Adaptive sliding mode control for a class of MIMO nonlinear systems with uncertainties

Abstract This paper proposes an adaptive scheme of designing sliding mode control (SMC) for affine class of multi-input multi-output (MIMO) nonlinear systems with uncertainty in the systems dynamics and control distribution gain. The proposed adaptive SMC does not require any a priori knowledge of the uncertainty bounds and therefore offers significant advantages over the non-adaptive schemes of SMC design. The closed loop stability conditions are derived based on Lyapunov theory. The effectiveness of the proposed approach is demonstrated via simulations considering an example of a two-link robot manipulator and has been found to be satisfactory.

[1]  A. Isidori.  Nonlinear Control Systems , 1985 .

[2]  Elbrous M. Jafarov.  Robust sliding mode controllers design techniques for stabilization of multivariable time-delay systems with parameter perturbations and external disturbances , 2005, Int. J. Syst. Sci..

[3]  Alessandro Pisano,et al.  Sliding mode control: A survey with applications in math , 2011, Math. Comput. Simul..

[4]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[5]  Lin Li,et al.  Second-order nonsingular terminal sliding mode control of uncertain MIMO linear systems , 2006, 2006 1st International Symposium on Systems and Control in Aerospace and Astronautics.

[6]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[7]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[8]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[9]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[10]  W.-S. Lin,et al.  Robust adaptive sliding mode control using fuzzy modelling for a class of uncertain MIMO nonlinear systems , 2002 .

[11]  Rainer Palm,et al.  Robust control by fuzzy sliding mode , 1994, Autom..

[12]  Sarah K. Spurgeon,et al.  Sliding Mode Control , 1998 .

[13]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[14]  Juntao Fei,et al.  ROBUST ADAPTIVE SLIDING MODE CONTROLLER FOR SEMI-ACTIVE VEHICLE SUSPENSION SYSTEM , 2012 .

[15]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[16]  C. Mahanta,et al.  Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems , 2011 .

[17]  M. Z. Jahromi,et al.  Chattering-free fuzzy sliding mode control in MIMO uncertain systems , 2009 .

[18]  Abdelaziz Hamzaoui,et al.  MIMO second order sliding mode fuzzy type-2 control , 2010, 2010 IEEE International Conference on Systems, Man and Cybernetics.

[19]  Tsung-Chih Lin,et al.  ROBUST ADAPTIVE FUZZY SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN DISCRETE-TIME NONLINEAR SYSTEMS , 2012 .

[20]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[21]  Wei-Song Lin,et al.  Adaptive fuzzy sliding mode controller design for nonlinear MIMO systems , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[22]  R. Bozorgmehry Boozarjomehry,et al.  A fuzzy sliding mode control approach for nonlinear chemical processes , 2009 .

[23]  Youmin Zhang,et al.  Sliding mode fault tolerant control dealing with modeling uncertainties and actuator faults. , 2012, ISA transactions.