Singular Perturbation Approach to Nonlinear Control System Design and Their Applications

The set of displayed references presents the up-to-date coverage of fundamental issues and recent research developments in design of nonlinear control systems based on the singular perturbation approach. An analytical uniform design methodology of continuous-time or discrete-time nonlinear control system design which guarantees desired transient performances in the presence of plant parameter variations and unknown external disturbances is discussed. The approach is based on an application of a dynamical control law with derivatives of the output signal in feedback loop. A distinctive feature of the control systems thus designed is that two-time-scale motions are artificially forced in the closed-loop system by selection of controller parameters. Stability conditions imposed on the fast and slow modes, and a sufficiently large mode separation rate, can ensure that the full-order closed-loop system achieves desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and plant's parameter variations. The method of singular perturbation is used to analyze the closed-loop system properties.
Valery D. Yurkevich, Design of Nonlinear Control Systems with the Highest Derivative in Feedback, World Scientific Publishing Co., 2004, 352 p. (ISBN 9812388990).

Yurkevich V.D. (2011). PI/PID Control for Nonlinear Systems via Singular Perturbation Technique, Advances in PID Control, Valery D. Yurkevich (Ed.), ISBN: 978-953-307-267-8, InTech, pp.113-142.

Yurkevich V.D. Singular Perturbation Approach to Pulse-Width Modulated Control in Nonlinear Dynamical Systems, In: Proc. of the Virtual Control Conference VCC-10, 22-nd September, 2010

Yurkevich V.D. 2009 AGNFCS - Pulse-Width Modulated Control via Singular Perturbation for a Spacecraft Attitude Maneuver, In: Preprints of IFAC Workshop Aerospace Guidance, Navigation and Flight Control Systems (AGNFCS' 09), Samara, RUSSIA, June 30 - July 2, 2009.

Yurkevich V.D. PID Adaptive Control Design Based on Singular Perturbation Technique: A Flight Control Example, In: Preprints of IFAC Workshop Aerospace Guidance, Navigation and Flight Control Systems (AGNFCS' 09), Samara, RUSSIA, June 30 - July 2, 2009.

Yurkevich V.D. Adaptive Gain Tuning in Nonlinear Control Systems Designed Via Singular Perturbation Technique, In: Proceedings of the 18th Int. Conf. on Control Applications Part of the 3rd IEEE Multi-conference on Systems and Control, Saint Petersburg, Russia, July 8-10, 2009, pp.37- 42.

Yurkevich V.D. Adaptive Output Feedback Control of Nonlinear SISO Systems via Singular Perturbation Technique, In: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, P.R. China, December 16-18, 2009, pp.3495- 3500.

V. Gavriloiu, V. Yurkevich, K. Khorasani Design of Dynamic Nonlinear Control Techniques for Flexible-Link Manipulators, Solid State Phenomena Vol.144. Mechatronic Systems and Materials II, 2009, pp.250-256. (ISSN: 1662-9779)

Yurkevich V.D. PI and PID Controller Design for Nonlinear Systems in the Presence of a Time Delay via Singular Perturbation Technique, In: Proc. of the 9-th Int. Conf. on Actual Problems of Electronic Instrument Engineering (APEIE-2008), Novosibirsk, Russia, 2008, Vol.1, pp.168-174.

Sanjib Kumar Sahoo, Sanjib Kumar Panda, Jian-Xin Xu, and Valery D. Yurkevich. Direct Torque Tracking PI-Controller Design for Switched Reluctance Motor Drive using Singular Perturbation Method, In: Proc. of the 17-th IFAC World Congress, Seoul, Korea, 6-11 July, 2008, pp. 3322-3327.

Yurkevich V.D., Hwang Kab-Ju Output Regulation of Uncertain Nonaffine in Control Systems via Singular Perturbation Technique, In: Proc. of the 17-th IFAC World Congress, Seoul, Korea, 6-11 July, 2008, pp. 13133-13138.

Yurkevich V.D., G.S.Zinoviev PI Controller Design via Singular Perturbation Technique for AC-AC Buck-Boost Converter, In: Proc. of the 3-rd. Int. Forum on Strategic Technologies (IFOST-2008), Novosibirsk-Tomsk, Russia, 23-29 June 2008, pp. 583-587.

Yurkevich V.D. Bifurcations Caused by Non-affinity of Singularly Perturbed Control Systems, In: Proc. of the 3-rd. Int. Forum on Strategic Technologies (IFOST-2008), 23-29 June 2008, Novosibirsk-Tomsk, Russia, pp.482-486.

Xinhui Wu, Sanjib Kumar Panda, Jianxin Xu, and Valery D. Yurkevich. Dual Frame Cascaded Controller Design for Three Phase PWM Boost Rectifier Under Generalized Supply Voltage Conditions Using Singular Perturbation Method, In: Proc. of 39th IEEE Power Electronics Specialists Conference (PESC 2008), Rhodes, Greece, 15-19 June 2008, pp.731-737.

Becerril-Arreola R., Aghdam A.G., and Yurkevich V.D. Decentralised two-time-scale motions control based on generalised sampling, IET Control Theory and Applications, 2007, 1 (5), pp. 1477-1486.

Arreola R.H.B., Aghdam A.G., Yurkevich V.D. Decentralised two-time-scale motions control based on generalised sampling (Author Correction), IET Control Theory Appl., 2007, 1 (6), pp.1736 - 1736.

Hwang Kab-Ju, Yurkevich V.D. Vehicle Following Longitudinal Decentralized Feedback Control Based on Two-Time-Scale Motions, In: Proc. of the 1-st. Int. Forum on Strategic Technology "e-Vehicle Technology" (IFOST-2006), Oct. 18-20, 2006, Ulsan, Korea, pp.5-9.

Yurkevich V.D. PID controller design for nonlinear systems based on two-time-scale motions, In: Proc. of the 8-th Int. Conf. on Actual Problems of Electronic Instrument Engineering (APEIE-2006), Novosibirsk, Russia, 2006, Vol.1, pp.251-258.

Yurkevich V.D. A Unified Approach to Two-Time-Scale Control Systems Design: A Tutorial, In: Proc. of the 2nd IASTED Int. Multi-Conference Automation, Control and Applications (ACIT-ACA), June 20-24, 2005, Novosibirsk, Russia, pp. 314-319.

Yurkevich V.D. Switching controller for buck-boost converter with inverting topology, In: Preprints of the 16-th IFAC World Congress, Prague, Czech Republic, 4-8 July, 2005.

Yurkevich V.D. Control of parabolic distributed systems with delay in feedback loop, In: Preprints of the 16-th IFAC World Congress, Prague, Czech Republic, 4-8 July, 2005.

Yurkevich V.D. Design of Controller for Buck-Boost Converter, In Proc. of the 9th Korean-Russian Int. Symposium on Science & Technology (KORUS 2005), June 26- July 2, 2005, Novosibirsk, Russia, pp.741-745.

Yurkevich V.D. Aircraft Pitch Attitude Control in Presence of Uncertain Aerodynamics, In Proc. of the 9th Korean-Russian Int. Symposium on Science & Technology (KORUS 2005), June 26- July 2, 2005, Novosibirsk, Russia, pp.746-748.

Yurkevich V.D. Parabolic Distributed Parameter Control Systems with Two-Time-Scale Motions, In: Proc. of the Int. Conf. "Physics and Control" (PhysCon 2005), August 24-26, 2005, St.Petersburg, Russia.

Gavriloiu V., Yurkevich V., Khorasani K., A Novel Dynamic Control Design Scheme for Flexible-Link Manipulators, In: Proc. of IEEE Conference on Control Applications, (CCA), Toronto, ON, Canada, 28-31 August 2005. N.Y., 2005. pp. 595-600.

Yurkevich V.D. Controller Design in Presence of Non-Smooth Nonlinearity: A Flight Control Example, In: Preprints of the 16-th IFAC Symposium on Automatic Control in Aerospace (ACA'2004), St.Petersburg, Russia, June 14-18, 2004, Vol.1, pp.501-506.

Becerril R., Aghdam A.G., and Yurkevich V.D. Decentralized Two-Time-Scale Motions Control with Generalized Sampled-Data Hold Functions, In: Proceedings of the American Control Conference, ACC-2004, June 30 - July 2, 2004, Boston, USA, pp.3369-3374.

Tudoroiu N., Khorasani K., Yurkevich V. Robust Two-Time Scale Control System Design for Reactive Ion Etching System, In: Proc. of European Control Conf. ECC 2003, 1 - 4 September, 2003, University of Cambridge, Cambridge, UK.

Tudoroiu K., Yurkevich V., Khorasani N. Discrete-Time Control System Design for a Reactive Ion Etching (RIE) System, In: Proc. of Int. Conf. "'Physics and Control", 20-22 Aug., 2003, St.-Petersburg, Russia.

Yurkevich V.D. Design of Digital MIMO Control Systems with Two-Time-Scale Motions, In: Proc. of the 15-th IFAC World Congress, Barcelona, Spain, 21-26 July, 2002.

Yurkevich V.D., Shatalov B.V. Tracking Digital Controller for Robot Manipulator, In: Preprints of the 5-th IFAC Symposium on Nonlinear Control Systems - NOLCOS'01, St.Petersburg, Russia, July 4-6, 2001, Vol.2, pp.526-531.

Yurkevich V.D. Universal Digital Controller for MIMO Continuous Plants with Uncertainty, In: Proc. of UKACC Int. Conf. on Control - 2000. University of Cambridge, UK, 4-7th Sept., 2000.

Yurkevich V.D., Blachuta M.J., and Wojciechowski K. Design of the universal digital flight controller for an aircraft with not exactly known parameters, In: Proc. of the 3rd IFAC Symposium on Robust Control Design (ROCOND-2000), Prague, Czech Republic, 21-23 June 2000, Vol.2.

Yurkevich V.D. Robust Two-Time-Scale Discrete-Time System Design, In: Preprints of the 14-th World Congress IFAC'99, Beijing, China, 1999, Vol.G, pp.343-348.

Blachuta M.J., V.D. Yurkevich, and Wojciechowski K. Robust quasi NID aircraft 3D flight control under sensor noise, In: Int. Journal "Kybernetika", 1999, Vol.35, No.5, pp.637-650.

Yurkevich V.D., M.J.Blachuta, and Wojciechowski K. Robust digital controller design for MIMO non-linear time-varying systems, In: Preprints of the 4-th IFAC Symposium on Nonlinear Control Systems Design (NOLCOS'98), Enschede, The Netherlands, 1998, Vol.3, pp.854-859.

Blachuta M.J., V.D. Yurkevich, and Wojciechowski K. Design of analog and digital aircraft flight controllers based on dynamic contraction method, In: A Collection of Technical Papers. AIAA Guidance, Navigation and Control Conference, 97'GN&C, New Orleans, LA, August 11-13, 1997, Part 3, pp.1719-1729.

Yurkevich V.D. Decoupling of uncertain continuous systems: Dynamic contraction method, In: Proc. of the 34-th IEEE Conference on Decision and Control, New Orleans, Louisiana, 1995, Vol.1, pp.196-201.

Yurkevich V.D. A new approach to design of control systems under uncertainty: dynamic contraction method, In: Preprints of the 3-rd IFAC Symposium on Nonlinear Control Systems Design (NOLCOS'95), Tahoe City, California, 1995, Vol.2, pp.443-448.


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