Study on active vibration isolation system using neural network sliding mode control

In this paper, an active vibration isolation system based on hybrid algorithm is presented in a wide frequency band. Initially, a nonlinear magnetostrictive actuator model is used to establish the appropriate parameters by experiments, which make the actuator using in vibration isolation system work in a better linear dynamic performance, then the sliding mode algorithm modified by neural network, a hybrid algorithm is proposed as the active control controller, and its stability is also analyzed by Lyapunov theory. Furthermore, a dynamic virtual prototype model of active vibration isolation is established to carry out the co-simulation with Adams and Matlab/Simulink, and the results show that under the difference excitations, the neural network sliding mode controller exhibits a good control performance, and the active vibration isolation can effectively improve the vibration isolation effect, reduce the force transmitted to the base and broaden the vibration isolation bandwidth

LPV Analysis and Control Using Fast Iterative Solutions to Rationally Parametric Lyapunov and Riccati Equations

Abstract-We consider the problem of analysis and control of Linear Parameter Varying(LPV) systems. With regard to such problems, solving rationally parametric Lyapunov and Riccati equations for parametric matrices often arises. In this paper, we develop computationally efficient iterative methods for finding rational approximations to solutions to such problems to arbitrary accuracy

Convergent LMI relaxations for robust analysis of uncertain linear systems using lifted polynomial parameter-dependent Lyapunov functions

This paper investigates the problems of checking robust stability and evaluating robust H-2 performance of uncertain continuous-time linear systems with time-invariant parameters lying in polytopic domains. The novelty is the ability to check robust stability by constructing a particular parameter-dependent Lyapunov function which is a polynomial function of the uncertain system matrices, as opposed to a general polynomial function of the uncertain parameter. The degree of the polynomial is tied to a certain integer kappa. The existence of such Lyapunov function can be proved by solving parameter-dependent Linear Matrix Inequalities (LMIs), which are guaranteed to be solvable for a sufficiently large yet finite value of kappa whenever the system is robustly stable. Extensions to guaranteed H-2 cost computation are also provided. Numerical aspects concerning the programming and the evaluations of the proposed tests are discussed and illustrated by examples. (C) 2008 Elsevier B.V. All rights reserved.57868068

Simulation and control of denitrification biofilters described by PDEs

Cette thèse concerne la simulation et la commande d'un biofiltre de dénitrification. Selon que l'on considère ou que l'on néglige la diffusion, des modèles d'EDP paraboliques ou hyperboliques sont considérés. En plus des classiques méthodes des lignes, des approches spécifiques au type d'EDP sont évaluées pour simuler le système. La méthode des caractéristiques s'applique aux systèmes d'EDP hyperboliques. L'analyse modale utilisée pour les systèmes d'EDP paraboliques permet de manipuler un système d'ordre réduit. L'objectif de commande est alors de réduire la concentration en azote en sortie du réacteur sous une certaine limite, en dépit des perturbations externes et des incertitudes du modèle. Deux stratégies de commande sont considérées. Une approche "early lumping" permet la synthèse d'une loi de commande linéaire H2 de type retour de sortie avec observateur. Une approche "late lumping" associe une loi de commande linéarisante à un observateur à paramètres distribués.This thesis addresses the simulation and control of a denitrification biofilter. Parabolic and hyperbolic PDE models may be considered, which depends on the fact of considering or neglecting the diffusion phenomenon. In plus of the classical methods of lines, approaches specific to the type of PDE system are evaluated to simulate the biofilter. The method of characteristics applies to hyperbolic PDE systems. The modal analysis used on the parabolic PDE system allows manipulating a reduced order model. The control objective is then the reduction of the nitrogen concentration at the output of the reactor below some pre-specified upper limit, in spite of the external disturbances and uncertainties of the model. Two control strategies are considered. An early lumping approach is used to synthesize an observer-based H2 output feedback linear controller. A late lumping approach associates a linearizing control to a distributed parameter observer

Robust State Feedback Control For Discrete-time Linear Systems Via Lmis With A Scalar Parameter

This paper proposes an improved approach to H2 and H ∞ robust state feedback control design for discrete-time polytopic time-invariant linear systems based on Linear Matrix Inequalities (LMIs) with a scalar parameter. The synthesis conditions, that depend on a real parameter lying in the interval (-1,1), become LMIs for fixed values of the scalar, reducing to standard conditions in the literature when the scalar is equal to zero. At the price of line searches combined with LMIs, less conservative results for robust state feedback control are obtained. The closed-loop stability and the H2 and H∞ guaranteed costs are certified by means of an affine parameter-dependent Lyapunov function. The validity and the efficiency of the method are illustrated by means of examples and exhaustive numerical comparisons. © 2013 AACC American Automatic Control Council.38703875Boeing,Eaton,Halliburton,Honeywell,MathWorksBoyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , Philadelphia, PA: SIAM Studies in Applied MathematicsLofberg, J., YALMIP: A toolbox for modeling and optimization in MATLAB (2004) Proc. 2004 IEEE Int. Symp. on Comput. Aided Control Syst. Des., pp. 284-289. , http://control.ee.ethz.ch/?joloef/yalmip.php, Taipei, Taiwan, SeptemberSturm, J.F., Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones (1999) Optim. Method Softw., 11 (1-4), pp. 625-653. , http://sedumi.ie.lehigh.edu/Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system (1985) J. Optim. Theory and Appl., 46 (4), pp. 399-408. , AugustHorisberger, H.P., Belanger, P.R., Regulators for linear, time invariant plants with uncertain parameters (1976) IEEE Trans. Autom. Control, 21, pp. 705-708. , OctoberGeromel, J.C., De Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Lin. Alg. Appl., 285 (1-3), pp. 69-80. , DecemberRamos, D.C.W., Peres, P.L.D., A less conservative LMI condition for the robust stability of discrete-time uncertain systems (2001) Syst. Control Letts., 43 (5), pp. 371-378. , AugustRamos, D.C.W., Peres, P.L.D., An LMI condition for the robust stability of uncertain continuous-time linear systems (2002) IEEE Trans. Autom. Control, 47 (4), pp. 675-678. , AprilOliveira, R.C.L.F., Peres, P.L.D., Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations (2007) IEEE Trans. Autom. Control, 52 (7), pp. 1334-1340. , JulyDe Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems Perspectives in Robust Control, 268, pp. 241-257. , ser. Lecture Notes in Control and Information Science, S. O. Reza Moheimani, Ed. New York, NY: Springer-Verlag, 2001Henrion, D., Arzelier, D., Peaucelle, D., Lasserre, J.B., On parameter-dependent Lyapunov functions for robust stability of linear systems Proc. 43rd IEEE Conf. Decision Control, pp. 887-892. , Paradise Island, Bahamas, December 2004Scherer, C.W., Relaxations for robust linear matrix inequality problems with verifications for exactness (2005) SIAM J. Matrix Anal. Appl., 27 (2), pp. 365-395. , JuneOliveira, R.C.L.F., De Oliveira, M.C., Peres, P.L.D., Convergent LMI relaxations for robust analysis of uncertain linear systems using lifted polynomial parameter-dependent Lyapunov functions (2008) Syst. Control Letts., 57 (8), pp. 680-689. , AugustGeromel, J.C., Peres, P.L.D., Bernussou, J., On a convex parameter space method for linear control design of uncertain systems (1991) SIAM J. Control Optim., 29 (2), pp. 381-402. , MarchDe Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discretetime robust stability condition (1999) Syst. Control Letts., 37 (4), pp. 261-265. , JulyEbihara, Y., Hagiwara, T., New dilated LMI characterizations for continuous-time multiobjective controller synthesis (2004) Automatica, 40 (11), pp. 2003-2009. , NovemberGeromel, J.C., Korogui, R.H., Analysis and synthesis of robust control systems using linear parameter dependent Lyapunov functions (2006) IEEE Trans. Autom. Control, 51 (12), pp. 1984-1989. , DecemberShimomura, T., Takahashi, M., Fujii, T., Extended-space control design with parameter-dependent Lyapunov functions (2001) Proc. 40th IEEE Conf. Decision Control, pp. 2157-2162. , Orlando, FL, USA, DecemberGarcia, G., Salhi, S., (2008) H2 and Hrobust Control for Continuoustime Linear Systems, , LAAS-CNRS, Tech. Rep. 08146, MarchPipeleers, G., Demeulenaere, B., Swevers, J., Vandenberghe, L., Extended LMI characterizations for stability and performance of linear systems (2009) Syst. Control Letts., 58 (7), pp. 510-518. , JulyDe Oliveira, M.C., Geromel, J.C., Bernussou, J., Extended H2 and Hcharacterization and controller parametrizations for discrete-time systems (2002) Int. J. Control, 75 (9), pp. 666-679. , JuneZhou, K., Doyle, J.C., Glover, K., (1996) Robust and Optimal Control. Upper Saddle River, , NJ, USA: Prentice HallGahinet, P., Apkarian, P., A linear matrix inequality approach to Hcontrol (1994) Int. J. Robust Nonlinear Control, 4 (4), pp. 421-448. , July/AugustOliveira, R.C.L.F., Peres, P.L.D., A convex optimization procedure to compute H2 and Hnorms for uncertain linear systems in polytopic domains (2008) Optim. Control Appl. Meth., 29 (4), pp. 295-312. , July/AugustTrofino, A., Coutinho, D.F., Barbosa, K.A., Improved H2 and Hconditions for robust analysis and control synthesis of linear systems (2005) SBA: Cont. Autom., 16 (4), pp. 427-434. , October/November/DecemberOgata, K., (1995) Discrete-Time Control Systems, , Upper Saddle River, NJ, USA: Prentice-Hall International, IncOliveira, R.C.L.F., De Oliveira, M.C., Peres, P.L.D., Robust state feedback LMI methods for continuous-time linear systems: Discussions, extensions and numerical comparisons (2011) Proc. 2011 IEEE Int. Symp. on Comput. Aided Control Syst. Des., pp. 1038-1043. , Denver, CO, USA, Septembe

Robust State Feedback Lmi Methods For Continuous-time Linear Systems: Discussions, Extensions And Numerical Comparisons

This paper provides a brief survey on the subject of LMI (Linear Matrix Inequality) methods for robust state feedback control design. The focus is on continuous-time linear systems with time-invariant uncertain parameters belonging to a polytope. Several LMI conditions from the literature are reviewed and discussed. The relationship between quadratic stabilizability (i.e. constant Lyapunov matrix) and LMI conditions based on parameter-dependent Lyapunov functions is highlighted. As a contribution, a generalization of a family of parameter-dependent conditions is proposed. Discussions, possible extensions and interpretations are provided along the presentation. Finally, the numerical efficacy of the LMI conditions in finding robust controllers when one stabilizing gain is known to exist is investigated. The methods have been tested against a set of hard uncertain systems that are guaranteed to be stabilized by some robust state feedback controller, including a large subset of problems which are known to be stabilized by some robust controller but not to be quadratically stabilizable by any controller. © 2011 IEEE.10381043Horisberger, H.P., Belanger, P.R., Regulators for linear, time invariant plants with uncertain parameters (1976) IEEE Trans. Autom. Control, 21, pp. 705-708Barmish, B.R., Stabilization of uncertain systems via linear control (1983) IEEE Trans. Autom. Control, 28 (8), pp. 848-850. , AugustBarmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system (1985) J. Optim. Theory and Appl., 46 (4), pp. 399-408. , AugustBoyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , Philadelphia, PA: SIAM Studies in Applied MathematicsBernussou, J., Peres, P.L.D., Geromel, J.C., A linear programming oriented procedure for quadratic stabilization of uncertain systems (1989) Syst. Control Letts, 13 (1), pp. 65-72. , JulyGeromel, J.C., Peres, P.L.D., Bernussou, J., On a convex parameter space method for linear control design of uncertain systems (1991) SIAM J. Control Optim., 29 (2), pp. 381-402. , MarchDaafouz, J., Bernussou, J., Parameter dependent lyapunov functions for discrete time systems with time varying parameter uncertainties (2001) Syst. Control Letts., 43 (5), pp. 355-359. , AugustLee, J.-W., On uniform stabilization of discrete-time linear parameter-varying control systems (2006) IEEE Trans. Autom. Control, 51 (10), pp. 1714-1721. , OctoberHaddad, W.M., Bernstein, D.S., Parameter-dependent lyapunov functions and the discrete-time popov criterion for robust analysis (1994) Automatica, 30 (6), pp. 1015-1021Gahinet, P., Apkarian, P., Chilali, M., Affine parameter-dependent lyapunov functions and real parametric uncertainty (1996) IEEE Trans. Autom. Control, 41 (3), pp. 436-442. , MarchShimomura, T., Takahashi, M., Fujii, T., Extended-space control design with parameter-dependent lyapunov functions (2001) Proc. 40th IEEE Conf. Decision Control, pp. 2157-2162. , Orlando, FL, USA, DecemberApkarian, P., Tuan, H.D., Bernussou, J., Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations (2001) IEEE Trans. Autom. Control, 46 (12), pp. 1941-1946. , DecemberShaked, U., Improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty (2001) IEEE Trans. Autom. Control, 46 (4), pp. 652-656. , AprilEbihara, Y., Hagiwara, T., New dilated LMI characterizations for continuous-time multiobjective controller synthesis (2004) Automatica, 40 (11), pp. 2003-2009. , NovemberGeromel, J.C., Korogui, R.H., Analysis and synthesis of robust control systems using linear parameter dependent lyapunov functions (2006) IEEE Trans. Autom. Control, 51 (12), pp. 1984-1989. , DecemberGeromel, J.C., De Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Lin. Alg. Appl., 285 (1-3), pp. 69-80. , DecemberDe Oliveira, M.C., Geromel, J.C., Hsu, L., LMI characterization of structural and robust stability: The discrete-time case (1999) Lin. Alg. Appl., 296 (1-3), pp. 27-38. , JuneDe Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems (2001) Perspectives in Robust Control, Ser. Lecture Notes in Control and Information Science, 268, pp. 241-257. , S. O. Reza Moheimani, Ed. New York, NY: Springer-VerlagGahinet, P., Apkarian, P., A linear matrix inequality approach to H∞ control (1994) Int. J. Robust Nonlinear Control, 4 (4), pp. 412-448. , July-AugustSkelton, R.E., Iwasaki, T., Grigoriadis, K., (1998) A Unified Algebraic Approach to Linear Control Design, , Bristol, PA: Taylor & FrancisPipeleers, G., Demeulenaere, B., Swevers, J., Vandenberghe, L., Extended LMI characterizations for stability and performance of linear systems (2009) Syst. Control Letts., 58 (7), pp. 510-518. , JulyPeaucelle, D., Arzelier, D., Bachelier, O., Bernussou, J., A new robust D-stability condition for real convex polytopic uncertainty (2000) Syst. Control Letts., 40 (1), pp. 21-30. , MayChughtai, S.S., Munro, N., Robust stability condition for continuous-time systems (2004) Electr. Lett., 40 (16), pp. 978-979. , AugustCao, Y.-Y., Lin, Z., A descriptor system approach to robust stability analysis and controller synthesis (2004) IEEE Trans. Autom. Control, 49 (11), pp. 2081-2084. , NovemberGarcia, G., Salhi, S., H2 and H∞ robust control for continuoustime linear systems (2008) LAAS-CNRS, Tech. Rep. 08146, , MarchDe Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discretetime robust stability condition (1999) Syst. Control Letts., 37 (4), pp. 261-265. , JulyDe Souza, C.E., Trofino, A., De Oliveira, J., Parametric lyapunov function approach to H2 analysis and control of linear parameter-dependent systems (2003) IEE Proc. - Control Theory and Appl., 150 (5), pp. 501-508. , SeptemberJia, Y., Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: A predictive approach (2003) IEEE Trans. Autom. 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