Recursive grid methods to compute value sets and Horowitz–Sidi bounds

In this paper, recursive extensions to the standard equidistant grid method are proposed whereby the gridding is adapted locally such that a prescribed distance is achieved between neighbouring points in the computed value set (template). Also presented is the Prune algorithm, which finds the outer border of a value set defined by a set of points whose nearest neighbour lies within a prescribed distance. The Prune algorithm is part of the recursive grid methods, but can also be used independently with other methods to compute value sets. As an alternative to analytical or search algorithms, a recursive grid algorithm is presented to compute Horowitz–Sidi bounds (QFT bounds, or boundaries). Isaac Horowitz's contribution to computational methods for QFT is outlined in the perspective of the presented algorithms. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  Karl Johan Åström.  Computer Aided Modeling, Analysis and Design of Control Systems—;A Survey , 1983 .

[2]  D. J. Ballance,et al.  A survey of template generation methods for quantitative feedback theory , 1996 .

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

[4]  Per-Olof Gutman,et al.  Self-oscillating adaptive design of systems with dry friction and significant parameter uncertainty , 1995 .

[5]  Guoxiang Gu,et al.  Two algorithms for frequency domain design of robust control systems , 1988 .

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

[7]  D. J. Ballance,et al.  Plant template generation for uncertain plants in quantitative feedback Theory , 1999 .

[8]  Christopher V. Hollot,et al.  A new algorithm for computing QFT bounds , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[9]  Mattias Nordin,et al.  Controlling mechanical systems with backlash - a survey , 2002, Autom..

[10]  Rami Guetta,et al.  Control of the Aero‐Electric Power Station—an exciting QFT application for the 21st century , 2003 .

[11]  M. Fu.  Computing the frequency response of linear systems with parametric perturbation , 1990 .

[12]  Steven J. Rasmussen,et al.  Quantitative feedback theory: fundamentals and applications: C. H. Houpis and S. J. Rasmussen; Marcel Dekker, New York, 1999, ISBN: 0-8247-7872-3 , 2001, Autom..

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

[14]  Martin C. Richardson,et al.  High-performance Numeric Com-putation and Visualization Software , 1992 .

[15]  Oded Yaniv,et al.  An algorithm for the adaptation of a robust controller to reduced plant uncertainty , 1990, Autom..

[16]  Edward Boje.  Finding Nonconvex Hulls of QFT Templates , 2000 .

[17]  C.-H. Hui,et al.  A fast algorithm for computing parametric rational functions , 1989 .

[18]  A. Rantzer,et al.  Algorithm for addition and multiplication of value sets of uncertain transfer functions , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[19]  Edward Boje,et al.  International Symposium on Quantitative Feedback Theory and Robust Frequency Domain Methods, 26 and 27 August 1999, University of Natal, Durban, South Africa , 1999 .

[20]  P. Gutman,et al.  Robust and adaptive control of a beam deflector , 1988 .

[21]  Richard R. Sating.  Development of an Analog MIMO Quantitative Feedback Theory (QFT) CAD Package , 1992 .

[22]  Laurence E. LaForge,et al.  Algorithmic Analysis of Geometrically Computed QFT Bounds , 1996 .

[23]  Per-Olof Gutman,et al.  An algorithm for computing value sets of uncertain transfer functions in factored real form , 1994, IEEE Trans. Autom. Control..

[24]  Ian R. Petersen,et al.  Exact computation of the Horowitz bound for interval plants , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[25]  Per Olof Gutman,et al.  Performance enhancing adaptive friction compensation for uncertain systems , 1997, IEEE Trans. Control. Syst. Technol..

[26]  Per-Olof Gutman,et al.  Quantitative design of a class of nonlinear systems with parameter uncertainty , 1994 .

[27]  Karl Johan Åström,et al.  Computer aided modeling, analysis and design of control systems - A perspective , 1983 .

[28]  I. Horowitz,et al.  Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances† , 1972 .

[29]  Csilla Bányász,et al.  Robust control design (ROCOND'97) : a proceedings volume from the IFAC Symposium, Budapest, Hungary, 25-27 June 1997 , 1997 .

[30]  S. Nash,et al.  Numerical methods and software , 1990 .

[31]  S. Sheela,et al.  Template Generation Algorithm Using Vectorized Function Evaluations and Adaptive Subdivisions , 2002 .

[32]  Per-Olof Gutman,et al.  Recursive grid methods to compute value sets for transfer functions with parametric uncertainty , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[33]  Andrew Bartlett,et al.  Robust Control: Systems with Uncertain Physical Parameters , 1993 .

[34]  I. Horowitz,et al.  A quantitative design method for MIMO linear feedback systems having uncertain plants , 1985, 1985 24th IEEE Conference on Decision and Control.