In this paper, a robust fuzzy observer-based tracking controller for continuous-time nonlinear systems presented by Takagi–Sugeno (TS) models with unmeasurable premise variables, is synthesized. Using the H∞ norm and Lyapunov approach, the control design for TS fuzzy systems with both unmeasurable premises and system states is developed to guarantee tracking performance of closed loop systems. Sufficient relaxed conditions for synthesis of the fuzzy observer and the fuzzy control are driven in terms of linear matrix inequalities (LMIs) constraints. The proposed method allows simplifying the design procedure and gives the observer and controller gains in only one step. Numerical simulation on a two tank system is provided to illustrate the tracking control design procedure and to confirm the efficiency of the proposed method.
Issue Section:
Research Papers
References
1.
Chadli
, M.
, and Hajjaji
, A. E.
, 2006
, “Observer-Based Robust Fuzzy Control of Nonlinear Systems With Parametric Uncertainties
,” J. Fuzzy Sets Syst.
, 157
(9
), pp. 1276
–1281
.10.1016/j.fss.2005.09.0042.
Chen
, B. S.
, Uang
, H. J.
, and Tseng
, C. S.
, 1998
, “Robust Tracking Enhancement of Robot Systems Including Motor Dynamics: A Fuzzy-Based Dynamic Game Approach
,” IEEE Trans. Fuzzy Syst.
, 6
, pp. 538
–552
.10.1109/91.7284493.
Messoussi
, W. E.
, Bosche
, J.
, Pages
, O.
, and Hajjaji
, A. E.
, 2008
, “Non-Fragile Observer-Based Control of Vehicle Dynamics Using T-S Fuzzy Approach
,” 17th IFAC World Congress, The International Federation of Automatic Control
, COEX, South Korea pp. 7098
–7103
.10.3182/20080706-5-KR-1001.012034.
Tanaka
, K.
, Ikeda
, T.
, and Wang
, H. O.
, 1996
, “Robust Stabilization of a Class of Uncertain Nonlinear System via Fuzzy Control
,” IEEE Trans.Fuzzy Syst.
, 4
, pp. 1
–13
.10.1109/91.4818405.
Tanaka
, K.
, Ikeda
, T.
, and Wang
, H. O.
, 1998
, “A Unified Approach to Controlling Chaos via an LMI-Based Fuzzy Control System Design
,” IEEE Trans.Circuits Syst.
, 45
, pp. 1021
–1040
.10.1109/81.7288576.
Wang
, H. O.
, Tanaka
, K.
, and Griffin
, M. F.
, 1995
, “Parallel Distributed Compensation of Nonlinear Systems by Takagi and Sugeno's Fuzzy Model
,” Proceedings of Fuzzy
, IEEE, pp. 531
–538
.7.
Wang
, H. O.
, Tanaka
, K.
, and Griffin
, M. F.
, 1996
, “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues
,” IEEE Trans. Fuzzy Syst.
, 4
, pp. 14
–23
.10.1109/91.4818418.
Wang
, Z.
, and Guo
, Y.
, 2012
, “Oscillatory Tracking Control of a Class of Nonlinear Systems
,” ASME J. Dyn. Syst., Meas., Control
, 134
(3
), p. 031011
.10.1115/1.40054959.
Huang
, R.
, Lin
, Y.
, and Lin
, Z.
, 2010
, “Robust Fuzzy Tracking Control Design for a Class of Nonlinear Stochastic Markovian Jump Systems
,” ASME J. Dyn. Syst., Meas., Control
, 132
(5
), p. 051005
.10.1115/1.400185010.
Kung
, C. C.
, and Li
, H. H.
, 1997
, “Tracking Control of Nonlinear Systems by Fuzzy Model-Based Controller
,” Proceedings of IEEE International Conference
, Vol. 2
, pp. 623
–628
.11.
Tseng
, C. S.
, and Chen
, B. S.
, 2000
, “Fuzzy Tracking Control Design for Nonlinear Discrete-Time Dynamic Systems via TS Fuzzy Model
,” Proceedings of IEEE International Conference on Fuzzy Systems
, 1
, pp. 405
–410
.12.
Tseng
, C. S.
, 2008
, “A Novel Approach to H∞ Decentralized Fuzzy-Observer-Based Fuzzy Control Design for Nonlinear Interconnected Systems
,” IEEE Trans. Fuzzy Syst.
, 16
(5
), pp. 1337
–1350
.10.1109/TFUZZ.2008.92435513.
Wang
, W. J.
, and Lin
, H. R.
, 1999
, “Fuzzy Control Design for the Trajectory Tracking on Uncertain Nonlinear Systems
,” IEEE Trans. Fuzzy Syst.
, 7
, pp. 53
–62
.10.1109/91.74630814.
Tseng
, C. S.
, Chen
, B. S.
, and Uang
, H. J.
, 2001
, “Synthesis of Observers for Fault Diagnosis in Discrete Time Nonlinear Systems Using a Takagi–Sugeno Multiple Model
,” IEEE Trans. Fuzzy Syst.
, 9
(3
), pp. 381
–392
.10.1109/91.92873515.
Zheng,
F.
, Wang
, Q.-G.
, and Lee
, T. H.
, 2002
, “Output Tracking Control of MIMO Fuzzy Nonlinear Systems Using Variable Structure Control Approach
,” IEEE Trans. Fuzzy Syst.
, 10
(6
), pp. 686
–697
.10.1109/TFUZZ.2002.80590516.
Lin
, C.
, Wang
, C.-G.
, and Lee
, T. H.
, 2006
, “H∞ Output Tracking Control for Nonlinear via T-S Fuzzy Model Approach
,” IEEE Trans. Syst. Cybern.
, 36
(2
), pp. 450
–457
.10.1109/TSMCB.2005.85672317.
Oudghiri-Bentaie
, M.
, Chadli
, M.
, and Hajjaji
, A. E.
, 2007
, “One-Step Procedure for Robust Output H∞ Fuzzy Control
,” Proceedings of the 15th Mediterranean Conference on Control and Automation
, IEEE-Med 07, pp. 1
–6
.18.
Kim
, E.
, Kang
, D.
, and Won
, S.
, 2009
, “Robust Tracking Control of T-S Fuzzy Systems Based on Fuzzy Lyapunov Approach
,” ICROS-SICE International Joint Conference
, pp. 2850
–2855
.19.
Agustinah
, T.
, Jazidie
, A.
, Nuh
, M.
, and Du
, H.
, 2010
, “Fuzzy Tracking Control Design Using Observer-Based Stabilizing Compensator for Nonlinear Systems
,” International Conference on System Science and Engineering
, ICSSE, pp. 275
–280
.20.
Allouche
, M.
, Chaabane
, M.
, Souissi
, M.
, and Mehdi
, D.
, 2011
, “Fuzzy Tracking Control for Indirect Field Oriented Induction Machine Using Integral Action Performance
,” IETE J. Res.
, 57
(6
), pp. 443
–451
.10.4103/0377-2063.9016421.
Chen
, B. S.
, Lin
, Y.-P.
, and Chuang
, Y.-J.
, 2011
, “Robust H∞ Observer Based Tracking Control of Stochastic Immune Systems Under Environmental Disturbances and Measurement Noises
,” Asian J. Control
, 13
(5
), pp. 667
–690
.10.1002/asjc.42122.
Ghorbel
, H.
, Souissi
, M.
, Hajjaji
, A. E.
, and Chaabane
, M.
, 2011
, “Design of Multi-Observers for Takagi–Sugeno Systems With Unmeasurable Premise Variables: Descriptor Approach
,” International Conference on Sciences and Techniques of Automatic Control and Computer Engineering
, STA.23.
Ichalal
, D.
, Marx
, B.
, Ragot
, J.
, and Maquin
, D.
, 2009
, “State Estimation of Nonlinear Systems Using Multiple Model Approach
,” American Control Conference
, ACC.24.
Nagy
, A.
, Marx
, B.
, Mourot
, G.
, Schutz
, G.
, and Ragot
, J.
, 2010
, “State Estimation of Two-Time Scale Multiple Models With Unmeasurable Premise Variables. Application to Biological Reactors
,” 49th IEEE
Conference on Decision and Control
, Atlanta, GA, Dec. 15–17, pp. 5689
–5694
.10.1109/CDC.2010.571803525.
Lin
, C.
, Wang
, Q. G.
, and Lee
, T. H.
, 2005
, “Improvement on Observer-Based H∞ Control for T-S Fuzzy Systems
,” Automatica
, 41
, pp. 1651
–1656
.10.1016/j.automatica.2005.04.00426.
Isidori
, A.
, 1994
, “H∞ Control via Measurement Feedback for Affine Non Linear Systems
,” Int. J. Rob. Nonlinear Control
, 4
(4
), pp. 553
–574
.10.1002/rnc.459004040927.
Lendek
, Z.
, Laubert
, J.
, Guerra
, T. M.
, Babuska
, R.
, and Schutter
, B. D.
, 2010
, “Adaptative Observers for TS Fuzzy Systems With Unknown Polynomial Inputs
,” Fuzzy Sets Syst.
, 161
, pp. 2043
–2065
.10.1016/j.fss.2010.03.01028.
Liu
, X.
, and Zhang
, Q.
, 2003
, “New Approaches to H∞ Controller Designs Based on Fuzzy Observers for TS Fuzzy Systems via LMI
,” Automatica
, 39
, pp. 1571
–1582
.10.1016/S0005-1098(03)00172-929.
Benzaouia
, A.
, Hmamed
, A.
, and Hajjaji
, A. E.
, 2010
, “Stabilization of Controlled Positive Discrete-Time T-S Fuzzy Systems by State Feedback Control
,” Int. J. Adapt. Control Signal Process.
, 24
, pp. 1091
–1106
.10.1002/acs.1185Copyright © 2014 by ASME
You do not currently have access to this content.
