Industrial applications of the Kalman filter:a review

International audienc

On-line state and parameter estimation in nonlinear systems

On-line, simultaneous state and parameters estimation in deterministic, nonlinear dynamic systems of known structure is the problem considered. Available methods are few and fall short of user needs in that they are difficult to apply, their applicability is restricted to limited classes of systems, and for some, conditions guaranteeing their convergence don\u27t exist. The new methods developed herein are placed into two categories: those that involve the use of Riccati equations, and those that do not. Two of the new methods do not use Riccati equations, and each is considered to be a different extension of Friedland\u27 s parameter observer for nonlinear systems with full state availability to the case of partial state availability. One is essentially a reduced-order variant of a state and parameter estimator developed by Raghavan. The other is developed by the direct extension of Friedland\u27 s parameter observer to the case of partial state availability. Both are shown to be globally asymptotically stable for nonlinear systems affine in the unknown parameters and involving nonlinearities that depend on known quantities, a class restriction also true of existing state and parameter estimation methods. The two new methods offer, however, the advantages of improved computational efficiency and the potential for superior transient performance, which is demonstrated in a simulation example. Of the new methods that do involve a Riccati equation, there are three. The first is the separate-bias form of the reduced-order Kalman filter. The scope of this filter is somewhat broader than the others developed herein in that it is an optimal filter for linear, stochastic systems involving noise-free observations. To apply this filter to the joint state and parameter estimation problem, one interprets the unknown parameters as constant biases. For the system class defined above, the method is globally asymptotically stable. The second Riccati equation based method is derived by the application of an existing method, the State Dependent Algebraic Riccati Equation (SDARE) filtering method, to the problem of state and parameter estimation. It is shown to work well in several nonlinear examples involving a few unknown parameters; however, as the number of parameters increases, the method\u27s applicability is diminished due to an apparent loss of observability within the filter which hinders the generation of filter gains. The third is a new filtering method which uses a State Dependent Differential Riccati Equation (SDDRE) for the generation of filter gains, and through its use, avoids the “observability” shortcomings of the SDARE method. This filter is similar to the Extended Kalman Filter (EKF), and is compared to the EKF with regard to stability through a Lyapunov analysis, and with regard to performance in a 4th order stepper motor simulation involving 5 unknown parameters. For the very broad class of systems that are bilinear in the state and unknown parameters, and potentially involving products of unmeasured states and unknown parameters, the EKF is shown to possess a semi-global region of asymptotic stability, given the assumption of observability and controllability along estimated trajectories. The stability of the new SDDRE filter is discussed

Advanced Computational-Effective Control and Observation Schemes for Constrained Nonlinear Systems

Constraints are one of the most common challenges that must be faced in control systems design. The sources of constraints in engineering applications are several, ranging from actuator saturations to safety restrictions, from imposed operating conditions to trajectory limitations. Their presence cannot be avoided, and their importance grows even more in high performance or hazardous applications. As a consequence, a common strategy to mitigate their negative effect is to oversize the components. This conservative choice could be largely avoided if the controller was designed taking all limitations into account. Similarly, neglecting the constraints in system estimation often leads to suboptimal solutions, which in turn may negatively affect the control effectiveness. Therefore, with the idea of taking a step further towards reliable and sustainable engineering solutions, based on more conscious use of the plants' dynamics, we decide to address in this thesis two fundamental challenges related to constrained control and observation. In the first part of this work, we consider the control of uncertain nonlinear systems with input and state constraints, for which a general approach remains elusive. In this context, we propose a novel closed-form solution based on Explicit Reference Governors and Barrier Lyapunov Functions. Notably, it is shown that adaptive strategies can be embedded in the constrained controller design, thus handling parametric uncertainties that often hinder the resulting performance of constraint-aware techniques. The second part of the thesis deals with the global observation of dynamical systems subject to topological constraints, such as those evolving on Lie groups or homogeneous spaces. Here, general observability analysis tools are overviewed, and the problem of sensorless control of permanent magnets electrical machines is presented as a case of study. Through simulation and experimental results, we demonstrate that the proposed formalism leads to high control performance and simple implementation in embedded digital controllers

Algorithmes et architectures pour la commande et le diagnostic de systèmes critiques de vol

Flight-Critical Systems such as Electromechanical Actuators driven by Engine Control Units (ECU) or Flight Control Units (FCU) are designed and developed regarding drastic safety requirements. In this study, an actuator control and monitoring ECU architecture based on analytic redundancy is proposed. In case of fault occurrences, material redundancies in avionic equipment allow certaincritical systems to reconfigure or to switch into a safe mode. However, material redundancies increase aircraft equipment size, weight and power (SWaP). Monitoring based on dynamical models is an interesting way to further enhance safetyand availability without increasing the number of redundant items. Model-base dfault detection and isolation (FDI) methods [58, 26, 47] such as observers and parity space are recalled in this study. The properties of differential flatness for nonlinear systems [80, 41, 73] and endogenous feedback linearisation are used with nonlinear diagnosis models. Linear and nonlinear observers are then compared with an application on hybrid stepper motor (HSM). A testing bench was specially designed to observe in real-time the behaviour of the diagnosis models when faults occur on the stator windings of a HSM.Les systèmes critiques de vol tels que les actionneurs électromécaniques ainsi que les calculateurs de commande moteur (ECU) et de vol (FCU),sont conçus en tenant compte des contraintes aéronautiques sévères de sureté defonctionnement. Dans le cadre de cette étude, une architecture calculateur pourla commande et la surveillance d’actionneurs moteur et de surfaces de vol est proposée et à fait l’objet d’un brevet [13]. Pour garantir ces mesure de sureté, les ECU et FCU présentent des redondances matérielles multiples, mais engendrent une augmentation de l’encombrement, du poids et de l’énergie consommée. Pour ces raisons, les redondances à base de modèles dynamiques, présentent un atout majeur pour les calculateurs car elles permettent dans certains cas de maintenir les exigences d’intégrité et de disponibilité tout en réduisant le nombre de capteurs ou d’actionneurs. Un rappel sur les méthodes de diagnostic par générateurs de résidus et estimateurs d’états [58, 26, 47] est effectué dans cette étude. Les propriétés de platitude différentielle et la linéarisation par difféomorphisme et bouclage endogène [80, 41, 73] permettent d’utiliser des modèles linéaires équivalents avec les générateurs de résidus. Un banc d’essai a été conçu afin de valider les performances des algorithmes de diagnostic

Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress