Generation of a reduced-order LPV/LFT model from a set of large-scale MIMO LTI flexible aircraft models
Charles Poussot-Vassal and Clément Roos
Control Engineering Practice, 20(9), p. 919-930, 2012
Abstract: In the civilian aviation industry, the aeroelastic behavior of an aircraft is often modeled at frozen flight and mass configurations using high fidelity numerical tools. Unfortunately, the resulting large-scale models cannot be handled in such form by modern analysis and control techniques, which generally require the considered models to be written as low-order Linear Fractional Representations (LFR). In this context, a methodology is described to derive a reduced-order Linear Parameter Varying (LPV) model from a reference set of large-scale Multiple Input Multiple Output (MIMO) Linear Time Invariant (LTI) models describing a given system at frozen configurations. The proposed approach is in two steps. The reference models are first reduced using recent advances in Krylov methods, leading to a set of low-order state-space representations with consistent state vectors. An LPV model is then obtained by polynomial approximation and converted into an LFR of reasonable size. A special effort is made to avoid data overfitting by using as simple as possible approximation formulas. The method is applied to a long-range commercial aircraft model developed in an industrial context: a set of large-scale flexible models linearized at different mass configurations is converted into a single low-order LPV model. More generally, any kind of purely numerical models for which the analytical structure is unknown can be considered.
Linear parameter varying analysis of switched controllers for attitude control systems
Jean-Marc Biannic, Christelle Pittet and Clément Roos
AIAA Journal of Guidance, Control and Dynamics, 34(5), p. 1561-1566, 2011
Abstract: This paper is devoted to the stability analysis of satellite attitude control loops involving switching controllers which have been designed so as to minimize the reaction wheels efforts during the mission mode. The central idea of the paper consists first in showing that the switching-based nonlinear control laws can be efficiently approximated by (quasi) Linear Parameter Varying (LPV) controllers which then enables to redraw the closed-loop plant in an LPV standard form. A new stability analysis algorithm, based on the optimization of parameter-dependent Lyapunov functions is then proposed and successfully applied to prove stability.
On-ground aircraft control design using a parameter-varying anti-windup approach
Clément Roos, Jean-Marc Biannic, Sophie Tarbouriech, Christophe Prieur and Matthieu Jeanneau
Aerospace Science and Technology, 14(7), p. 459-471, 2010
Abstract: As an original alternative to dynamic inversion techniques, a non-standard anti-windup control strategy is developed in this paper in order to improve the on-ground control system of a civilian aircraft. Using a linear fractional representation (LFR) of the aircraft in combination with an original approximation of the nonlinear ground forces by saturation-type nonlinearities, the proposed design method delivers low-order and robust controllers, which are automatically adapted to the runway state and to the aircraft longitudinal velocity. The efficiency of the design scheme is assessed by several nonlinear simulations.
A practical approach to dynamical anti-windup synthesis
Clément Roos
Journal Européen des Systèmes Automatisés, 44(7), p. 853-879, 2010
Abstract: A complete methodology is proposed in this paper to design a fixed-order anti-windup controller. A convex formulation is notably obtained in the full-order case. Convexity is lost in the general case but can be recovered as soon as the poles of the anti-windup controller are fixed. In this context, an algorithm is introduced, which allows to determine a set of relevant poles and to synthesize a reduced-order controller. A strategy is then elaborated to constrain the controller poles, so as to avoid slow dynamics which often lead to poor time-domain performance. The proposed algorithms are finally applied to a fighter aircraft model and prove conclusive. Indeed, the resulting anti-windup controllers ensure stability for large amplitude input signals, while minimizing the loss of performance due to the saturations.
A convex characterization of dynamically-constrained anti-windup controllers
Clément Roos and Jean-Marc Biannic
Automatica, 44(9), p. 2449-2452, 2008
Abstract: Based on a recent description of deadzone nonlinearities via local sector conditions, a new LMI characterization is proposed to compute full-order continuous-time anti-windup controllers with pole constraints. More precisely, an upper bound is introduced on the real part of the controller poles to avoid slow dynamics, which often leads to poor time-domain performance. As is demonstrated in a short applicative part, the introduction of such a bound allows to efficiently handle the trade-off between stability domain enlargement and time-domain response relevance.
Robust feedforward design in the presence of LTI/LTV uncertainties
Gilles Ferreres and Clément Roos
International Journal of Robust and Nonlinear Control, 17(14), p. 1278-1293, 2007
Abstract: A practical method is proposed for the convex design of robust feedforward controllers which ensure Hinf / L2 performance in the face of LTI and arbitrarily time-varying model uncertainties. A technique that computes the global minimum of this difficult infinite dimensional optimization problem is proposed, as well as a suboptimal but computationally less involving algorithm. Convergence is proved. An efficient way to analyze the robustness properties of a closed loop with or without feedforward controller is obtained as a subproblem. A missile example finally illustrates the efficiency of the scheme: a robust feedforward controller is designed either on the continuum of linearized time invariant models (corresponding to trim points) or on a quasi-LPV model representing the non-linear one.
Aircraft load alleviation during maneuvers using optimal control surface combinations
Sebastian Gaulocher, Clément Roos and Christelle Cumer
AIAA Journal of Guidance, Control and Dynamics, 30(2), p. 591-600, 2007
Abstract: Control laws in aeronautics are designed to ensure, above all, good handling qualities. However, during extreme maneuvers, which have to be taken into account for aircraft certification, a number of critical structural load limits cannot be guaranteed by this baseline controller. In order to avoid some modifications of the control law, a solution consists of judiciously exploiting the redundancy of the control surfaces. The aim of this paper is first to find an optimal strategy of the control surface use, which leaves the initial flight behavior unmodified but alleviates a structural load during a selected maneuver. Model predictive control theory solves this off-line control allocation problem under actuator saturation constraints. In addition, an identification procedure is proposed to synthesize a new mixing unit that can reproduce this optimal strategy. This methodology is applied to a flexible transport aircraft in order to alleviate the bending moment at the external wing during a sudden and strong roll maneuver.
Design and robustness analysis of fighter aircraft flight control laws
Jean-Marc Biannic, Clément Roos and Andreas Knauf
European Journal of Control, 12(1), p. 71-85, 2006
Abstract: In this paper, a complete methodology is detailed for the design and analysis of robust gain-scheduled fighter aircraft flight control laws. The proposed approach consists of three steps. A set of locally robust controllers is first generated using LMI optimization. The global controller is then obtained by a standard linear interpolation and transformed into LFT format. Finally, a validation step is achieved using both LTI and LTV analysis techniques, for which specific methods and tools have been developed.
Control-oriented aeroelastic BizJet low-order LFT modeling
Charles Poussot-Vassal, Clément Roos, Pierre Vuillemin, Olivier Cantinaud and Jean-Patrick Lacoste
Control-oriented modelling and identification: theory and practice, chapter 11, p. 241-268
Control Engineering Series, vol. 80, IET, 2015
Abstract: To accelerate aircraft conception and reduce development costs, computer-aided preliminary design is widely used (e.g. for controller design, performance analysis...). The computer-based approach has been rendered possible thanks to advances in modeling tools, allowing to faithfully reproduce complex physical phenomena with limited - expensive - experimental tests. Due to these economical considerations and technological advances, aeronautical control engineers can rely and work with a considerable amount of very accurate models. The counterpart of this accuracy is the resulting numerical complexity which leads (i) to a prohibitively large number of variables to manage, rendering the control design task very complex (i.e. numerical tools become nearly inefficient), and (ii) to models with an accuracy level too high for the control synthesis purpose (indeed modern control techniques usually require low-order representations). In this chapter, based on multiple initial large-scale linear time invariant models, the problem of constructing a suitable low-order parameter dependent model, appropriate to the control design purpose, is addressed. The proposed solution is illustrated on a complex generic Business Jet aeroelastic control-design problem.
Generation of LFRs for a flexible aircraft model
Clément Roos
Optimization based clearance of flight control laws, chapter 4, p. 59-77
Lecture Notes in Control and Information Sciences, vol. 416, Springer-Verlag, 2012
Abstract: The flexible aircraft described in Chapter 2 is modelled as a collection of linear time-invariant models which correspond to different combinations of aircraft payload configurations and flight conditions. In this chapter we propose a methodology to convert such a set of models into a linear fractional representation (LFR), to be used in several robustness analysis methods. The modelling challenge consists in building a unique LFR starting from a set of large order state-space models, having different sizes and different
physical meanings of state vectors. The resulting LFR has a moderate size and satisfactorily approximates the aircraft behaviour, by providing almost exact match of the system eigenvalues and frequency responses. This model serves as basis of the clearance techniques relying on mu-analysis, Lyapunov-based analysis and IQC-based analysis.
Generation of LFRs for a nonlinear controller and closed-loop aircraft models
Carsten Döll, Fabien Lescher and Clément Roos
Optimization based clearance of flight control laws, chapter 5, p. 79-109
Lecture Notes in Control and Information Sciences, vol. 416, Springer-Verlag, 2012
Abstract: In this chapter the block-diagram based generation approach of low order Linear Fractional Representations (LFRs) is applied to the nonlinear controller described in Chapter 2. For this purpose, all individual parameter dependent blocks as well as all nonlinear blocks like saturations or rate limiters are replaced by their LFR counterparts in the block-diagram structure of the controller. Look-up tables are approximated by rational expressions before their replacements. The overall controller LFR is extracted from the resulting block-diagram by a standard linearization technique. The resulting controller LFR is interconnected with the LFRs of the actuators, sensors and of the nonlinear rigid aircraft or linear flexible aircraft generated in Chapters 3 and 4 to obtain the LFRs of the corresponding closed-loop systems. These closed-loop LFRs are used for stability and performance analysis in Chapters 12-16.
Enhanced mu-analysis techniques for clearance
Jean-Marc Biannic and Clément Roos
Optimization based clearance of flight control laws, chapter 7, p. 131-147
Lecture Notes in Control and Information Sciences, vol. 416, Springer-Verlag, 2012
Abstract: A practical method based on mu-analysis is proposed in this chapter to compute a stability robustness margin for high-order LTI plants with real parametric uncertainties. In contrast to grid-based approaches, the validity of this margin is guaranteed on a continuous frequency interval, without any risk of missing critical frequency values. The algorithm to compute the stability margin underlies a recursive procedure to determine a guaranteed stability domain for possibly uncertain parameter dependent plants. Extensions to non-standard robustness problems as well as algorithmic variants to handle the trade-off between conservatism and computational time are also discussed. The application of the proposed method to the clearance of flight control laws is finally addressed for two stability related clearance criteria.
Application of mu-analysis techniques to clearance
Clément Roos and Jean-Marc Biannic
Optimization based clearance of flight control laws, chapter 12, p. 223-234
Lecture Notes in Control and Information Sciences, vol. 416, Springer-Verlag, 2012
Abstract: An efficient algorithm based on an enhanced mu-analysis technique has been proposed in Chapter 7 to compute a guaranteed robust stability domain for a linear parameter dependent plant. This algorithm is applied in this chapter to the clearance of flight control laws, more precisely, for the robustness analysis of the eigenvalue and the stability margin criteria. Numerous performed tests revealed that the proposed methodology allows to handle very complex flexible plant models, that cannot be fully handled using traditional methods as grid-based worst-case search or Monte-Carlo simulation. The low conservatism of the method and the reasonably low computational effort allow its application to highly demanding problems. Thus, the enhanced mu-analysis technique represents an attractive alternative to traditional approaches to analyse stability, loads and comfort related clearance criteria.
On-ground aircraft control design using an LPV anti-windup approach
Clément Roos, Jean-Marc Biannic, Sophie Tarbouriech and Christophe Prieur
Nonlinear analysis and synthesis techniques for aircraft control, chapter 7, p. 117-145
Lecture Notes in Control and Information Sciences, vol. 365, Springer-Verlag, 2007
Abstract: Based on the LFT model of the on-ground aircraft, which was developed in Chapter 6, an anti-windup control technique is proposed to improve lateral control laws. The original idea of this work consists in taking advantage of a simplified representation of the nonlinear lateral ground forces, which are approximated by saturation-type nonlinearities. The anti-windup compensator is then implemented on the full nonlinear aircraft model using an on-line estimator of the ground forces. Several simulations demonstrate the efficiency of the resulting adaptive controller.
Robustness analysis versus mixed LTI/LTV uncertainties for on-ground aircraft
Clément Roos and Jean-Marc Biannic
Nonlinear analysis and synthesis techniques for aircraft control, chapter 9, p. 175-194
Lecture Notes in Control and Information Sciences, vol. 365, Springer-Verlag, 2007
Abstract: The robustness properties of the adaptive anti-windup controller designed in Chapter 7 are evaluated, and a special emphasis is laid on the high uncertainty level affecting the nonlinear ground forces. It is first shown how to convert the initial nonlinear problem into a fairly standard robustness analysis problem versus mixed time-invariant/time-varying uncertainties. An original approach, based on the notion of semi-positive realness, is then introduced to solve the problem. The application of this method to the on-ground aircraft finally reveals the good robustness properties of the lateral controller despite uncertainties and saturation effects. It also gives some relevant information that enables to further improve the design.
Improved mu upper bound computation using the mu-sensitivities
Jérémy Lesprier, Clément Roos and Jean-Marc Biannic
Proceedings of the 8th IFAC Symposium on Robust Control Design
Bratislava, Slovak Republic, July 8-11, 2015
Abstract: Three new methods are proposed in this paper to reduce the gap between the structured singular value mu and its upper bounds with a reasonable computation time. The first one is based on the classical (D,G)-scalings formulation, the second one on a more general multiplier based approach and the third one on an advanced branch-and-bound algorithm. They all use the mu-sensitivities to evaluate which uncertainties are worth considering for either partly solving some costly LMIs or intelligently cutting the uncertainty domain. They are successfully assessed on a list of realistic benchmarks.
Flare control law design via multi-channel Hinf synthesis: illustration on a freely available nonlinear aircraft benchmark
Jean-Marc Biannic and Clément Roos
Proceedings of the American Control Conference, p. xxx-xxx
Chicago, Illinois, July 1-3, 2015
Abstract: Recent advances in the resolution of multi-channel Hinf control problems via nonsmooth optimization are exploited in this paper to provide a novel design methodology in the challenging context of flare control systems optimization. More precisely, the objective is to control the vertical speed of an aircraft before touchdown while minimizing the impact of airspeed variations, windshear and ground effects. A realistic and rather complete aircraft benchmark (freely available from the SMAC project) is also described in the paper.
Nonlinear structured Hinfinity controllers for parameter-dependent uncertain systems with application to aircraft landing
Jérémy Lesprier, Jean-Marc Biannic and Clément Roos
Proceedings of the IEEE Multiconference on Systems and Control, p. 433-438
Antibes, France, October 8-10, 2014
Abstract: A new design methodology inspired by dynamic inversion techniques is proposed in this paper. It combines partially linearizing inner-loops with structured and robust outer-loops, which are designed by a non-smooth multi-model Hinfinity optimization approach. The proposed methodology also includes a robustness analysis scheme providing worst-case configurations, which are then used to enrich the bank of design models and thus iteratively improve the robustness properties of the designed outer-loops. Our approach is successfully tested on a realistic nonlinear aircraft control problem subject to large parametric variations and uncertainties.
Polynomial and rational approximation with the APRICOT Library of the SMAC Toolbox
Clément Roos, Georges Hardier and Jean-Marc Biannic
Proceedings of the IEEE Multiconference on Systems and Control, p. 1473-1478
Antibes, France, October 8-10, 2014
Abstract: The APRICOT Library of the new SMAC Toolbox for Matlab implements a set of optimization tools to convert numerical data into simple yet accurate polynomial or rational expressions. Approximants are obtained, for which the number of terms in the numerator and denominator is as low as possible. The motivations for generating sparse expressions are twofold. First, it is a natural way to prevent data overfitting and to ensure a smooth behavior between the points used for approximation. Then, it allows simple Linear Fractional Representations to be obtained, which are tractable for analysis and design purposes. This paper surveys the main existing approximation techniques, which are all implemented in the APRICOT Library. It also applies them to model the drag coefficient of a generic fighter aircraft benchmark.
A comparison of techniques to get sparse rational approximations for linear fractional representations
Clément Roos, Georges Hardier and Carsten Döll
Proceedings of the 29th Congress of the International Council of the Aeronautical Sciences
Saint Petersburg, Russia, September 7-12, 2014
Abstract: The objective of this paper is to stress that the size of a Linear Fractional Representation (LFR) significantly depends on the way tabulated or irrational data are approximated during the prior modeling process. It is notably shown that rational approximants can result in much smaller LFR than polynomial ones. Accordingly, 2 new methods are proposed to generate sparse rational models, which avoid data overfitting and lead to simple yet accurate LFR. The first one builds a parsimonious modeling based on surrogate models and a new powerful global optimization method, and then translates the result into a fractional form. The second one looks for a rational approximant in a single step thanks to a symbolic regression technique, and relies on genetic programming to select sparse monomials. This work takes place in a more general project led by ONERA/DCSD and aimed at developing a Systems Modeling, Analysis and Control Toolbox (SMAC) for Matlab.
A detailed comparative analysis of mu lower bound algorithms
Andrea Fabrizi, Clément Roos and Jean-Marc Biannic
Proceedings of the 13th European Control Conference, p. 220-226
Strasbourg, France, June 25-27, 2014
Abstract: This paper presents a detailed comparison of the most significant methods developed to compute lower bounds on the structured singular value. The objective is to characterize the behavior of these robustness analysis tools on the basis of a common framework constituted by a wide set of various real-world applications.
Creating sparse rational approximations for Linear Fractional Representations using surrogate modeling
Georges Hardier, Clément Roos and Cédric Seren
Proceedings of the 3rd IFAC International Conference on Intelligent Control and Automation Science, p. 238-243
Chengdu, China, September 2-4, 2013
Abstract: The objective of this paper is to stress that the size of a Linear Fractional Representation (LFR) significantly depends on the way tabulated or irrational data are approximated during the modeling process. It is notably shown that rational approximants can result in much smaller LFR than polynomial ones. In this context, a new method is introduced to generate sparse rational models, which avoid data overfitting and lead to simple yet accurate LFR. This method builds a parsimonious model based on neural networks, and then translates the result into a fractional form. A stepwise selection algorithm is used, combining the benefits of forward orthogonal least squares to estimate the regression parameters with a new powerful global optimization to determine the best location of the regressors. The proposed method is evaluated on an aeronautical example and successfully compared to more classical approaches.
Creating sparse rational approximations for Linear Fractional Representations using genetic programming
Georges Hardier, Clément Roos and Cédric Seren
Proceedings of the 3rd IFAC International Conference on Intelligent Control and Automation Science, p. 232-237
Chengdu, China, September 2-4, 2013
Abstract: The objective of this paper is to stress that the size of a Linear Fractional Representation (LFR) significantly depends on the way tabulated or irrational data are approximated during the modeling process. It is notably shown that rational approximants can result in much smaller LFR than polynomial ones. In this context, a new method is introduced to generate sparse rational models, which avoid data overfitting and lead to simple yet accurate LFR, thanks to a symbolic regression technique. Genetic Programming is implemented to select sparse monomials and coupled with a nonlinear iterative procedure to estimate the coefficients of the surrogate model. Furthermore, a mu-analysis based proof is given to check the nonsingularity of the resulting rational functions. The proposed method is evaluated on an aeronautical example and successfully compared to more classical approaches.
Swarm intelligence and system identification: a hybrid discrete jumping frogs algorithm for optimal input design
Cédric Seren, Georges Hardier and Clément Roos
Proceedings of the 3rd IFAC International Conference on Intelligent Control and Automation Science, p. 218-223
Chengdu, China, September 2-4, 2013
Abstract: The representativeness of the flight dynamics model has become a major concern in aviation industry since numerical simulation is now inevitable in aeronautics and widely used for every new aircraft program. Consequently, the requirements on its accuracy and reliability increase constantly. To build a flight dynamics model of acceptable quality, flight tests are designed and flown to adjust some relevant coefficients of the preflight aerodynamic model to the real A/C. But, the constraint of building more accurate models from shorter flight tests campaigns leads to revisit this identification process by designing optimal inputs since the aerodynamic parameter estimation is dependent on the quality of the inputs sent to the aircraft. Optimal Input Design (OID) for dynamical systems corresponds to complex and difficult optimization problems characterized by an infinite-dimensional search space combined with the presence of multiple local extrema. Even if signals can be parametrized using function basis, so that problem becomes of finite dimension, OID dedicated to flight dynamics identification still remains hard to solve. Indeed, flight tests protocol optimization must be tackled in its entirety (single/multiple input/s for one or several flight tests) which means that problem dimension can be high. Moreover, decision variables correspond pratically to real-valued discrete parameters due to the tabulated aerodynamic data structure of the model. This article describes some recent advances in the field of OID for flight dynamics identification through an original and innovative bio-inspired evolutionary algorithm based on the theoretical principles of the Jumping Frogs Optimization (JFO) technique.
Systems Modeling, Analysis and Control (SMAC) Toolbox: an insight into the robustness analysis library
Clément Roos
Proceedings of the IEEE Multiconference on Systems and Control, p. 176-181
Hyderabad, India, August 28-30, 2013
Abstract: The analysis library of the new SMAC Toolbox for Matlab implements a set of mu-analysis based tools to evaluate the robustness properties of linear time-invariant systems affected by time-invariant uncertainties. These tools allow to compute both lower and upper bounds on the (skewed) robust stability margin, the worst-case Hinf performance level, as well as the worst-case gain, phase, modulus and time-delay margins. The key idea is to solve the problem on just a coarse frequency grid and to perform a fast validation on the whole frequency range, which results in guaranteed but conservative bounds on the aforementioned quantities. Some heuristics are then applied to determine a set of worst-case parametric configurations leading to over-optimistic bounds. A branch and bound scheme is finally implemented, so as to tighten these bounds with the desired accuracy, while still guaranteeing a reasonable computational complexity.
Stability and performance analysis in the presence of LTV perturbations with bounded rates of variation: a Lyapunov based approach
Clément Roos, Laure Lafourcade and Jean-Marc Biannic
Proceedings of the 51st IEEE Conference on Decision and Control, p. 6659-6664
Maui, Hawaii, December 10-13, 2012
Abstract: Evaluating the stability and the performance properties of a system in the presence of time-varying parameters is often computationally demanding. A practical method is proposed in this paper to alleviate this computational cost. The stability conditions are first formulated as an LMI feasibility problem involving the search of a suitable parameter-dependent Lyapunov function. This problem is then solved for a finite number of parametric configurations and the validity of the resulting Lyapunov function is checked on the whole parametric domain using a mu-analysis based test. In case the validation fails, a worst-case configuration is determined using particle swarm optimization and the whole process is repeated using an augmented set of parametric configurations. The resulting iterative algorithm is successfully applied to a realistic fighter aircraft model.
Analyse de stabilité en présence d'incertitudes variant dans le temps par une approche de type Lyapunov
Laure Lafourcade, Clément Roos and Jean-Marc Biannic
Proceedings of the 7th Conférence Internationale Francophone d'Automatique, p. 412-417
Grenoble, France, July 4-6, 2012
Abstract: Lorsque les dimensions des systèmes augmentent, les techniques d'analyse de stabilité présentent des difficultés dès lors que l'on considère des incertitudes variant dans le temps. Dans cet article, une approche itérative fondée sur l'optimisation de fonctions de Lyapunov dépendant de paramètres est proposée. Les conditions de stabilité sont d'abord exprimées sous forme d'inégalités matricielles linéaires (LMI), et le problème de faisabilité qui en résulte est résolu sur les points d'un maillage du domaine paramétrique. La validité de la fonction de Lyapunov est ensuite vérifiée a posteriori entre les points du maillage grâce à un test de valeur singulière structurée. En cas d'échec, des configurations pire-cas obtenues grâce à un algorithme d'optimisation par essaims de particules sont ajoutées au maillage. Cette méthode est appliquée avec succès à un modèle réaliste d'avion de chasse.
Robust stability of time-delay systems with structured uncertainties: a mu-analysis based algorithm
Fabien Lescher and Clément Roos
Proceedings of the 50th IEEE Conference on Decision and Control, p. 4955-4960
Orlando, Florida, December 12-15, 2011
Abstract: This paper considers robust stability of uncertain time-delay systems affected by structured uncertainties and multiple constant delays. The objective is to compute the maximum value tau the delays can reach without destabilizing the system over the uncertainty domain. A suitable modeling of the phase variations induced by the delays along the frequency range first allows to obtain an equivalent mu-analysis problem, where the bounds on some uncertain parameters depend on frequency. An algorithm is then proposed to solve this specific problem and to compute upper and lower bounds on tau. It is finally shown that the gap between both bounds can be reduced to any positive value in case of purely real uncertainties. The computational efficiency of the method and its ability to analyze large-scale systems are demonstrated on a numerical example, which aims at computing the MIMO time-delay margin of a high-fidelity parameter-dependent flexible aircraft model.
A set of mu-analysis based tools to evaluate the robustness properties of high-dimensional uncertain systems
Clément Roos, Fabien Lescher, Jean-Marc Biannic, Carsten Döll and Gilles Ferreres
Proceedings of the IEEE Multiconference on Systems and Control, p. 644-649
Denver, Colorado, September 28-30, 2011
Abstract: This paper reviews a set of mu-analysis based tools developed by the authors during the last decade to evaluate the robustness properties of high-dimensional linear plants subject to numerous time-invariant uncertainties. These tools allow to compute both upper and lower bounds on the robust stability margin, the worst-case Hinf performance level, as well as the traditional gain, phase, modulus and time-delay margins. The key idea is to solve the problem on just a coarse frequency grid and to perform a fast validation on the whole frequency range, which results in guaranteed but conservative bounds on the aforementioned quantities. Some heuristics are then applied to determine a set of worst-case parametric configurations leading to over-optimistic bounds. A branch and bound scheme is finally implemented, so as to tighten these bounds with the desired accuracy, while still guaranteeing a reasonable computational complexity. The proposed algorithms are successfully assessed on a challenging real-world application.
Flexible aircraft reduced-order LPV model generation from a set of large-scale LTI models
Charles Poussot-Vassal and Clément Roos
Proceedings of the American Control Conference, p. 745-750
San Francisco, California, June 29-July 1, 2011
Abstract: In the civilian aeronautical industry, flexible aircraft models are often built and validated at frozen flight and mass configurations. Unfortunately, these medium(large)-scale models derived from high fidelity numerical tools are generally not well adapted for simulation, control and analysis. In this paper, a methodology to derive a reduced-order Linear Parameter Varying (LPV) model from a set of medium(large)-scale Linear Time Invariant (LTI) models describing a given system at frozen configurations is described. The proposed methodology is in three steps: (i) first, local model approximation is applied using recent advances in SVD-Krylov methods, (ii) then, an appropriate base change is applied to allow interpolation, (iii) and finally, an LPV model is derived and converted into a Linear Fractional Representation (LFR) of suitable size for analysis and control purposes. Results are thoroughly assessed on a set of industrial aeroelastic aircraft models.
A practical approach to worst-case Hinf performance computation
Clément Roos
Proceedings of the IEEE Multiconference on Systems and Control, p. 380-385
Yokohama, Japan, September 8-10, 2010
Abstract: A practical method is proposed in this paper to compute a lower bound on the worst-case Hinf performance for a linear time-invariant system affected by parametric uncertainties. The problem is first solved for a few frequencies by combining a gradient computation with a hamiltonian-like method. A series of linear programming problems are then solved using the previous results as an initialization, and worst-case values of both the frequency and the uncertainties are determined. The application of the resulting algorithm to a challenging industrial problem proves conclusive and shows that high-order systems with highly repeated uncertainties can be handled: the impact of wind on passengers' comfort on board a flexible transport aircraft is indeed evaluated, and worst-case values of both the flight and the mass parameters are obtained.
LPV analysis of switched controllers in satellite attitude control systems
Jean-Marc Biannic, Christelle Pittet, Laure Lafourcade and Clément Roos
Proceedings of the AIAA Guidance, Navigation and Control Conference
Toronto, Canada, August 2-5, 2010
Abstract: This paper is devoted to the stability analysis of satellite attitude control loops involving switching controllers which have been designed so as to minimize the reaction wheels efforts during the mission mode. The central idea of the paper consists first in showing that the switching-based nonlinear control laws can be efficiently approximated by a quasi-LPV controller which then enables to redraw the closed-loop plant in an LPV standard form. Next, a new stability analysis algorithm, based on parameter-dependent Lyapunov functions, is developed and successfully applied on a realisitic satellite benchmark.
Efficient computation of a guaranteed stability domain for a high-order parameter dependent plant
Clément Roos and Jean-Marc Biannic
Proceedings of the American Control Conference, p. 3895-3900
Baltimore, Maryland, June 30-July 2, 2010
Abstract: A practical method based on mu-analysis is proposed in this paper to compute a robustness margin for high-order LTI plants with highly repeated parametric uncertainties. This margin is guaranteed on a continuous frequency interval and there is no risk of missing a critical frequency. The resulting algorithm is then encompassed in a recursive procedure, which computes a guaranteed stability domain for possibly uncertain parameter dependent plants. Several extensions and variations to handle the trade-off between conservatism and computational time are also highlighted. The efficiency of the method is finally demonstrated on a challenging industrial problem: assessing the stability of a flexible passenger aircraft over its entire flight envelope and for all admissible mass configurations.
Generation of flexible aircraft LFT models for robustness analysis
Clément Roos
Proceedings of the 6th IFAC Symposium on Robust Control Design
Haifa, Israel, June 16-18, 2009
Abstract: In the aeronautical industry, the robustness properties of an aircraft are usually assessed using intensive and time-consuming simulations. Fortunately, several optimization techniques can be implemented and applied for clearance of flight control laws, in order to improve the efficiency and reliability of the certification process. Some of them, such as Lyapunov-based analysis and mu-analysis, require the considered models to be written as Linear Fractional Representations (LFR), which is unfortunately not the case of the aeroelastic models available in an industrial context. A whole methodology is thus proposed in this paper to convert a set of numerical flexible aircraft models into a suitable LFR which depends on the aircraft configuration and the flight conditions. This is a challenging issue, since the size of the initial models is very large and the state vector does not have the same physical meaning for the whole model set. Nevertheless, an LFR is obtained, which is representative of the aircraft behavior in the sense that its eigenvalues and frequency responses almost exactly match those of the initial flexible models. Moreover, its complexity proves compatible with the use of robustness analysis tools. Numerical results indeed show that the considered clearance problem is computationally tractable.
Introduction to AWAST: the Anti-Windup Analysis and Synthesis Toolbox
Jean-Marc Biannic and Clément Roos
Proceedings of the 9th IEEE International Symposium on Computer-Aided Control System Design, p. 589-594
San Antonio, Texas, September 3-5, 2008
Abstract: Anti-windup compensators are widely used in control systems in order to minimize the negative effects of actuators saturations on stability and performance. But despite recent theoretical advances in this field, the computation of such compensators is often realized by a trial-and-error simulation-based approach. An alternative method is proposed in this paper, which is essentially devoted to the presentation of a new Matlab toolbox. This freely-available software implements a collection of routines which are based on recent results in anti-windup analysis and synthesis techniques. Moreover, a user-friendly Simulink interface allows to fasten the definition of anti-windup design and simulation diagrams (see the tools page).
A practical method for fixed-order anti-windup design
Jean-Marc Biannic, Clément Roos and Sophie Tarbouriech
Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, p. 527-532
Pretoria, South Africa, August 22-24, 2007
Abstract: Using a recent description of deadzone-type nonlinearities via modified sector conditions, a new LMI characterization of full-order continuous-time anti-windup controllers is first proposed. The reduced-order case is then considered. Here, convexity is lost but can be recovered as soon as the poles of the anti-windup controller are fixed. Based on this result, a two-step design procedure is then implemented in the applicative part of the paper. By convex optimization, the first step consists of designing a full-order anti-windup controller. Then, in the second step, the poles of this full-order controller are analyzed and a selection is made. This selection is finally used to fix the poles of the reduced-order controller, which is easily computed as the solution of an LMI problem. The proposed methodology is evaluated on a real-world application, which reveals that the reduced controller - from which slow dynamics have been removed - even performs better than the full-order one.
Aircraft-on-ground lateral control by an adaptive LFT-based anti-windup approach
Clément Roos and Jean-Marc Biannic
Proceedings of the IEEE Conference on Control Applications, p. 2207-2212
Munich, Germany, October 4-6, 2006
Abstract: Using a simplified LFT model of an aircraft-on-ground, a robust anti-windup control technique is efficiently applied to improve lateral control laws. The original idea of this work consists in taking advantage of a simplified representation of the nonlinear lateral ground forces which are reduced to saturation-type nonlinearities.
Nonlinear simplified LFT modelling of an aircraft on ground
Jean-Marc Biannic, Andres Marcos, Matthieu Jeanneau and Clément Roos
Proceedings of the IEEE Conference on Control Applications, p. 2213-2218
Munich, Germany, October 4-6, 2006
Abstract: In this paper, a simplified nonlinear LFT model of an aircraft-on-ground is developed and compared to a full nonlinear model. The proposed simplifications are shown to be not so restrictive. The main contribution of the paper consists of an original approximation of the ground forces. Based on this approximation, which yet remains quite close to reality, some strong nonlinearities of the initial model are conveniently replaced by saturations and time-varying uncertainties. Thus, the proposed simplified model boils down to a reduced order LFT where the Delta block only contains time-varying or constant (but uncertain) parameters on the one hand, and saturation-type non-linearities on the other hand. Such a model is then very useful for applying modern analysis and synthesis techniques.
On robustness analysis versus mixed LTI/LTV uncertainties
Clément Roos and Jean-Marc Biannic
Proceedings of the 5th IFAC Symposium on Robust Control Design
Toulouse, France, July 5-7, 2006
Abstract: In this paper, the notion of semi-positive realness for complex-valued systems is defined and characterized through a generalized version of the positive real lemma. This result provides an efficient state-space method for computing robustness margins versus mixed LTI/LTV real/complex uncertainties, which cannot be easily addressed by more classical gridding-based techniques. The conservatism of this approach is shown to be very low on several examples.
A positivity approach to robust controllers analysis and synthesis versus mixed LTI/LTV uncertainties
Clément Roos and Jean-Marc Biannic
Proceedings of the American Control Conference, p. 3661-3666
Minneapolis, Minnesota, June 14-16, 2006
Abstract: The notion of semi-positive realness for complex-valued systems is first defined and characterized through a generalized version of the positive real lemma. This result is then exploited to compute robustness margins versus mixed LTI/LTV real/complex uncertainties. Extensions to fixed-order robust synthesis are also highlighted and a practical algorithm is proposed for the combined design of robust feedback and feedforward controllers. A fighter aircraft example finally illustrates the efficiency and the low conservatism of the scheme.
Efficient convex design of robust feedforward controllers
Gilles Ferreres and Clément Roos
Proceedings of the 44th IEEE Conference on Decision and Control, p. 6460-6465
Seville, Spain, December 12-15, 2005
Abstract: A practical method is proposed for the convex design of robust feedforward controllers, which ensure Hinf / L2 performance in the face of LTI and arbitrarily time-varying model uncertainties. A technique which computes the global minimum of this difficult infinite dimensional optimization problem is proposed, as well as a suboptimal but computationally less involving algorithm. A missile example illustrates the efficiency of the scheme: a robust feedforward controller is designed, either on the continuum of linearised time invariant models (corresponding to trim points), or on a quasi-LPV model representing the non-linear one.
