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Published in IFAC-PapersOnLine, 54(11):55-60, 2021; International audience; The problem of reducing vibrations during continuous hot-dip galvanizing process is addressed. Using the finite difference method the concerned part of the steel production line is modeled by a state space version of the axially moving strip equation which takes into account disturbances that may affect its efficient functioning. The synthesis of an appropriate control law for this process aims to reduce the impact of these disturbances and its implementation requires a definition of the position and the number of the sensor/actuator allowing an optimal reduction. Some numerical simulation of the steel strip behavior are presented and discussed for different sources of vibrations with and without a control system.

International audience; The aim of this article is the state estimation of uncertain polytopic dynamic systems. The parametric uncertainties affecting the system are time varying, unknown and bounded with known bounds. The objective is to determine the state estimates consisting in the smallest interval containing the real state value caused by the parametric uncertainties. This set will be characterized by the lower and upper bounds of the state trajectory. Given the uncertainty bounds, the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a Luenberger-type observer, fed with the system measurements. The proposed observer is designed to minimize the interval width of the estimates. The observer gains are obtained by solving an optimization problem under LMI constraints. The efficiency of the proposed approach is illustrated by numerical examples.

International audience; The detection of outliers in a series of measurements, but even more so their location, is a necessity when these measurements are to be used in a monitoring system. This detection/localization can only be done if redundant information is available, which may be based on the model of the system on which the measurements were collected.In some cases, however, it is not necessary to detect and locate outliers. Instead, a robust approach to their use may be preferred, one that minimizes the influence of these outliers, such as using a median rather than a mean.In this paper, the focus will be on the notion of robustness through a few examples and notably by proposing extensions to two well-known data processing techniques (data reconciliation and principal component analysis). The numerical examples proposed clearly show how to implement these two techniques and how to use them in a system monitoring procedure.

International audience; As systems become more and more complex, the use of nonlinear models for modeling is often unavoidable. However, nonlinear models naturally increase the difficulty of designing state estimation observers, control laws, and fault-tolerant control strategies. In fact, a specific analysis of the nonlinearities is needed to propose appropriate theoretical tools to deal with these problems. An interesting way to avoid analysis of the nonlinearities is by using the polytopic model approach to reduce the complexity of the automatic control problems. The goal of this chapter is to show the interesting properties of polytopic models as well as their eventual limits. By means of pedagogical examples, this chapter shows how polytopic models can be employed to model nonlinear systems. Stability results are also proposed to design a state feedback controller, and observers for state and unknown input estimations. A fault-tolerant control strategy is also proposed based on an appropriate combination of the state feedback law and the proposed unknown input observer. This strategy is applied to the control of the lateral dynamics of a vehicle in the presence of actuator faults in order to illustrate its validity. A rich survey bibliography is also proposed by the authors.

The estimation of the parameters of a system by a set membership approach consists in characterizing the set of parameters completely compatible with all the measurements made on the system, the model of this system and the characteristics of the errors and uncertainties that affect the measurements and the system. In this context, it is assumed that the error affecting the measurements is bounded and belongs to a set that is realizable a priori. The estimation problem to be solved then consists in finding the set of admissible values of the model parameters in adequacy with the measurements, the errors and the uncertainties. These uncertainties are handled by an approach that takes into account the unknowns that are the structural error of the model and the values of these parameters. From a practical point of view, the result obtained is a domain of parameters varying in time, domain which is characterized by its bounds. The volume of this domain is minimized, the proposed model explaining the measurements made at each time by optimizing a criterion of precision of the volume in consideration.

The objective of this study is the analysis of dynamic systems represented by multi-model with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires to consider all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment. This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger type observer, fed with the system measurements.