Smooth second-order sliding mode controller for multivariable mechanical systems

This paper proposes a smooth second-order sliding mode controller for a class of multi-input multi-output mechanical systems with uncertain parameters and external disturbances. Since the control law is smooth, the chattering effect that can occur with non-smooth controllers is reduced. Lyapunov-based theorems are used to prove global and finite-time convergence of the sliding mode controller. Numerical simulations are presented to illustrate the performance of the proposed controller by applying it first to a variable-length pendulum and then to a two-link robotic manipulator. For the robotic manipulator, a detailed comparison is given of the finite-time convergence and chattering properties of the proposed controller, a super-twisting controller and a super-twisting like controller.

[1]  Zheng Wang.  Adaptive smooth second-order sliding mode control method with application to missile guidance , 2017 .

[2]  J. Moreno,et al.  Robust trajectory‐tracking in finite‐time for robot manipulators using nonlinear proportional‐derivative control plus feed‐forward compensation , 2020, International Journal of Robust and Nonlinear Control.

[3]  Hassani Messaoud,et al.  Sliding Mode Control, with Integrator, for a Class of Mimo Nonlinear Systems , 2011 .

[4]  Chutiphon Pukdeboon.  Finite-Time Second-Order Sliding Mode Controllers for Spacecraft Attitude Tracking , 2013 .

[5]  Franck Plestan,et al.  Experimental Comparisons Between Implicit and Explicit Implementations of Discrete-Time Sliding Mode Controllers: Toward Input and Output Chattering Suppression , 2015, IEEE Transactions on Control Systems Technology.

[6]  Xinghuo Yu,et al.  Discrete-Time Terminal Sliding Mode Control Systems Based on Euler's Discretization , 2014, IEEE Transactions on Automatic Control.

[7]  C. Mahanta,et al.  Adaptive integral higher order sliding mode controller for uncertain systems , 2013 .

[8]  Zong-Yao Sun,et al.  Finite-time Controller Design for Four-wheel-steering of Electric Vehicle Driven by Four In-wheel Motors , 2018 .

[9]  Franck Plestan,et al.  Higher order sliding mode control based on integral sliding mode , 2007, Autom..

[10]  Qingling Zhang,et al.  Static output feedback sliding mode control for stochastic descriptor systems , 2016, 2016 Chinese Control and Decision Conference (CCDC).

[11]  Jun Yang,et al.  Design and implementation of continuous finite-time sliding mode control for 2-DOF inertially stabilized platform subject to multiple disturbances. , 2019, ISA transactions.

[12]  Franck Plestan,et al.  Higher order sliding mode control based on optimal approach of an electropneumatic actuator , 2006 .

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

[14]  Xinghuo Yu,et al.  Chattering free full-order sliding-mode control , 2014, Autom..

[15]  Peng Shi,et al.  Sliding Mode Control of Singular Stochastic Markov Jump Systems , 2017, IEEE Transactions on Automatic Control.

[16]  Yuri B. Shtessel,et al.  Smooth second-order sliding modes: Missile guidance application , 2007, Autom..

[17]  M. Hamerlain,et al.  Higher order sliding mode control structure for a scale model autonomous helicopter , 2013, 3rd International Conference on Systems and Control.

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

[19]  Shengyuan Xu,et al.  Global second‐order sliding mode control for nonlinear uncertain systems , 2018, International Journal of Robust and Nonlinear Control.

[20]  Arie Levant,et al.  Principles of 2-sliding mode design , 2007, Autom..

[21]  Vadim I. Utkin,et al.  Conventional and high order sliding mode control , 2020, J. Frankl. Inst..

[22]  Vadim I. Utkin,et al.  Discussion Aspects of High-Order Sliding Mode Control , 2016, IEEE Transactions on Automatic Control.

[23]  Arie Levant,et al.  Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence , 2001, IEEE Trans. Autom. Control..

[24]  Antonios Armaou,et al.  Fault‐tolerant process control , 2012 .

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

[26]  Alessandro Astolfi,et al.  Nonlinear and adaptive control with applications , 2008 .

[27]  Suwat Kuntanapreeda,et al.  Finite-time synchronization of hyperchaotic systems based on feedback passivation , 2020 .

[28]  Christopher Edwards,et al.  Sliding Mode Control and Observation , 2013 .

[29]  May-Win L. Thein,et al.  Quasi-Continuous Higher Order Sliding-Mode Controllers for Spacecraft-Attitude-Tracking Maneuvers , 2010, IEEE Transactions on Industrial Electronics.

[31]  M. Basin,et al.  Multivariable continuous fixed-time second-order sliding mode control: design and convergence time estimation , 2017 .

[32]  K. Benmahammed,et al.  An adaptive finite‐time stable control law for manipulator robots with unknown parameters , 2021, International Journal of Robust and Nonlinear Control.

[33]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

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

[35]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[36]  Zhihong Man,et al.  Continuous finite-time control for robotic manipulators with terminal sliding mode , 2003, Autom..

[37]  Zhiyong Geng,et al.  Finite-time attitude control: a finite-time passivity approach , 2015, IEEE/CAA Journal of Automatica Sinica.

[38]  Alessandro Pisano,et al.  On the multi‐input second‐order sliding mode control of nonlinear uncertain systems , 2012 .

[39]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[40]  Michael Defoort,et al.  A novel higher order sliding mode control scheme , 2009, Syst. Control. Lett..

[41]  Danxu Zhang,et al.  Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises , 2018, Int. J. Syst. Sci..

[42]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[43]  Jaime A. Moreno,et al.  Strict Lyapunov Functions for the Super-Twisting Algorithm , 2012, IEEE Transactions on Automatic Control.

[44]  Yeung Yam,et al.  Sliding Mode Control for Discrete-Time Systems With Markovian Packet Dropouts , 2017, IEEE Transactions on Cybernetics.

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

[46]  Xinghuo Yu,et al.  On the Discrete-Time Integral Sliding-Mode Control , 2007, IEEE Transactions on Automatic Control.

[47]  Changyun Wen,et al.  Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations , 2008 .

[48]  Marko Bacic,et al.  Model predictive control , 2003 .

[49]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[50]  Michel Zasadzinski,et al.  High order iterative learning control to solve the trajectory tracking problem for robot manipulators using Lyapunov theory , 2018, Trans. Inst. Meas. Control.

[51]  Yury Orlov,et al.  Robust stabilization of infinite-dimensional systems using sliding-mode output feedback control , 2004 .

[52]  Bing Huang,et al.  Integral sliding mode control for Euler‐Lagrange systems with input saturation , 2018 .

[53]  Cong Zhang,et al.  Finite-time convergence of an nth nonlinear system with unmatched disturbance and its application in integrated guidance and control system , 2018, Int. J. Model. Simul. Sci. Comput..

[54]  Jianhua Zhang,et al.  Sliding mode control for discrete time switched systems with uncertain parameters and time delay , 2014, 2015 7th International Conference on Modelling, Identification and Control (ICMIC).

[55]  Vadim I. Utkin,et al.  Adaptive sliding mode control in discrete-time systems , 1995, Autom..

[56]  Vadim I. Utkin,et al.  Road Map for Sliding Mode Control Design , 2020 .