Simultaneous automated design of structured QFT controller and prefilter using nonlinear programming

Summary This paper describes a nonlinear programming-based robust design methodology for controllers and prefilters of a predefined structure for the linear time-invariant systems involved in the quantitative feedback theory. This controller and prefilter synthesis problem is formulated as a single optimization problem with a given performance optimization objective and constraints enforcing stability and various specifications usually enforced in the quantitative feedback theory. The focus is set on providing constraints expression that can be used in standard nonlinear programming solvers. The nonlinear solver then computes in a single-step controller and prefilter design parameters that satisfy the prescribed constraints and maximizes the performance optimization objective. The effectiveness of the proposed approach is demonstrated through a variety of difficult design cases like resonant plants, open-loop unstable plants, and plants with variation in the time delay. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Paluri S. V. Nataraj,et al.  An Interval Analysis Algorithm for Automated Controller Synthesis in QFT Designs , 2007 .

[2]  Vishwesh A. Vyawahare,et al.  Real time implementation of robust QFT controller and prefilter for magnetic levitation system , 2015, 2015 International Conference on Industrial Instrumentation and Control (ICIC).

[3]  Alfonso Baños,et al.  Automatic Loop Shaping in QFT Using CRONE Structures , 2008 .

[4]  Constantine Garcia-Sanz,et al.  Wind Energy Systems: Control Engineering Design , 2012 .

[5]  I. Horowitz,et al.  Optimization of the loop transfer function , 1980 .

[6]  Paluri S. V. Nataraj,et al.  Computation of QFT bounds for robust tracking specifications , 2002, Autom..

[7]  A. Hurwitz.  Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt , 1895 .

[8]  Frédéric Benhamou,et al.  Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques , 2006, TOMS.

[9]  Alex M. Andrew,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2002 .

[10]  Paluri S. V. Nataraj,et al.  Automated Synthesis of Fixed Structure QFT Controller using Interval Constraint Satisfaction Techniques , 2008 .

[11]  Isaac Horowitz,et al.  Quantitative feedback design theory : QFT , 1993 .

[12]  P. Dorato,et al.  A historical review of robust control , 1987, IEEE Control Systems Magazine.

[13]  Montserrat Gil-Martínez,et al.  Analytical formulation to compute QFT bounds: The envelope method , 2009 .

[14]  Christopher V. Hollot,et al.  Automatic loop-shaping of QFT controllers via linear programming , 1999 .

[15]  Manuel Berenguel,et al.  Improvements on the computation of boundaries in QFT , 2006 .

[16]  Montserrat Gil-Martínez,et al.  Nonconservative QFT bounds for tracking error specifications , 2012 .

[17]  Mario Garcia-Sanz,et al.  Automatic loop-shaping of QFT robust controllers , 2009, Proceedings of the IEEE 2009 National Aerospace & Electronics Conference (NAECON).

[18]  Luc Jaulin,et al.  Contractor programming , 2009, Artif. Intell..

[19]  Suhada Jayasuriya,et al.  Robust Stability of Plants with Mixed Uncertainties and Quantitative Feedback Theory , 1993, 1993 American Control Conference.

[20]  Gilles Trombettoni,et al.  Inner Regions and Interval Linearizations for Global Optimization , 2011, AAAI.

[21]  M. Araki,et al.  Two-Degree-of-Freedom PID Controllers , 2003 .

[22]  Nikolaos V. Sahinidis,et al.  Global optimization in stabilizing controller design , 2007, J. Glob. Optim..

[23]  Oded Yaniv,et al.  Multi-input/single-output computer-aided control design using the quantitative feedback theory , 1993 .

[24]  Nataraj S. V. Paluri,et al.  Automatic loop shaping in QFT using hybrid optimization and constraint propagation techniques , 2007 .

[25]  P.S.V. Nataraj,et al.  Automatic design of QFT prefilter using interval analysis , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[26]  Suhada Jayasuriya,et al.  A Frequency Domain Criterion for Robustly Stabilizing a Family of Interval Plants , 1992, 1992 American Control Conference.

[27]  Shih-Feng Yang,et al.  Generation of QFT bounds for robust tracking specifications for plants with affinely dependent uncertainties , 2011 .

[28]  Oded Yaniv,et al.  Automatic Loop Shaping of MIMO Controllers Satisfying Sensitivity Specifications , 2006 .

[29]  Eric Walter,et al.  Guaranteed tuning, with application to robust control and motion planning , 1996, Autom..

[30]  Wen-Hua Chen,et al.  Genetic algorithm enabled computer-automated design of QFT control systems , 1999, Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404).

[31]  Paluri S. V. Nataraj,et al.  Implementation of fixed structure QFT prefilter synthesised using interval constraint satisfaction techniques , 2012 .

[32]  Osita D. I. Nwokah,et al.  Analytic Loop Shaping Methods in Quantitative Feedback Theory , 1994 .

[33]  P. S. V. Nataraj,et al.  Optimized and automated synthesis of robust PID controller with quantitative feedback theory , 2015, 2015 International Conference on Industrial Instrumentation and Control (ICIC).

[34]  Wen-Hua Chen,et al.  Automatic loop-shaping in QFT using genetic algorithms , 1998 .

[35]  Gilles Trombettoni,et al.  Upper bounding in inner regions for global optimization under inequality constraints , 2014, J. Glob. Optim..

[36]  V. Kharitonov.  Asympotic stability of an equilibrium position of a family of systems of linear differntial equations , 1978 .

[37]  ASYMPTOTIC STABILITY OF AN EQUILIBRIUM P . OSITION OF A FAMILY OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS , 2022 .

[38]  Argyrios C. Zolotas,et al.  Optimal design of PID controllers using the QFT method , 1999, ArXiv.

[39]  Mario Garcia-Sanz.  The Nyquist stability criterion in the Nichols chart , 2016 .

[40]  Alfonso Baños,et al.  AUTOMATIC LOOP SHAPING IN QFT BY USING CRONE STRUCTURES , 2006 .