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A LMI Approach to Tracking Control of Nonlinear Polynomial Systems

Khalil Jouili(1*), Naceur Benhadj Braiek(2)

(1) Laboratory of Advanced Systems. Address: PolytechnicSchool of Tunisia (EPT) BP. 743, 2078, Marsa, Tunisia
(2) Laboratory of Advanced Systems. Address: PolytechnicSchool of Tunisia (EPT) BP. 743, 2078, Marsa, Tunisia
(*) Corresponding author


DOI: https://doi.org/10.15866/ireaco.v8i3.6294

Abstract


This paper presents a tracking control approach for a class of nonlinear non-minimum phase systems. This control approach is the combination between an input-output feedback linearization technique and a gain scheduling method to obtain a tracking control structure. The latter is mainly based on the Linear Matrix Inequalities method which allows us to estimate and to enlarge the domain of attraction around operating points. The nonlinear system is represented locally by variation polynomial models. The polynomial models are then used to design a family of feedback controllers. We propose a nonlinear gain scheduling procedure for the problem of guaranteed transition from an actual operating point to a desired one along the reference trajectory. The theoretical results are applied to a non-minimum phase continuously stirred tank reactor in order to illustrate the effectiveness of the proposed approach
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Keywords


Non-Minimum Phase Systems; Input-Output Feedback Linearization; Gain Scheduling; Domain of Attraction; Linear Matrix Equality

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References


H. Badihi, Y. Zhang, H. Hong, Fuzzy gain-scheduled active fault-tolerant control of a wind turbine, Journal of the Franklin Institute, Vol. 351: 3677-3706 (2014).
http://dx.doi.org/10.1016/j.jfranklin.2013.05.007

C. Tao, Y. Daren, B. Wen, Y. Yongbin, Gain Scheduling Control of Nonlinear Shock Motion Based on Equilibrium Manifold Linearization Model, Chinese Journal of Aeronautics, Vol. 20: 481-487. (2007).
http://dx.doi.org/10.1016/s1000-9361(07)60071-5

J. Veenman, W. Scherer Carsten, A synthesis framework for robust gain scheduling controllers, Automatica, Vol. 50: 2799-281 (2014).
http://dx.doi.org/10.1016/j.automatica.2014.10.002

M. Cannon, M. Bacic, B. Kouvaritakis, Dynamic non-minimum phase compensation for SISO nonlinear, affine in the input systems, Automatica, Vol. 42: 1969-1975 (2006).
http://dx.doi.org/10.1016/j.automatica.2006.06.008

S. Dubljevic and N. Kazantsis, A new Lyapunov design approach for nonlinear systems based on Zubov’s method, Automatica, Vol. 38: 1999–2007 (2007).
http://dx.doi.org/10.1016/s0005-1098(02)00110-3

J. S. Shamma and M. Athans, Gain scheduling: potential hazards and possible remedies, IEEE Control Systems Magazine, Vol. 12: 101-107 (1992).
http://dx.doi.org/10.1109/37.165527

J. S. Shamma and M. Athans, Guaranteed properties of gain scheduled control for linear parameter-varying plants, Automatica, Vol. 27: 559-564 (1991).
http://dx.doi.org/10.1016/0005-1098(91)90116-j

K. Jouili, H. Jerbi, N. Benhadj Braiek, An advanced fuzzy logic gain scheduling trajectory control for nonlinear systems, Journal of Process Control, Vol. 20: 426–440 (2010).
http://dx.doi.org/10.1016/j.jprocont.2010.01.001

H. K. Khalil, Nonlinear systems, Prentice Hall, Upper Saddle River,2nd Edition.
http://dx.doi.org/10.1002/rnc.1054

M. W. McConley, B. D. Appleby, M. A. Dahleh and E. Feron, A computationally Efficient Lyapunov-based scheduling procedure for control of nonlinear systems with stability guarantees, IEEE Transactions on Automatic Control, Vol. 45: 33–49 (2000).
http://dx.doi.org/10.1109/9.827354

K. U. Klatt, S. Engell, Gain-scheduling trajectory control of a continuous stirred tank reactor, Computers & Chemical Engineering, Vol. 22: 491-502 (1998).
http://dx.doi.org/10.1016/s0098-1354(97)00261-5

K. Jouili, H. Jerbi, Tracking Control of Nonlinear Polynomial Systems via a Geometrical Stabilizing Approach, (2009) International Review of Automatic Control (IREACO), 2 (2), pp. 128-138.

C. Panjapornpon, M. Soroush, Control of Non-Minimum-Phase Nonlinear Systems through Constrained Input-Output Linearization, Proceedings of the 2006 American Control Conference, ( 2006).
http://dx.doi.org/10.1109/acc.2006.1657432

J. Brewer, Kronecker product and calculus in system theory, IEEE Transactions on Circuits and Systems, Vol. 25: 772-781 (1978).
http://dx.doi.org/10.1109/tcs.1978.1084534

G. Chesi, Computing output feedback controllers to enlarge the domain of attraction in polynomial systems, IEEE Transactions on Automatic Control, Vol. 49: 1846–1850 (2004).
http://dx.doi.org/10.1109/tac.2004.835589

A. Isidori, Nonlinear control systems. 2nd Edition, New York: Springer Verlag, (1998).


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