Robust Adaptive Inverse Control of a Class of Nonlinear Systems With Prandtl-Ishlinskii Hysteresis Model

The exhibition of hysteresis effects in smart actuators highly affect the accuracy and stability of the control systems. The common approaches are the use of inverse hysteresis as a compensator. However, when the hysteresis is unknown, the inverse compensation will introduce notably inverse compensation error with an estimated inverse construction. The challenge is that the expression for the inverse compensation error is required for stability analysis. In this note, by developing an error expression of the inverse compensation, an inverse based robust adaptive control approach is proposed, leading to a strict stability proof. Simulation results show that the proposed controller has certain advantages comparing with the one without using an inverse compensator.

[1]  Shuzhi Sam Ge,et al.  Adaptive Neural Control for a Class of Uncertain Nonlinear Systems in Pure-Feedback Form With Hysteresis Input , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Mohammad Al Janaideh,et al.  Inverse compensation error of the Prandtl-Ishlinskii model , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[3]  Ying Zhang,et al.  Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis , 2004, IEEE Trans. Autom. Control..

[4]  Xinkai Chen,et al.  Adaptive control of system involving complex hysteretic nonlinearities: a generalised Prandtl–Ishlinskii modelling approach , 2009, Int. J. Control.

[5]  Gang Tao,et al.  Adaptive control of plants with unknown hystereses , 1995 .

[6]  Qingsong Xu,et al.  Rate-Dependent Hysteresis Modeling and Control of a Piezostage Using Online Support Vector Machine and Relevance Vector Machine , 2012, IEEE Transactions on Industrial Electronics.

[7]  Tieshan Li,et al.  Adaptive Output Feedback Control of Uncertain Nonlinear Systems With Hysteresis Nonlinearity , 2012, IEEE Transactions on Automatic Control.

[8]  Kam K. Leang,et al.  Accounting for hysteresis in repetitive control design: Nanopositioning example , 2012, Autom..

[9]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis , 2000, IEEE Trans. Autom. Control..

[10]  Xinkai Chen,et al.  Adaptive Control for Uncertain Continuous-Time Systems Using Implicit Inversion of Prandtl-Ishlinskii Hysteresis Representation , 2010, IEEE Transactions on Automatic Control.

[11]  Frank L. Lewis,et al.  Adaptive Control of Nonsmooth Dynamic Systems , 2001 .

[12]  C. Su,et al.  An Analytical Generalized Prandtl–Ishlinskii Model Inversion for Hysteresis Compensation in Micropositioning Control , 2011, IEEE/ASME Transactions on Mechatronics.

[13]  Xinkai Chen,et al.  Adaptive Control for Plants in the Presence of Actuator and Sensor Uncertain Hysteresis , 2011, IEEE Transactions on Automatic Control.

[14]  R. Iyer,et al.  Control of hysteretic systems through inverse compensation , 2009, IEEE Control Systems.

[15]  John S. Baras,et al.  Adaptive identification and control of hysteresis in smart materials , 2005, IEEE Transactions on Automatic Control.

[16]  Subhash Rakheja,et al.  Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis , 2005, IEEE Transactions on Automatic Control.

[17]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations , 2006, Autom..

[18]  K. Kuhnen,et al.  Inverse control of systems with hysteresis and creep , 2001 .

[19]  Shuzhi Sam Ge,et al.  Adaptive Neural Control for a Class of Nonlinear Systems With Uncertain Hysteresis Inputs and Time-Varying State Delays , 2009, IEEE Transactions on Neural Networks.

[20]  Pavel Krejčí,et al.  Hysteresis, convexity and dissipation in hyperbolic equations , 1996 .

[21]  Hassan K. Khalil,et al.  Control of systems with hysteresis via servocompensation and its application to nanopositioning , 2010, Proceedings of the 2010 American Control Conference.