Certainty equivalence adaptation combined with super-twisting sliding-mode control

ABSTRACT In this paper, a Lyapunov-based control concept is presented that combines variable structure and adaptive control. The considered system class consists of nonlinear single input systems which are affected by matched structured and unstructured uncertainties. Resorting to the certainty equivalence principle, the controller exploits advantages of both the sliding-mode and the adaptive control methodology. It is demonstrated that the gains of the discontinuous control action may be reduced remarkably when compared with pure sliding-mode-based approaches. The efficiency of the presented concept is demonstrated in detail, using results of numerical simulations.

[1]  Alessandro Pisano,et al.  Parameter tuning and chattering adjustment of Super-Twisting sliding mode control system for linear plants , 2012, 2012 12th International Workshop on Variable Structure Systems.

[2]  L. Fridman,et al.  Design of compensators for second order sliding modes , 2010, 2010 11th International Workshop on Variable Structure Systems (VSS).

[3]  Antonella Ferrara,et al.  A combined backstepping/second order sliding mode approach to control a class of nonlinear systems , 1996, Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS'96 -.

[4]  Liu Hsu,et al.  Variable structure model reference adaptive control using only input and output measurements , 1989 .

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

[6]  Martin Horn,et al.  Cascaded sliding-mode control of permanent magnet synchronous motors , 2012, 2012 12th International Workshop on Variable Structure Systems.

[7]  Yuri B. Shtessel,et al.  Super-twisting adaptive sliding mode control: A Lyapunov design , 2010, 49th IEEE Conference on Decision and Control (CDC).

[8]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[9]  Martin Horn,et al.  Lyapunov-design for a super-twisting sliding-mode controller using the certainty-equivalence principle , 2015 .

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

[11]  Jaime A. Moreno,et al.  A Lyapunov approach to second-order sliding mode controllers and observers , 2008, 2008 47th IEEE Conference on Decision and Control.

[12]  Leonid M. Fridman,et al.  Cascade control of PM-DC drives via second-order sliding mode technique , 2008, 2008 International Workshop on Variable Structure Systems.

[13]  Sarah K. Spurgeon,et al.  Tuning rules for second order sliding mode based output feedback synthesis , 2012, 2012 12th International Workshop on Variable Structure Systems.

[14]  Yuri B. Shtessel,et al.  Adaptive twist sliding mode control: A Lyapunov design , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  Franck Plestan,et al.  Adaptive sliding mode control for an electropneumatic actuator , 2010, 2010 11th International Workshop on Variable Structure Systems (VSS).

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

[17]  Lyapunov design of adaptive super-twisting controller applied to a pneumatic actuator , 2011 .

[18]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[19]  Leonid M. Fridman,et al.  Analysis of Chattering in Systems With Second-Order Sliding Modes , 2007, IEEE Transactions on Automatic Control.

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

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

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

[23]  Antonella Ferrara,et al.  Properties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems , 2000, IEEE Trans. Autom. Control..

[24]  H. Sira-Ramirez,et al.  Adaptive dynamical sliding mode control via backstepping , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[25]  Yuri B. Shtessel,et al.  A novel adaptive-gain supertwisting sliding mode controller: Methodology and application , 2012, Autom..