Tensor product model transformation based decoupled terminal sliding mode control

The main objective of this paper is to propose a tensor product model transformation based decoupled terminal sliding mode controller design methodology. The methodology is divided into two steps. In the first step, tensor product model transformation is applied to the single-input-multi-output system and a parameter-varying weighted linear time-invariant system is obtained. Then, decoupled terminal sliding mode controller is designed based on the linear time-invariant systems. The main novelty of this paper is that the nonsingular terminal sliding mode control design is based on a numerical model rather than an analytical one. Finally, simulations are tested on cart-pole system and translational oscillations with a rotational actuator system.

[1]  Giuseppe Oriolo,et al.  Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[2]  P. Baranyi,et al.  Centralized tensor product model form , 2008, 2008 6th International Symposium on Applied Machine Intelligence and Informatics.

[3]  F. Kolonic,et al.  Experimental Control Design by TP Model Transformation , 2006, 2006 IEEE International Conference on Mechatronics.

[4]  Xinghuo Yu,et al.  Sliding-Mode Control With Soft Computing: A Survey , 2009, IEEE Transactions on Industrial Electronics.

[5]  Péter Baranyi,et al.  TP model transformation as a way to LMI-based controller design , 2004, IEEE Transactions on Industrial Electronics.

[6]  Yeung Yam,et al.  Reduction of fuzzy rule base via singular value decomposition , 1999, IEEE Trans. Fuzzy Syst..

[7]  Hung-Yuan Chung,et al.  Decoupled fuzzy controller design with single-input fuzzy logic , 2002, Fuzzy Sets Syst..

[8]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[9]  Hideki Hashimoto,et al.  Sliding sector design for nonlinear systems , 2008 .

[10]  P. Baranyi,et al.  Computational relaxed TP model transformation: restricting the computation to subspaces of the dynamic model , 2009 .

[11]  Lon-Chen Hung,et al.  Design of self-tuning fuzzy sliding mode control for TORA system , 2007, Expert Syst. Appl..

[12]  Péter Várlaki,et al.  HOSVD Based Canonical Form for Polytopic Models of Dynamic Systems , 2009, J. Adv. Comput. Intell. Intell. Informatics.

[13]  Dennis S. Bernstein,et al.  A BENCHMARK PROBLEM FOR NONLINEAR CONTROL DESIGN , 1998 .

[14]  Fetah Kolonić,et al.  Tensor Product Model Transformation-based Controller Design for Gantry Crane Control System – An Application Approach , 2006 .

[15]  Péter Gáspár,et al.  TP model transformation for control-oriented qLPV modeling , 2008 .

[16]  Annamária R. Várkonyi-Kóczy,et al.  TP transformation based dynamic system modeling for nonlinear control , 2005, IEEE Transactions on Instrumentation and Measurement.

[17]  Peter Baranyi,et al.  Approximation and complexity trade‐off by TP model transformation in controller design: A case study of the TORA system , 2010 .

[18]  Dennis S. Bernstein,et al.  Benchmark Problems for Robust Control Design , 1991, 1991 American Control Conference.

[19]  Lei Guo,et al.  Composite disturbance-observer-based control and terminal sliding mode control for uncertain structural systems , 2009, Int. J. Syst. Sci..

[20]  Xinghuo Yu,et al.  On nonsingular terminal sliding-mode control of nonlinear systems , 2013, Autom..

[21]  James F. Whidborne,et al.  Linear Parameter Varying control of a quadrotor , 2011, 2011 6th International Conference on Industrial and Information Systems.

[22]  Reza Olfati-Saber,et al.  Normal forms for underactuated mechanical systems with symmetry , 2002, IEEE Trans. Autom. Control..

[23]  Y. Yam,et al.  Tensor Product Model Transformation in Polytopic Model-Based Control , 2013 .

[24]  Shaoyuan Li,et al.  A new terminal sliding mode control for robotic manipulators , 2009, Int. J. Control.

[25]  Mrdjan Jankovic,et al.  TORA example: cascade- and passivity-based control designs , 1996, IEEE Trans. Control. Syst. Technol..

[26]  Peter Korondi.  Tensor product model transformation-based sliding surface design , 2006 .

[27]  Peter Korondi,et al.  TP model transformation based sliding mode control design for nonlinear systems , 2010, Proceedings of 14th International Power Electronics and Motion Control Conference EPE-PEMC 2010.

[28]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[29]  Hideki Hashimoto,et al.  Trajectory Tracking by TP Model Transformation: Case Study of a Benchmark Problem , 2007, IEEE Transactions on Industrial Electronics.

[30]  M. Basin,et al.  Optimal Filtering for Incompletely Measured Polynomial States over Linear Observations , 2008, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

[31]  Bela Takarics,et al.  TP model transformation based sliding mode control and friction compensation , 2011 .

[32]  Li Wang,et al.  On modeling and control of a flexible air-breathing hypersonic vehicle based on LPV method , 2012 .

[33]  Hasan Komurcugil,et al.  Nonsingular decoupled terminal sliding-mode control for a class of fourth-order nonlinear systems , 2013, Commun. Nonlinear Sci. Numer. Simul..

[34]  Ji-Chang Lo,et al.  Decoupled fuzzy sliding-mode control , 1998, IEEE Trans. Fuzzy Syst..

[35]  B. Takarics.  Parallel Distributed Compensation based sector sliding mode control of Takagi-Sugeno type polytopic models , 2012, 2012 IEEE 10th International Symposium on Applied Machine Intelligence and Informatics (SAMI).

[36]  Fetah Kolonić,et al.  Linear Matrix Inequalities Based H∞ Control of Gantry Crane using Tensor Product Transformation , 2011 .

[37]  Jie Huang,et al.  On an output feedback finite-time stabilization problem , 2001, IEEE Trans. Autom. Control..

[38]  Tao Zou,et al.  A finite-time approach to formation control of multiple mobile robots with terminal sliding mode , 2012, Int. J. Syst. Sci..

[39]  Xinghuo Yu,et al.  Model reference adaptive control systems with terminal sliding modes , 1996 .

[40]  R. Patton,et al.  APPROXIMATION PROPERTIES OF TP MODEL FORMS AND ITS CONSEQUENCES TO TPDC DESIGN FRAMEWORK , 2007 .

[41]  Claudia-Adina Dragos,et al.  Novel Tensor Product Models for Automatic Transmission System Control , 2012, IEEE Systems Journal.

[42]  Peter Baranyi,et al.  TP tool - A MATLAB toolbox for TP model transformation , 2007 .

[43]  Hongxing Li,et al.  Tensor Product Model Transformation Based Adaptive Integral-Sliding Mode Controller: Equivalent Control Method , 2013, TheScientificWorldJournal.

[44]  M. Basin,et al.  Optimal filtering for polynomial system states with polynomial multiplicative noise , 2006, 2006 American Control Conference.

[45]  Robert T. Bupp s,et al.  A BENCHMARK PROBLEM FOR NONLINEAR CONTROL DESIGN , 1998 .

[46]  F. Kolonic,et al.  Tensor Product Transformation based Speed Control of Permanent Magnet Synchronous Motor Drives , 2011 .

[47]  Xinghuo Yu,et al.  Terminal sliding mode control of MIMO linear systems , 1997 .

[48]  Andras Rovid,et al.  On tensor-product model based representation of neural networks , 2011, 2011 15th IEEE International Conference on Intelligent Engineering Systems.

[49]  M. Basin.  New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems , 2008 .

[50]  Robert E. Mahony,et al.  Control of a quadrotor helicopter using visual feedback , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[51]  Yeung Yam,et al.  Fuzzy approximation via grid point sampling and singular value decomposition , 1997, IEEE Trans. Syst. Man Cybern. Part B.