Global High-Order Sliding Mode Controller Design Subject to Mismatched Terms: Application to Buck Converter

This paper studies the high-order sliding mode (HOSM) control for a general class of uncertain nonlinear systems. Firstly, the standard sliding mode system is extended to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the system uncertainties in the control channel and relax the well defined relative degree assumption. Secondly, the conventional constant upper bounds assumption is relaxed to time-varying positive functions, which enables us to obtain a global result. For the new sliding mode system under the new global assumption, a novel HOSM controller, that has a simple relay polynomial form, is then proposed. By introducing a new continuous component in the controller, the discontinuous component of the controller only needs to be selected to suppress the uncertainties and thus a controller with minimal discontinuous component magnitude can be implemented. Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented.

[1]  Giorgio Bartolini,et al.  Simplex sliding mode methods for the chattering reduction control of multi-input nonlinear uncertain systems , 2009, Autom..

[2]  Wei Xing Zheng,et al.  Second-Order Sliding Mode Control for Nonlinear Uncertain Systems Bounded by Positive Functions , 2015, IEEE Transactions on Industrial Electronics.

[3]  Ligang Wu,et al.  Event-triggering dissipative control of switched stochastic systems via sliding mode , 2019, Autom..

[4]  Xinghuo Yu,et al.  Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances , 2013, Autom..

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

[6]  Shihua Li,et al.  Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Mismatched Term , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Yuri B. Shtessel,et al.  Continuous Finite-Time Higher Order Output Regulators for Systems With Unmatched Unbounded Disturbances , 2016, IEEE Transactions on Industrial Electronics.

[8]  Leonid M. Fridman,et al.  Variable Gain Super-Twisting Sliding Mode Control , 2012, IEEE Transactions on Automatic Control.

[9]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[10]  Shihua Li,et al.  Output feedback continuous terminal sliding mode guidance law for missile-target interception with autopilot dynamics , 2019, Aerospace Science and Technology.

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

[12]  Shengyuan Xu,et al.  Practically Finite-Time Control for Nonlinear Systems With Mismatching Conditions and Application to a Robot System , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[13]  Di Zhang,et al.  Reduced-Order Observer-Based Sliding Mode Control for Singular Markovian Jump System With Time-Varying Transition Rate , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[15]  Shengyuan Xu,et al.  Global Fixed-Time Consensus Tracking of Nonlinear Uncertain Multiagent Systems With High-Order Dynamics , 2020, IEEE Transactions on Cybernetics.

[16]  Arie Levant,et al.  Quasi-continuous high-order sliding-mode controllers , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[17]  Emmanuel Cruz-Zavala,et al.  Homogeneous High Order Sliding Mode design: A Lyapunov approach , 2017, Autom..

[18]  Shengyuan Xu,et al.  Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application , 2019, Autom..

[19]  Jin Bae Park,et al.  Adaptive Neural Sliding Mode Control of Nonholonomic Wheeled Mobile Robots With Model Uncertainty , 2009, IEEE Transactions on Control Systems Technology.

[20]  Ping Li,et al.  Disturbance Observer-Based Fault-Tolerant Adaptive Control for Nonlinearly Parameterized Systems , 2019, IEEE Transactions on Industrial Electronics.

[21]  Shengyuan Xu,et al.  Robust Fixed-Time Consensus Tracking Control of High-Order Multiple Nonholonomic Systems , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[22]  Wenhai Qi,et al.  Observer-Based Adaptive SMC for Nonlinear Uncertain Singular Semi-Markov Jump Systems With Applications to DC Motor , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Shengyuan Xu,et al.  Further Results on Adaptive Stabilization of High-Order Stochastic Nonlinear Systems Subject to Uncertainties , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[25]  Giorgio Bartolini,et al.  Global stabilization for nonlinear uncertain systems with unmodeled actuator dynamics , 2001, IEEE Trans. Autom. Control..

[26]  Leonid M. Fridman,et al.  Quasi-continuous HOSM control for systems with unmatched perturbations , 2008, 2008 International Workshop on Variable Structure Systems.

[27]  Weihua Gui,et al.  A Novel Asynchronous Control for Artificial Delayed Markovian Jump Systems via Output Feedback Sliding Mode Approach , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[28]  Xinghuo Yu,et al.  Sliding-mode control for systems with mismatched uncertainties via a disturbance observer , 2011, IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society.

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

[30]  Arie Levant,et al.  Simple homogeneous sliding-mode controller , 2016, Autom..

[31]  Shengyuan Xu,et al.  Robust output-feedback finite-time regulator of systems with mismatched uncertainties bounded by positive functions , 2017 .

[32]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[33]  Shengyuan Xu,et al.  Composite-Observer-Based Output-Feedback Control for Nonlinear Time-Delay Systems With Input Saturation and Its Application , 2018, IEEE Transactions on Industrial Electronics.

[34]  Zhang Hao,et al.  Synchronization of complex-valued neural network with sliding mode control , 2016 .

[35]  Sing Kiong Nguang,et al.  Stability Analysis of Genetic Regulatory Networks With General Random Disturbances , 2019, IEEE Transactions on NanoBioscience.

[36]  Shihong Ding,et al.  Second-Order Sliding Mode Controller Design Subject to an Upper-Triangular Structure , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[37]  Xinghuo Yu,et al.  Continuous Output Feedback TSM Control for Uncertain Systems With a DC–AC Inverter Example , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  Antonella Ferrara,et al.  Chattering avoidance by second-order sliding mode control , 1998, IEEE Transactions on Automatic Control.

[39]  Shaocheng Tong,et al.  Fuzzy adaptive sliding-mode control for MIMO nonlinear systems , 2003, IEEE Trans. Fuzzy Syst..

[40]  Shengyuan Xu,et al.  Output-Feedback Control for Stochastic Nonlinear Systems Subject to Input Saturation and Time-Varying Delay , 2019, IEEE Transactions on Automatic Control.