Self-tuning in integral sliding mode control with a Levenberg–Marquardt algorithm

In high-precision motion systems, tracking often comes with the problem of overshoot or poor settling behavior. To deal with this problem, a sliding mode controller with saturated integrator is studied. For large servo signals, sufficiently removed from the sliding surface, the controller will operate in PD mode. This limits the integrator buffer, and thus the overshoot. At the sliding surface (for small servo signals) the controller operates in PID mode with the aim to avoid steady-state error. Tuning of the controller parameters: the switching gain and the saturation length, strongly affects the tracking performance. For this reason, a self-tuning method is proposed. In the method, the required gradients are partly computed using models of the system and the controller. For the remaining part, sampled data is used to deal with disturbances and model uncertainties. With a Levenberg–Marquardt algorithm numerical problems associated with the gradient computations are avoided. The sliding mode controller with optimized parameters is implemented on an industrial wafer scanner to improve throughput during the wafer stage (chuck) exchange.

[1]  Hassan K. Khalil,et al.  Regulation of nonlinear systems using conditional integrators , 2005 .

[2]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[3]  Qingwei Li,et al.  Adaptive sliding mode control for a class of uncertain nonlinear systems , 2009, 2009 4th IEEE Conference on Industrial Electronics and Applications.

[4]  Chih-Jer Lin,et al.  Observer-based robust controller design and realization of a gantry stage , 2011 .

[5]  Hassan K. Khalil,et al.  Lyapunov redesign approach to output regulation of nonlinear systems using conditional servocompensators , 2010, 2008 American Control Conference.

[6]  Martin Horn,et al.  Application of Higher Order Sliding-Mode Concepts to a Throttle Actuator for Gasoline Engines , 2009, IEEE Transactions on Industrial Electronics.

[7]  Hector Puebla,et al.  High Order Sliding Mode Control for Suppression of Nonlinear Dynamics in Mechanical Systems with Friction , 2011 .

[8]  Stefano Di Gennaro,et al.  Discrete time sliding mode control with application to induction motors , 2008, Autom..

[9]  Metin Gokasan,et al.  High order sliding mode control of a space robot manipulator , 2011, Proceedings of 5th International Conference on Recent Advances in Space Technologies - RAST2011.

[10]  Yi Zhang,et al.  Improved integral fuzzy sliding mode control for a class of nonlinear uncertain systems , 2011, Proceedings of the 30th Chinese Control Conference.

[11]  Hassan K. Khalil,et al.  Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators , 2005, Autom..

[12]  Huann-Keng Chiang,et al.  Second-order sliding mode control for a magnetic levitation system , 2011, 2011 8th Asian Control Conference (ASCC).

[13]  Lon-Chen Hung,et al.  Design of self-tuning fuzzy sliding mode control for TORA system , 2007, Expert Syst. Appl..

[14]  Johari Halim Shah Osman,et al.  A class of proportional-integral sliding mode control with application to active suspension system , 2004, Syst. Control. Lett..

[15]  S. Seshagiri,et al.  On introducing integral action in sliding mode control , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[16]  Kazuhiro Tsuruta,et al.  High-Speed and High-Precision Position Control Using a Nonlinear Compensator , 2011 .

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

[18]  Hsin-Jang Shieh,et al.  Trajectory tracking of piezoelectric positioning stages using a dynamic sliding-mode control , 2006, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[19]  John Y. Hung,et al.  Variable structure control: a survey , 1993, IEEE Trans. Ind. Electron..

[20]  Wei Wang,et al.  Using second order sliding mode principle to design tracking controller for a kind of piezoelectric actuators , 2010, 2010 2nd International Conference on Advanced Computer Control.

[21]  Ming-Tzu Ho,et al.  Integral sliding mode control for trajectory tracking control of an omnidirectional mobile robot , 2011, 2011 8th Asian Control Conference (ASCC).

[22]  Chun-Ming Huang,et al.  Sliding-mode torque control of a permanent magnet synchronous motor , 2001, 4th IEEE International Conference on Power Electronics and Drive Systems. IEEE PEDS 2001 - Indonesia. Proceedings (Cat. No.01TH8594).

[23]  M. Tomizuka,et al.  Iterative learning control design for synchronization of wafer and reticle stages , 2008, 2008 American Control Conference.

[24]  Kenichiro Nonaka,et al.  Integral sliding mode altitude control for a small model helicopter with ground effect compensation , 2011, Proceedings of the 2011 American Control Conference.

[25]  Qun Zong,et al.  Brief paper: Higher order sliding mode control with self-tuning law based on integral sliding mode , 2010 .

[26]  Elsayed A. Sallam,et al.  Adaptive fuzzy sliding mode control using supervisory fuzzy control for 3 DOF planar robot manipulators , 2011, Appl. Soft Comput..

[27]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[28]  J. C. Clegg.  A nonlinear integrator for servomechanisms , 1958, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[29]  Ling Zhu,et al.  Adaptive neural network PID sliding mode dynamic control of nonholonomic mobile robot , 2010, The 2010 IEEE International Conference on Information and Automation.

[30]  S. Janardhanan.  Relay-free Second Order Sliding Mode Control , 2006, 2006 IEEE International Conference on Industrial Technology.

[31]  Zhiqiang Gao,et al.  An application of nonlinear PID control to a class of truck ABS problems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[32]  Kwanho You,et al.  Augmented sliding-mode control of an ultra-precision positioning system , 2011 .

[33]  Yasemin Vardar,et al.  Self-tuning in sliding mode control of high-precision motion systems , 2013 .

[34]  David W. L. Wang,et al.  Output feedback sliding mode control in the presence of unknown disturbances , 2009, Syst. Control. Lett..

[35]  B. Francis,et al.  A lifting technique for linear periodic systems with applications to sampled-data control , 1991 .

[36]  Qing Li,et al.  Design and Application of Fuzzy Sliding Mode Control in the 3-DOF Helicopter , 2009, 2009 International Workshop on Intelligent Systems and Applications.

[37]  Igor M. Boiko,et al.  Analysis of chattering in sliding mode control systems with continuous boundary layer approximation of discontinuous control , 2011, Proceedings of the 2011 American Control Conference.

[38]  Alessandro Pisano,et al.  Sliding mode control: A survey with applications in math , 2011, Math. Comput. Simul..

[39]  Henk Nijmeijer,et al.  Self-tuning of a switching controller for scanning motion systems , 2012 .

[40]  Hassan K. Khalil,et al.  Robust stabilization of non-minimum phase nonlinear systems using extended high gain observers , 2011, 2008 American Control Conference.

[41]  Helio Mitio Morishita,et al.  Dynamic positioning systems: An experimental analysis of sliding mode control , 2010 .

[42]  Orhan Beker,et al.  Plant with integrator: an example of reset control overcoming limitations of linear feedback , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[43]  Geok Soon Hong,et al.  Improving CNC contouring accuracy by integral sliding mode control , 2010 .

[44]  Youyi Wang,et al.  Discrete-Time Sliding Mode Control With Time-Varying Surface for Hard Disk Drives , 2009, IEEE Transactions on Control Systems Technology.

[45]  Lei Guo,et al.  Cascade Sliding Mode Control for Bicycle Robot , 2010, 2010 International Conference on Artificial Intelligence and Computational Intelligence.

[46]  N. Pariz,et al.  Position control of induction and DC servomotors: a novel adaptive fuzzy PI sliding mode control , 2006, 2006 IEEE Power Engineering Society General Meeting.

[47]  Hassan K. Khalil,et al.  Universal integral controllers with anti-reset windup for minimum phase nonlinear systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[48]  Leila Notash,et al.  Adaptive sliding mode control with uncertainty estimator for robot manipulators , 2010 .

[49]  Hassan K. Khalil,et al.  Robust output regulation of minimum phase nonlinear systems using conditional servocompensators , 2005 .

[50]  Li Ying,et al.  The self-adjustable fuzzy sliding mode control for AC speed drive systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[51]  Nathan van de Wouw,et al.  Variable gain motion control for transient performance improvement , 2012, 2012 American Control Conference (ACC).

[52]  B. Jouvencel,et al.  Using a high order sliding modes for diving control a torpedo autonomous underwater vehicle , 2003, Oceans 2003. Celebrating the Past ... Teaming Toward the Future (IEEE Cat. No.03CH37492).

[53]  Ilyas Eker,et al.  Sliding mode control with PID sliding surface and experimental application to an electromechanical plant. , 2006, ISA transactions.

[54]  Katsuhisa Furuta,et al.  Self-tuning control based on generalized minimum variance criterion for auto-regressive models , 2008, Autom..

[55]  Hiromu Hirai,et al.  Mode switching control design with initial value compensation and its application to head positioning control on magnetic disk drives , 1996, IEEE Trans. Ind. Electron..

[56]  Franck Plestan,et al.  Higher order sliding mode control based on integral sliding mode , 2007, Autom..

[57]  Yung-Yaw Chen,et al.  PD-type vs. PID-type fuzzy controllers , 1992, TENCON'92 - Technology Enabling Tomorrow.

[58]  Hassan K. Khalil,et al.  On the Transient Response of a Nonlinear Output Regulator , 2010, IEEE Transactions on Automatic Control.

[59]  Dale E. Seborg,et al.  Relative gain array analysis for uncertain process models , 2002 .

[60]  C. Y. Chen,et al.  Adaptive Sliding Mode Control with PID Tuning for Uncertain Systems , 2008, Eng. Lett..

[61]  Shin-Hung Chang,et al.  Sliding mode control with self-tuning law for uncertain nonlinear systems. , 2008, ISA transactions.

[62]  Christopher Edwards,et al.  Sliding mode control for time-varying delayed systems based on a reduced-order observer , 2010, Autom..