52 research outputs found
Design of a fractional control using performance contours. Application to an electromechanical system
The article proposes a frequency-based method to design a controller ensuring dynamic behavior of a closed-loop control: the first overshoot of the step response in the tracking mode or in the regulation mode, the damping ratio and the natural frequency of its dominant oscillatory mode. This method uses two contours called âperformance contoursâ and constructed on the Nichols diagram. The first contour is the common Nichols magnitude contour which can be considered as an iso-overshoot contour. The second contour, whose construction and analytic expression are given in this article, is a new contour defined on the Nichols diagram and parameterized by the damping ratio. The proposed method uses complex non-integer (or fractional) differentiation to compute a transfer function whose open-loop Nichols locus tangents both performance contours, thus ensuring stability margins (or stability degree). The method is applied to a DC motor whose speed is controlled
Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers
Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open-loop transfer function. However, these contours have been built using non band-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. It is also presented how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response. It is presented how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers
Input-output linearization and fractional robust control of a non-linear system
This article deals with the association of a linear robust controller and an input-output linearization feedback for the control of a perturbed and non-linear system. This technique is applied to the control of a hydraulic system whose actuator is non-linear and whose load is time-variant. The piston velocity of the actuator needs to be controlled and a pressure-difference inner-loop is used to improve the performance. To remove the effect of the non-linearity, an input-output linearization under
diffeomorphism and feedback is achieved. CRONE control, based on complex fractional differentiation, is applied to design a controller for piston-velocity loop even when parametric variations occu
Crone control of a nonlinear hydraulic actuator
The CRONE control (fractional robust control) of a hydraulic actuator whose dynamic model is nonlinear is presented. An input-output linearization under diffeomorphism and feedback is first achieved for the nominal plant. The relevance of this linearization when the parameters of the plant vary is then analyzed using the Volterra input-output representation in the frequency domain. CRONE control based on complex fractional differentiation is finally applied to control the velocity of the input-output linearized model when parametric variations occur
Study of two robust controls for an hydraulic actuator
Two robust control design methodologies are analyzed and compared in this article: the H-infinity control system design and the CRONE control system design. The aim of this article is to give practical considerations that will help a designer to choose between these two methodologies. The example of an electrohydraulic actuator is given in order to evaluate the implementation of each methodology and to compare the final performance
Fractional robust control of ligthly damped systems
The article proposes a method to design a robust controller ensuring the damping ratio of a closed-loop control. The method uses a contour para-meterized by the damping ratio in the Nichols plane and the complex non-integer (or fractional)differentiation to compute a transfer function whose open-loop Nichols locus tangents this contour, thus ensuring dynamic performance. The proposed method is applied to a flexible structure (a clamped-free beam with piezoelectric ceramics). The aims of the control loop are to decrease the vibrations and to ensure the damping ratio of the controlled system
Fractional robust control with iso-damping property
This article deals with the problem of the reduction of structural vibrations with isodamping property. The proposed methodology is based on:
- a contour defined in the Nichols plane and significant of the damping ratio of the closed-loop response
- a robust control method that uses fractional order integration. The methodology is applied to an aircraft wing model made with a beam and a tank whose different levels of fillings are considered as uncertainties
Robust Control System Design for Multivariable Plants with Lightly Damped Modes
International audienceA robust controller design is proposed for the active suspension system benchmark problem. The CRONE control system design used is extended to unstable multivariable plants with lightly damped modes and RHP zeros. Decoupling and stabilizing controller K, is achieved for the open-loop transfer matrix. Fractional order transfer functions are used to define all the components of the diagonal open-loop transfer matrix, ÎČ. In defining the fractional open-loop transfer function ÎČ 0i some elements of the plants, G0 and its inverse must be considered to achieve the stable controller. Optimisation provides the best fractional open-loop ÎČopt. Finally, frequency domain system identification is used to find controller K=G0-1 ÎČopt
DETC2011/MESA-47286 CRONE CONTROL-SYSTEM DESIGN TOOLBOX FOR THE CONTROL ENGINEERING COMMUNITY
ABSTRACT The CRONE CSD methodology proposes to design robust controllers by using fractional order operators. A Matlab toolbox has been developed based on this methodology and is freely available for the international scientific and industrial communities. This paper presents both the methodology and the toolbox. The design of two robust controllers for irrigation canals show how the toolbox can be used. INTRODUCTION The CRONE Toolbox, developed gradually since the ninetie
Extension de la commande CRONE multivariable aux systÚmes non carrés (application à un systÚme d'air de moteurs essence et diesel)
Les travaux prĂ©sentĂ©s dans ce manuscrit s inscrivent dans le cadre du dĂ©veloppement de la commande robuste de l Ă©quipe CRONE (Commande Robuste d Ordre Non Entier). Ils portent plus prĂ©cisement sur le dĂ©veloppement d une mĂ©thodologie de synthĂšse de la commande CRONE pour les systĂšmes multivariables avec une application au contrĂŽle des moteurs Ă combustion interne. AprĂšs un chapitre d introduction sur la commande robuste d ordre non entier dans le but de garantir une robustesse des performances dynamiques par rapport aux variations des paramĂštres du modĂšle du systĂšme, une reformulation des conditions de stabilitĂ© de la mĂ©thodologie CRONE des systĂšmes multivariables (MIMO) carrĂ©es existante est proposĂ©e. Un ensemble de thĂ©orĂšmes est aussi proposĂ© afin de pouvoir Ă©tendre la commande CRONE des systĂšmes MIMO carrĂ©s au cas plus gĂ©nĂ©ral des systĂšmes multivariables ayant des retards purs et un comportement oscillatoire avec des pĂŽles et des zĂ©ros qui ne sont pas nĂ©cessairement situĂ©s dans le domaine de stabilitĂ©. Le chapitre 3 de ce manuscrit est consacrĂ© d une part Ă la commande des systĂšmes MIMO non-carrĂ©s (nombre d entrĂ©es diffĂ©rent de celui des sorties), instables et Ă non-minimum de phase et d autre part a la simplification des diffĂ©rentes mĂ©thodologies de commande proposĂ©es dans ce manuscrit. Cette simplification est basĂ©e sur une analyse des effets de couplage du systĂšme et sur l hypotheses que dans certain cas des Ă©lĂ©ments de la matrice de transfert du systĂšme peuvent ĂȘtre considĂ©rĂ©s comme des incertitudes lors de l optimisation de la boucle ouverte nominale non entiere. Outre un ensemble de cas acadĂ©mique pris dans la littĂ©rature, la validation de ces travaux est rĂ©alisĂ©e Ă travers la commande du systĂšme d'air de deux moteurs Ă combustion interne : un moteur Ă essence avec une loi de commande CRONE MIMO carrĂ©e ; un moteur diesel avec une loi de commande CRONE MIMO non carrĂ©e. Le but fixĂ© par l'industriel Ă l'origine de ces applications est d optimiser le compromis performances-pollution-consommation de ces moteurs tout en minimisant les efforts liĂ©s Ă la conception de ces nouvelles lois de commande.The works presented in this thesis are led within the framework of robust control developments of the CRONE team (Robust Control of fractional order). They are carried more precisely on the development of a synthesis methodology of the CRONE control for multivariable systems with an application of controlling internal combustion engine. After an introductive chapter on the robust control of fractional order with a view to garanty dynamic performance robustness compared with parameter uncertainties of the system model, another stability condition formulation of the CRONE methodology for multivariable square systems is put forward. A set of theorems is also offered in order to extend the square MIMO system CRONE control to the most general case of multivariable systems having delays and oscillatory behaviours with zeros and poles that are not necessarily on the stability domain. Chapter 3 is devoted on one hand to the control of non square (number of entries differents from the output number), instable and non minimal phase MIMO systems and on the other hand on the simplification of different control methodologies detailed in this thesis. This simplification is based on the analysis of system coupling effects and under the assumptions that in some cases, elements of the system transfer matrix can be considered as uncertainties when optimizing the fractional nominal open loop. Beyond a set of academic cases out of the literature, the validation of these works is achieved through the control of the air intake of two internal combustion engines : a gasoline engine with a square CRONE MIMO control ; a diesel engine with a non square CRONE MIMO control. The aim specified by the industrial is to optimize the compromise between performances-pollution-consumption of these engines.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF
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