Non-linear sliding surface: towards high performance robust control

The study proposes a method to design a non-linear sliding surface to achieve better transient response for a class of single-input and single-output (SISO) non-linear uncertain system represented in a Brunowsky canonical form. The proposed surface can also be used for linear uncertain systems with matched perturbations. The proposed surface increases the damping ratio of the closed-loop system from its initial low value; as the output approaches the setpoint from its initial value. Initially, the system is lightly damped resulting in a quick response and as the output approaches the setpoint, the system is overdamped to avoid overshoot. The existence of sliding mode is proved and a new control law is proposed to enforce sliding motion. The scheme is able to achieve low overshoot and short settling time simultaneously which is not possible with a linear sliding surface. To ease the synthesis of the non-linear surface, linear matrix inequalities-based algorithm is proposed. Effectiveness of the proposed scheme is illustrated by the simulation results.

[1]  Tong Heng Lee,et al.  Composite nonlinear feedback control for linear systems with input saturation: theory and an application , 2003, IEEE Trans. Autom. Control..

[2]  P. Olver.  Nonlinear Systems , 2013 .

[3]  Andrzej Bartoszewicz,et al.  SMC without the reaching phase - the switching plane design for the third-order system , 2007 .

[4]  José Ángel Acosta,et al.  Non-linear sliding mode surfaces for a class of underactuated mechanical systems [Brief Paper] , 2010 .

[5]  Andrzej Bartoszewicz,et al.  Sliding Mode Control , 2007 .

[6]  Tong Heng Lee,et al.  COMPOSITE NONLINEAR FEEDBACK CONTROL: THEORY AND AN APPLICATION , 2002 .

[7]  Seung-Bok Choi,et al.  A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems , 1994, Autom..

[8]  Avrie Levent,et al.  Robust exact differentiation via sliding mode technique , 1998, Autom..

[9]  Seung-Bok Choi,et al.  Moving switching surfaces for robust control of second-order variable structure systems , 1993 .

[10]  Ben M. Chen,et al.  On Improving Transient Performance in Tracking Control for a Class of Nonlinear Discrete-Time Systems With Input Saturation , 2007, IEEE Transactions on Automatic Control.

[11]  Christopher Edwards,et al.  Sliding mode stabilization of uncertain systems using only output information , 1995 .

[12]  Bijnan Bandyopadhyay,et al.  High-Performance Tracking Controller for Discrete Plant Using Nonlinear Sliding Surface , 2009, IEEE Transactions on Industrial Electronics.

[13]  Seung-Bok Choi,et al.  Moving sliding surfaces for high-order variable structure systems , 1999 .

[14]  Matthew C. Turner,et al.  Non-linear tracking control for multivariable constrained input linear systems , 2000 .

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

[16]  Roland S. Burns,et al.  Advanced control engineering , 2001 .

[17]  B. Bandyopadhyay,et al.  A robust tracking controller for uncertain MIMO plant using non-linear sliding surface , 2009, 2009 IEEE International Conference on Industrial Technology.

[18]  Christopher Edwards,et al.  ROBUST OUTPUT TRACKING USING A SLIDING MODE CONTROLLER/OBSERVER SCHEME , 1996 .

[19]  Bijnan Bandyopadhyay,et al.  Sliding Mode Control Using Novel Sliding Surfaces , 2009 .

[20]  Andrzej Bartoszewicz,et al.  Time-varying sliding modes for second-order systems , 1996 .

[21]  Meir Pachter,et al.  Toward improvement of tracking performance nonlinear feedback for linear systems , 1998 .

[22]  Christopher Edwards,et al.  Sliding mode output feedback controller design using linear matrix inequalities with application to aircraft systems , 2008 .