Fractional power rate reaching law for augmented sliding mode performance

Abstract High-frequency control switching, chattering, limits the practical application of sliding mode controllers. This paper proposes an enhanced reaching law, viz., Fractional Power Rate Reaching Law (FPRRL), for the design of sliding mode controllers to mitigate the chattering problem. Controller gains are selected to accommodate variations in switching function dynamically to prevent over-actuation near the sliding surface, which is the primary reason for chattering. Chattering mitigation is achieved without compromising other attributes of sliding mode control. Performance enhancements in the attributes, viz., reaching time, robustness, and reduced chattering magnitude have been established through the methodical analysis of the new reaching law. The proposed control strategy is then bench-marked with the state of the art reaching law methods through simulations by considering a twin-rotor MIMO system control problem.

[1]  Leonid M. Fridman,et al.  An averaging approach to chattering , 2001, IEEE Trans. Autom. Control..

[2]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[3]  Marco Caponigro,et al.  Regularization of Chattering Phenomena via Bounded Variation Controls , 2013, IEEE Transactions on Automatic Control.

[4]  Yuri B. Shtessel,et al.  Chattering Analysis of HOSM Controlled Systems: Frequency Domain Approach , 2017, IEEE Transactions on Automatic Control.

[5]  Yannick Aoustin,et al.  Finite Time Stabilization of a Perturbed Double Integrator—Part I: Continuous Sliding Mode-Based Output Feedback Synthesis , 2011, IEEE Transactions on Automatic Control.

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

[7]  A. Levant.  Sliding order and sliding accuracy in sliding mode control , 1993 .

[8]  Vadim I. Utkin,et al.  Chattering suppression methods in sliding mode control systems , 2007, Annu. Rev. Control..

[9]  Xiongxiong He,et al.  Adaptive fixed‐time fault‐tolerant control for rigid spacecraft using a double power reaching law , 2019, International Journal of Robust and Nonlinear Control.

[10]  Charles J. Fallaha,et al.  Sliding-Mode Robot Control With Exponential Reaching Law , 2011, IEEE Transactions on Industrial Electronics.

[11]  Maarouf Saad,et al.  Sliding Mode Control of PMSG Wind Turbine Based on Enhanced Exponential Reaching Law , 2016, IEEE Transactions on Industrial Electronics.

[12]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

[13]  Susy Thomas,et al.  Power rate exponential reaching law for enhanced performance of sliding mode control , 2017 .

[14]  Alexander S. Poznyak,et al.  Reaching Time Estimation for “Super-Twisting” Second Order Sliding Mode Controller via Lyapunov Function Designing , 2009, IEEE Transactions on Automatic Control.

[15]  Wilfrid Perruquetti,et al.  Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems , 2003, Autom..

[16]  Susy Thomas,et al.  Sliding mode controller design for MIMO nonlinear systems: A novel power rate reaching law approach for improved performance , 2018, J. Frankl. Inst..

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

[18]  Andrzej Bartoszewicz,et al.  A new reaching law for sliding mode control of continuous time systems with constraints , 2015 .

[19]  Weibing Gao,et al.  Variable structure control of nonlinear systems: a new approach , 1993, IEEE Trans. Ind. Electron..

[20]  Stanislav V. Emelyanov,et al.  Variable-Structure Control Systems , 1995 .

[21]  Vadim I. Utkin,et al.  On multi-input chattering-free second-order sliding mode control , 2000, IEEE Trans. Autom. Control..

[22]  B. Draenovi.  The invariance conditions in variable structure systems , 1969 .

[23]  Masayoshi Tomizuka,et al.  Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems , 1996, IEEE Trans. Autom. Control..

[24]  G. Bartolini,et al.  Chattering avoidance by second-order sliding mode control , 1998, IEEE Trans. Autom. Control..

[25]  Mingxuan Sun,et al.  Adaptive Nonsingular Fixed-Time Attitude Stabilization of Uncertain Spacecraft , 2018, IEEE Transactions on Aerospace and Electronic Systems.

[26]  Chin-Wang Tao,et al.  Design of a parallel distributed fuzzy LQR controller for the twin rotor multi-input multi-output system , 2010, Fuzzy Sets Syst..

[27]  U. Itkis,et al.  Control systems of variable structure , 1976 .

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