A Nested Saturated Second-order Sliding Mode Controller Design

In this paper, a nested saturated second-order sliding mode (SOSM) controller has been constructed based on the saturation technique and geometric method. The proposed controller includes a saturation function, which could change the phase trajectory of the sliding variables under the traditional SOSM algorithms. The geometric method has been used to test the finite-time convergence of the sliding variables and reveal the relations between the control parameters and the shape of the phase trajectory. Finally, a numerical example has been given to validate the effectiveness and feasibility of the proposed method.

[1]  Shihua Li,et al.  Global Stabilization of a Class of Feedforward Systems with Lower-Order Nonlinearities , 2010, IEEE Transactions on Automatic Control.

[2]  Humberto González,et al.  Zoned HVAC control via PDE-constrained optimization , 2015, 2016 American Control Conference (ACC).

[3]  Chunjiang Qian,et al.  A semi-global finite-time convergent observer for a class of nonlinear systems with bounded trajectories , 2012 .

[4]  J. J. Slotine,et al.  Tracking control of non-linear systems using sliding surfaces with application to robot manipulators , 1983, 1983 American Control Conference.

[5]  Zhihong Man,et al.  Non-singular terminal sliding mode control of rigid manipulators , 2002, Autom..

[6]  Jesús Picó,et al.  Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm , 2013, Autom..

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

[8]  Zhigang Zeng,et al.  Robust probabilistic sampling H∞ output tracking control for a class of nonlinear networked systems with multiplicative noises , 2013, J. Frankl. Inst..

[9]  Chunjiang Qian,et al.  A generalised homogeneous solution for global stabilisation of a class of non-smooth upper-triangular systems , 2014, Int. J. Control.

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

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

[12]  Chunjiang Qian,et al.  Global stabilization of inherently non-linear systems using continuously differentiable controllers , 2014 .

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

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

[15]  Xinghuo Yu,et al.  On nonsingular terminal sliding-mode control of nonlinear systems , 2013, Autom..

[16]  Peng Shi,et al.  Robust Constrained Control for MIMO Nonlinear Systems Based on Disturbance Observer , 2015, IEEE Transactions on Automatic Control.

[17]  Wei Xing Zheng,et al.  Nonsmooth stabilization of a class of nonlinear cascaded systems , 2012, Autom..

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

[19]  Humberto González,et al.  Numerical synthesis of pontryagin optimal control minimizers using sampling-based methods , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

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

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

[22]  Leonid M. Fridman,et al.  Super twisting control algorithm for the attitude tracking of a four rotors UAV , 2012, J. Frankl. Inst..

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

[24]  Jean-Jacques E. Slotine,et al.  Tracking control of non-linear systems using sliding surfaces with application to robot manipulators , 1983 .

[25]  Giorgio Bartolini,et al.  A survey of applications of second-order sliding mode control to mechanical systems , 2003 .

[26]  Salah Laghrouche,et al.  Robust and adaptive Higher Order Sliding mode controllers , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[27]  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.