Robust observer-based adaptive fuzzy sliding mode controller

Abstract In this paper, a new observer-based adaptive fuzzy integral sliding mode controller is proposed based on the Lyapunov stability theorem. The plant is subjected to a square-integrable disturbance and is assumed to have mismatch uncertainties both in state- and input-matrices. Based on the classical sliding mode controller, the equivalent control effort is obtained to satisfy the sufficient requirement of sliding mode controller and then the control law is modified to guarantee the reachability of the system trajectory to the sliding manifold. In order to relax the norm-bounded constrains on the control law and solve the chattering problem of sliding mode controller, a fuzzy logic inference mechanism is combined with the controller. An adaptive law is then introduced to tune the parameters of the fuzzy system on-line. Finally, for evaluating the controller and the robust performance of the closed-loop system, the proposed regulator is implemented on a real-time mechanical vibrating system.

[1]  A. Keane,et al.  Stochastic Reduced Basis Methods , 2002 .

[2]  H. Durrant-Whyte,et al.  Robust sliding mode control with application , 1999 .

[3]  Robert J. Bernhard,et al.  Measurement of the Statistical Variation of Structural-Acoustic Characteristics of Automotive Vehicles , 1993 .

[4]  Christian Soize,et al.  Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies , 2008 .

[5]  Wen-Jun Cao,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Trans. Autom. Control..

[6]  Seyyed M. Hasheminejad,et al.  Active vortex-induced vibration control of a circular cylinder at low Reynolds numbers using an adaptive fuzzy sliding mode controller , 2014 .

[7]  Wei-Song Lin,et al.  Synthesis of upper-triangular non-linear systems with marginally unstable free dynamics using state-dependent saturation , 1999 .

[8]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .

[9]  Andy J. Keane,et al.  Hybridization of stochastic reduced basis methods with polynomial chaos expansions , 2006 .

[10]  C Soize,et al.  Maximum entropy approach for modeling random uncertainties in transient elastodynamics. , 2001, The Journal of the Acoustical Society of America.

[11]  Chaouki Mnasri,et al.  LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems , 2011, Int. J. Appl. Math. Comput. Sci..

[12]  Tamara Nestorović,et al.  Optimal actuator and sensor placement based on balanced reduced models , 2013 .

[13]  Atta Oveisi,et al.  Active vibration control of an arbitrary thick smart cylindrical panel with optimally placed piezoelectric sensor/actuator pairs , 2016 .

[14]  Yuri B. Shtessel,et al.  New methodologies for adaptive sliding mode control , 2010, Int. J. Control.

[15]  Frank Fahy.  Foundations Of Engineering Acoustics , 2000 .

[16]  Sondipon Adhikari,et al.  Experimental case studies for uncertainty quantification in structural dynamics , 2009 .

[17]  Rong-Jong Wai,et al.  Adaptive fuzzy sliding-mode control for electrical servo drive , 2004, Fuzzy Sets Syst..

[18]  V. Utkin,et al.  Sliding mode control design based on Ackermann's formula , 1998, IEEE Trans. Autom. Control..

[19]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[20]  Sondipon Adhikari,et al.  Experimental Data for Uncertainty Quantification , 2005 .

[21]  John Y. Hung,et al.  Variable structure control: a survey , 1993, IEEE Trans. Ind. Electron..

[22]  V. Singh.  Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[23]  Tamara Nestorović,et al.  ROBUST MIXED H2/H8 ACTIVE VIBRATION CONTROLLER IN ATTENUATION OF SMART BEAM , 2014 .

[24]  Atta Oveisi,et al.  Modeling, identification and active vibration control of a funnel-shaped structure used in MRI throat , 2013 .

[25]  Si-Zhao Joe Qin,et al.  An overview of subspace identification , 2006, Comput. Chem. Eng..

[26]  Atta Oveisi,et al.  Adaptive Sliding Mode Vibration Control of a Nonlinear Smart Beam: A Comparison with Self-Tuning Ziegler-Nichols PID Controller , 2013 .

[27]  H. F. Ho,et al.  Adaptive fuzzy sliding mode control design: Lyapunov approach , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[28]  A. Gholami,et al.  A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems , 2012 .

[29]  Wang Yongji,et al.  Robust control of uncertain time delay system: A novel sliding mode control design via LMI , 2006 .

[30]  Hugh F. Durrant-Whyte,et al.  Fuzzy sliding-mode controllers with applications , 2001, IEEE Trans. Ind. Electron..

[31]  Sondipon Adhikari,et al.  Matrix Variate Distributions for Probabilistic Structural Dynamics , 2007 .

[32]  Tamara Nestorović,et al.  Optimal placement of piezoelectric actuators and sensors on a smart beam and a smart plate using multi-objective genetic algorithm , 2015 .

[33]  Han Ho Choi,et al.  LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems , 2007, IEEE Transactions on Automatic Control.