows the detection of stiffness variations equivalent to about 15 DNA molecules. Here, it is shown that this resolution is inversely proportional to the resonance frequency of the whole system and that real-time feedback control with state observer can drastically improve the performances of the tweezers used as biosensors. Such improvement is experimentally validated in the case of the manipulation of fibronectin molecules. The results are promising for the accurate characterization of biopolymers such as DNA molecules.

Gain Scheduling Control of a Nonlinear Electrostatic Microgripper: Design by an Eigenstructure Assignment With an Observer-Based Structure

This paper deals with the modeling and the robust control of a nonlinear electrostatic microgripper dedicated to embedded microrobotics applications. We first propose a polynomial linear parameter varying model of the system, where the varying parameter is the mean position of the microgripper that is used for the linearization. The controller is then derived using a multimodel and scheduled observer-based control strategy. The structure and the order of the controller are defined a priori allowing the derivation of a robust low-order controller suitable for a real-time implementation in embedded on-chip environments. Results show that a very wide (several tens of micrometers) and fast positioning of the gripping arm can be achieved using the control strategy. A robustness analysis and experimental implementation results show the efficiency of the controller and the relevance of the theoretical approach.

Study of thermal and acoustic noise interferences in low stiffness atomic force microscope cantilevers and characterization of their dynamic properties

The atomic force microscope (AFM) is a powerful tool for the measurement of forces at the micro/nano scale when calibrated cantilevers are used. Besides many existing calibration techniques, the thermal calibration is one of the simplest and fastest methods for the dynamic characterization of an AFM cantilever. This method is efficient provided that the Brownian motion (thermal noise) is the most important source of excitation during the calibration process. Otherwise, the value of spring constant is underestimated. This paper investigates noise interference ranges in low stiffness AFM cantilevers taking into account thermal fluctuations and acoustic pressures as two main sources of noise. As a result, a preliminary knowledge about the conditions in which thermal fluctuations and acoustic pressures have closely the same effect on the AFM cantilever (noise interference) is provided with both theoretical and experimental arguments. Consequently, beyond the noise interference range, commercial low stiffness AFM cantilevers are calibrated in two ways: using the thermal noise (in a wide temperature range) and acoustic pressures generated by a loudspeaker. We then demonstrate that acoustic noises can also be used for an efficient characterization and calibration of low stiffness AFM cantilevers. The accuracy of the acoustic characterization is evaluated by comparison with results from the thermal calibration.

Energy shaping of boundary controlled linear port Hamiltonian systems

In this paper, we consider the asymptotic stabilization of a class of one dimensional boundary controlled port Hamiltonian systems by an immersion/reduction approach and the use of Casimir invariants. We first extend existing results on asymptotic stability of linear infinite dimensional systems controlled at their boundary to the case of stable Port Hamiltonian controllers including some physical constraints as clamping. Then the relation between structural invariants, namely Casimir functions, and the controller structure is computed. The Casimirs are employed in the selection of the controllers Hamiltonian to shape the total energy function of the closed loop system and introduce a minimum in the desired equilibrium configuration. The approach is illustrated on the model of a micro manipulation process with partial-actuation on one side of the spatial domain.