Jacques Lottin

A nonlinear approach to the control of magnetic bearings

In this paper, nonlinear aspects of the control of magnetic bearings are studied. The authors design a nonlinear feedback law for the positioning of a shaft, and study the possibility of avoiding premagnetization currents, usually required when applying tangent linearization techniques. Using the flatness property, they propose simple solutions to the motion planning and stabilization problems according to the current complementarity condition or the current almost complementarity condition, that ensures that only one electromagnet in each actuator works at a time, or that one approaches arbitrarily close to this situation. The feedback synthesis is presented in both current and voltage control cases. In the latter case, a hierarchical control scheme, based on time-scale separation, is proposed, to avoid unbounded voltages at switchings that might result from the voltage linearizing feedback. Some implementation aspects are described and some experiments presented.

INTEGRATOR BACKSTEPPING USING CONTRACTION THEORY: A BRIEF METHODOLOGICAL NOTE.

Abstract While the use of Lyapunov function candidates for integrator backstepping has been extensively studied in the literature, little research has been conducted regarding the applicability of the so-called incremental stability approaches. This note addresses the problem of the use of an incremental approach, i.e. contraction theory to the integrator backstepping design on the methodological aspect. After briefly recalling basic results from contraction theory, a full contraction-based integrator backstepping procedure is presented. An example is given to illustrate the method.

Precise positioning and active vibration isolation using piezoelectric actuator with hysteresis compensation

This article investigates precise positioning at the micrometer scale using piezoelectric actuators. A special focus is given to the rejection of ambient vibration disturbances. An original experimental setup composed of two superposed piezoelectric actuator stages is used to evaluate the performances of the proposed approach. The bottom one is devoted to the disturbance generation, whereas the upper one allows position tracking and active stabilization. The experimental dynamic and hysteretic characterizations of the top actuator are performed. Based on the identified dynamic model, a linear controller is designed. Its performances are improved with a hysteresis compensation method. Such methods usually imply either simple symmetrical hysteresis (e.g. General Maxwell Slip) or operators able to model asymmetric loops (e.g. Preisach) at the cost of more memory usage and computational time. In the present study, a previously published lightweight asymmetric operator hysteresis is successfully used for the first time within a piezoelectric positioning closed-loop control.

Control of Magnetic Bearings: Flatness with Constraints

Abstract In this paper, we use the flatness property of the magnetic levitation model of a beam to design a non linear control scheme for its positionning. Our main objective is to avoid premagnetisation currents, which are usually required to apply tangent linearization techniques, since they produce undesired heat dissipation. Using the flatness property, we propose simple solutions to the motion planning and stabilization problems according to the current almost complementarity principle, that ensure that we approach arbitrarily close to the situation where only one electromagnet in each actuator works at a time. The control synthesis is presented in both current and voltage control cases. In the latter case, singularities are circumvented by means of a hierarchical control scheme based on time-scale separation.

EXPERIMENTAL EVALUATION OF A NEW ACTIVE VIBRATION CONTROL ALGORITHM

Abstract This work deals with little mock up experimentations of a vibration rejection algorithm. In a first time, bases of the algorithm are presented. Next section is devoted to the description of the prototype used to validate the process. Then, the settling of the algorithm using Matlab Simulink XPC Target is described and experimental results are presented and commented. From these results, future works are outlined.

Emphasizing Interdisciplinary of Control in Laboratory Courses: Illustration with the Inverted Pendulum

Abstract The importance of control laboratory courses is widely recognized as a crucial part of control education. This paper addresses the role of interdisciplinarity (meaning the different aspects of control) in laboratory courses for undergraduate students. Explanations and ideas are given based on the example of the inverted pendulum. Different aspects of control are studied throughout this paper : it is first stressed that constraints carried by engineering and industrial environment may have a significant impact when modelling a system. Then, the control structures used in this course are presented. After running the simulation of the system, qualitative results are described. Finally, some remarks are given to conclude the paper.

Disturbance Estimation and Compensation in Active Magnetic Bearings Control

Abstract This paper deals with constant or slowly variable disturbance reconstruction by means of extended observer for a multivariable system, namely an active magnetic suspension. Due to the nonlinear feature of the process, a cascaded continuous control scheme is first established. The structure of the model used in the high-level synthesis allows a decomposition in four simpler subsystems by means of a decoupling control law. Then an observer is built for disturbances and non measured state variables estimation. A digital control scheme is deduced using first order discretization of the continuous law. This paper ends with the presentation of experimental results that are obtained with a four degrees of freedom magnetic suspension controlled by means of a transputer specific board.

Internal Model Control with State Affine Representation Methodology and Application Software

Abstract This paper describes an approach that leads to the synthesis of robust controllers. In a methodological part, we recall the main features of the Internal Model Control, and of the state affine representation of varylinear systems. After that, we show how these two methods can be combined to improve the robustness of control algorithms. In the next section, we describe an application software. Its main aims are to allow an easy simulation of the above mentionned control structures, associated with different types of processes and additive disturbances. The last part deals with several results of simulation: we show the versatibility of that application software and some contributions of these different methods to the synthesis of robust control.