Dynamic Compensators for Nonlinear Systems Using T-S Fuzzy Models: A Comparative Study and HIL Implementation

This paper studies the computational burden of discrete-time nonlinear control systems using T-S fuzzy models considering a Hardware-in-the-loop (HIL) implementation. The classical T-S modeling is compared to a recent fuzzy modeling technique which is based on the use of nonlinear local rules. This technique allows that certain nonlinearities satisfying a sector bounded condition remain in the T-S fuzzy model representation, reducing number of fuzzy rules. Particularly, the digital implementation of dynamic compensators is addressed in this paper considering an FPGA development board. HIL simulations are applied to demonstrate the advantages of the nonlinear fuzzy modeling approach.

[1]  Enrico Santi,et al.  FPGA-Based Model Predictive Controller for Direct Matrix Converter , 2016, IEEE Transactions on Industrial Electronics.

[2]  Gang Feng,et al.  Analysis and Synthesis of Fuzzy Control Systems , 2010 .

[3]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[4]  Youyi Wang,et al.  Output Feedback Fuzzy Controller Design With Local Nonlinear Feedback Laws for Discrete-Time Nonlinear Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Marcelo C. M. Teixeira,et al.  Stabilizing controller design for uncertain nonlinear systems using fuzzy models , 1999, IEEE Trans. Fuzzy Syst..

[6]  J. Lauber,et al.  An Efficient Lyapunov Function for Discrete T–S Models: Observer Design , 2012, IEEE Transactions on Fuzzy Systems.

[7]  João Yoshiyuki Ishihara,et al.  Robust H∞ Output Tracking Control for a Class of Nonlinear Systems with Time-Varying Delays , 2014, Circuits Syst. Signal Process..

[8]  Kavita Khare,et al.  Efficient Design and Fpga Implementation of Digital Controller Using Xilinx SysGen® , 2010 .

[9]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Jianbin Qiu,et al.  Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions , 2013, IEEE Transactions on Fuzzy Systems.

[11]  Guang-Hong Yang,et al.  Nonfragile $H_{\infty}$ Filter Design for T–S Fuzzy Systems in Standard Form , 2014, IEEE Transactions on Industrial Electronics.

[12]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[13]  Omar F. Ruiz,et al.  On the Implementation of Advanced Hybrid Controllers of AC/DC Converters , 2017, IEEE Latin America Transactions.

[14]  Reinaldo M. Palhares,et al.  Stability analysis of linear time-varying systems: Improving conditions by adding more information about parameter variation , 2011, Syst. Control. Lett..

[15]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[16]  E. Castelan,et al.  INTERACTIVE SOFTWARE FOR MODELING AND CONTROL OF NONLINEAR SYSTEMS: A T-S FUZZY APPROACH , 2015 .

[17]  G. Borges,et al.  Delay-Dependent Robust Stability Analysis for Time-Delay T–S Fuzzy Systems with Nonlinear Local Models , 2013 .

[18]  Eugênio B. Castelan,et al.  Fuzzy dynamic output feedback control through nonlinear Takagi-Sugeno models , 2015, Fuzzy Sets Syst..

[19]  Eduardo S. Tognetti,et al.  LMI Relaxations for $$\mathcal{H }_{\infty }$$ and $$\mathcal{H }_{2}$$ Static Output Feedback of Takagi–Sugeno Continuous-Time Fuzzy Systems , 2013 .

[20]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[21]  Erik Schaltz,et al.  An Advanced HIL Simulation Battery Model for Battery Management System Testing , 2016, IEEE Transactions on Industry Applications.