Stable Iterative Correlation-based Tuning algorithm for servo systems

This paper proposes an iterative Correlation-based Tuning (CbT) algorithm which guarantees the control system stability throughout the iterations. The new algorithm is based on a Robbins-Monro procedure which ensures the iterative tuning of controller parameters such that to minimize a cost function expressed as the squared sum of the cross-correlation function between the output error and the reference input. The control system stability is tested using the coprime factor uncertainty of the controller, and the small gain theorem for discrete-time systems is applied. Nonparametric frequency domain models are employed in the calculation of the bounds on systems' gains. A case study concerning the speed control of a nonlinear servo system is included to validate the new stable CbT algorithm, and experimental results are given.

[1]  A. Karimi,et al.  Iterative correlation‐based controller tuning , 2004 .

[2]  Ouassima Akhrif,et al.  Stabilisation and control synthesis of switching systems subject to actuator saturation , 2010, Int. J. Syst. Sci..

[3]  P. Korondi,et al.  Opto-Mechanical Filtering Applied for Orientation and Length Selective Contour Detection , 2007, IECON 2007 - 33rd Annual Conference of the IEEE Industrial Electronics Society.

[4]  Marian P. Kazmierkowski,et al.  DSP-Based Control of Grid-Connected Power Converters Operating Under Grid Distortions , 2011, IEEE Transactions on Industrial Informatics.

[5]  H. Robbins.  A Stochastic Approximation Method , 1951 .

[6]  Z. Johanyák.  Student Evaluation Based On Fuzzy Rule Interpolation , 2010 .

[7]  Igor Škrjanc,et al.  Adaptive law with a new leakage term , 2010 .

[8]  J. Spall.  A stochastic approximation algorithm for large-dimensional systems in the Kiefer-Wolfowitz setting , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[9]  Lin Cong,et al.  Application issues of virtual reference feedback tuning and non-iterative correlation-based tuning , 2010, The 2010 IEEE International Conference on Information and Automation.

[10]  Okyay Kaynak,et al.  Computing Gradient Vector and Jacobian Matrix in Arbitrarily Connected Neural Networks , 2008, IEEE Transactions on Industrial Electronics.

[11]  E. Petriu,et al.  Novel iterative formulation of Correlation-Based Tuning , 2012, 2012 IEEE International Conference on Industrial Technology.

[12]  Heikki Hyötyniemi,et al.  Data-based parameter optimization of dynamic simulation models , 2006 .

[13]  Stefan Preitl,et al.  Stable iterative feedback tuning method for servo systems , 2011, 2011 IEEE International Symposium on Industrial Electronics.

[14]  Tomasz Bartczak,et al.  Comparative Study of Derivative Free Optimization Algorithms , 2011, IEEE Transactions on Industrial Informatics.

[15]  Ljubisa Miskovic,et al.  Iterative correlation-based controller tuning with application to a magnetic suspension system , 2003 .

[16]  Junji Hirai,et al.  Implementation of direct parameters tuning method for multivariable controller using a couple of closed-loop I/O data , 2009, 2009 35th Annual Conference of IEEE Industrial Electronics.

[17]  Hideki Hashimoto,et al.  Trajectory Tracking by TP Model Transformation: Case Study of a Benchmark Problem , 2007, IEEE Transactions on Industrial Electronics.

[18]  Biao Huang,et al.  A data driven subspace approach to predictive controller design , 2001 .

[19]  A. Karimi,et al.  Data‐driven model reference control with asymptotically guaranteed stability , 2011 .

[20]  N. K. Poulsen,et al.  Improving Convergence of Iterative Feedback Tuning , 2009 .

[21]  József K. Tar,et al.  Fuzzy Control System Performance Enhancement by Iterative Learning Control , 2008, IEEE Transactions on Industrial Electronics.

[22]  Kazuhiro Yubai,et al.  Correlation-based direct tuning of MIMO controllers by least-squares and its application to tension-and-speed control apparatus , 2009, 2009 ICCAS-SICE.

[23]  Sudip K. Mazumder,et al.  Primary-Side-Converter-Assisted Soft-Switching Scheme for an AC/AC Converter in a Cycloconverter-Type High-Frequency-Link Inverter , 2011, IEEE Transactions on Industrial Electronics.

[24]  Milos Manic,et al.  Fuzzy Force-Feedback Augmentation for Manual Control of Multirobot System , 2011, IEEE Transactions on Industrial Electronics.

[25]  Dominique Bonvin,et al.  Non-iterative data-driven controller tuning with guaranteed stability: Application to direct-drive pick-and-place robot , 2010, 2010 IEEE International Conference on Control Applications.

[26]  Michel Gevers,et al.  Correlation-based tuning of decoupling multivariable controllers , 2007, Autom..

[27]  Stefan Preitl,et al.  Application of IFT and SPSA to Servo System Control , 2011, IEEE Transactions on Neural Networks.

[28]  Robert R. Bitmead,et al.  Direct iterative tuning via spectral analysis , 2000, Autom..

[29]  Junji Hirai,et al.  Correlation-based direct tuning of 2DOF controller by least squares , 2010, 2010 11th IEEE International Workshop on Advanced Motion Control (AMC).

[30]  Ping Wang,et al.  Design of a Data-Driven Predictive Controller for Start-up Process of AMT Vehicles , 2011, IEEE Transactions on Neural Networks.

[31]  S. Gunnarsson,et al.  A convergent iterative restricted complexity control design scheme , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[32]  Sergio M. Savaresi,et al.  Virtual reference feedback tuning (VRFT): a new direct approach to the design of feedback controllers , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[33]  Daniel Hladek,et al.  MULTI-ROBOT CONTROL SYSTEM FOR PURSUIT-EVASION PROBLEM , 2009 .

[34]  H. Bourles,et al.  A local small gain theorem for discrete-time systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[35]  Plamen P. Angelov,et al.  Adaptive Inferential Sensors Based on Evolving Fuzzy Models , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[36]  Håkan Hjalmarsson,et al.  Iterative feedback tuning—an overview , 2002 .

[37]  Kok-Meng Lee,et al.  Open-Loop Controller Design and Dynamic Characteristics of a Spherical Wheel Motor , 2010, IEEE Transactions on Industrial Electronics.