Ph. D. Project
Sensor and actuator optimal location for dynamic controller design. Application to active vibration reduction in a galvanizing process.
2019/10/15 - 2023/06/30
Industrial context
In galvanizing lines, the steel strip, after being heated and cooled in an annealing furnace, is immersed in a liquid zinc bath and then wrung out by means of air-jet nozzles to form a thin layer of zinc on the surface of the strip. The properties of the steel's surface depend on the thickness of the coating layer, therefore, its control is of great interest.
However, some disturbances generate vibrations on the strip that can significantly degrade the quality of the coating layer. To limit the impact of these disturbances, electromagnets associated with an active control system are installed above the wiping system to actively reduce these vibrations.
As a first step, it will be necessary to develop a behavioral model (Kim, 2003 ; Li, 2012) of the steel strip in the galvanizing line that takes into account the presence and propagation of the strip vibrations. Once this model has been established, one of the key problems of this device is the search for the optimal placement of the sensor(s), to measure the strip vibrations most effectively, but also of the actuator(s) to minimize the amplitude of these vibrations by an adapted control law. These optimal location problems, which can be solved one after the other or jointly, are at the heart of active vibration control themes and are found in many application areas (Gawronski, 2002 ; Starek, 2010 ; Zhang, 2018}.

Thesis' interest
The proposed project combines theoretical reflection and practical implementation. The thesis work will take place partly on a R&D (research and development) site where ArcelorMittal Maizières Research has an industrial-scale benchmark, adapted and dedicated to carrying out full-scale tests to validate the strip model and the optimal placement strategy for sensor(s) and actuator (s).

Expected researches
From a fundamental point of view, the problem raised concerns the optimization of the placement of sensors and actuators in a dynamic system according to observability and controllability criteria. A first approach aims to maximize the controllability (respectively observability) of the system state by positioning the actuators (respectively the sensors). The second and more global approach aims to optimize the controllability of outputs by inputs by jointly positioning sensors and actuators. The optimization of the sensors and/or actuators location should also take into account the minimization of the disturbance influence (strip vibrations, unmodelled dynamics, etc.). Obviously, cost and positioning constraints will have to be taken into consideration.
One of the paths to be explored is to solve the problem of optimal location of sensors or actuators by maximizing the grammians of observability or controllability. In the case of joint placement of sensors and actuators, the maximization of balanced grammians can be considered (Manohar, 2018 ; Marx, 2004). This technique has the advantage of not depending on the command used (Van de Wal, 2001). Moreover, it can be generalized and applied to nonlinear systems (Georges, 1995), singular systems (Marx, 2004), etc.

(Gawronski, 2002) W. Gawronski. Actuators and Sensors in Structural Dynamics. In Responsive Systems for Active Vibration Control, A. Preumont (Ed.), NATO Science Series book series, 85, 2002.
(Georges, 1995) D. Georges. The use of observability and controllability Gramians or functions for optimal sensor and actuator location in finite-dimensional systems. 34th IEEE Conference on Decision and Control, New Orleans, LA, USA, 3319-3324, 1995.
(Kim, 2003) C. Kim, N. Perkins, C. Lee, Parametric resonance of plates in a sheet metal coating process, Journal of sound and vibration, 2003.
(Li, 2012) J. Li, Y. Yan, X. Guo, Y. Wang, Research on Vibration Control Method of Steel Strip for a Continuous Hot-dip Galvanizing Line, ISIJ International, 2012.\bibitem[Manohar, 2018]{Manohar18} K. Manohar, J.N. Kutz. Optimal Sensor and Actuator Placement using Balanced Model Reduction., 2018.
(Marx, 2004) B. Marx, D. Koenig, G. Georges. Optimal sensor and actuator location for descriptor systems using generalized Gramians and balanced realizations. American Control Conference, Boston, Massachusetts, 2004.
(Starek, 2010) L. Starek, D. Starek, P. Solek, A. Starekova. Suppression of vibration with optimal actuators and sensors placement. Archives of Control Sciences, 20 (1), 2010.
(Van de Wal, 2001) M. Van de Wal, B. De Jager. A review of methods for input/output selection. Automatica, 37(4) :487-510, 2001.
(Zhang, 2018) X.Y. Zhang, R.X. Wang, S.Q. Zhang, Z.X. Wang, X.S. Qin, R. Schmidt. Generalized-Disturbance Rejection Control for Vibration Suppression of Piezoelectric Laminated Flexible Structures, Shock and Vibration, 2018.
sensor and actuator location, active noise control, galvanizing proccess
Control Identification Diagnosis