H ∞ control of railroad vehicle active suspension

Abstract The design of a controller such that the closed-loop system will track reference signals or reject disturbance signals from a specified class is known as the ‘servomechanism problem’ or the ‘regulator problem’. For the regulator problem to be solvable with robust closed-loop stability, the plant obviously needs to be such that the regulation problem and the robust stabilization problem are solvable separately. In this paper we determine the extra conditions that are necessary and sufficient for the two problems to be solved simultaneously. It turns out that these conditions can be given a simple geometric interpretation in terms of a multivariable version of the Nyquist curve of the plant.

[1]  R. Brockett,et al.  Multivariable Nyquist criteria, root loci, and pole placement: A geometric viewpoint , 1981 .

[2]  Toshio Yoshimura,et al.  An active lateral suspension to a track/vehicle system using stochastic optimal control , 1987 .

[3]  Toshiro Noritsugu,et al.  Design of Optimal Pneumatic Servosystem Considering Control Valve Delay Time , 1988 .

[4]  Keith Glover,et al.  Robust control design using normal-ized coprime factor plant descriptions , 1989 .

[5]  G. Vinnicombe.  Frequency domain uncertainty and the graph topology , 1993, IEEE Trans. Autom. Control..

[6]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[7]  H. Kimura,et al.  On the structure of H/sup infinity / control systems and related extensions , 1991 .

[8]  L. Rodman,et al.  Interpolation of Rational Matrix Functions , 1990 .

[9]  Robert Hermann,et al.  Applications of Algebraic Geometry to Systems Theory: The McMillan Degree and Kronecker Indices of Transfer Functions as Topological and Holomorphic System Invariants , 1978 .

[10]  Harry L. Trentelman,et al.  Essays on control : perspectives in the theory and its applications , 1993 .

[11]  J. Freudenberg,et al.  Frequency Domain Properties of Scalar and Multivariable Feedback Systems , 1988 .

[12]  J. Sefton,et al.  Stability of control systems and graphs of linear systems , 1991 .

[13]  Shiro Koyanagi.  The influences of nonlinearities on air spring vibration isolation characteristics. , 1986 .

[14]  Dante C. Youla,et al.  Modern Wiener-Hopf Design of Optimal Controllers. Part I , 1976 .

[15]  T. Georgiou,et al.  Optimal robustness in the gap metric , 1990 .

[16]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

[17]  Toshiharu Sugie,et al.  H∞ control problem with jω-axis zeros , 1992, Autom..

[18]  B. Francis,et al.  A Course in H Control Theory , 1987 .

[19]  P. Fuhrmann.  Linear Systems and Operators in Hilbert Space , 1982 .

[20]  J. M. Schumacher,et al.  Interpretations of the gap topology: A survey , 1992, Kybernetika.

[21]  J. Ball,et al.  Optimal Hankel Norm model reductions and Weiner-Hopf factorization I: the canonical case , 1987 .

[22]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[23]  T. Sugie,et al.  H ∞ -suboptimal control problem with boundary constraints , 1989 .

[24]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[25]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[26]  Mathukumalli Vidyasagar,et al.  Robust controllers for uncertain linear multivariable systems , 1984, Autom..

[27]  I. Postlethwaite,et al.  Robust Multivariable Control Using H∞ Methods: Analysis, Design and Industrial Applications , 1993 .

[28]  Johannes Schumacher,et al.  A pointwise criterion for controller robustness , 1991 .

[29]  Masashi Yamashita,et al.  H, CONTROL OF AN AUTOMOTIVE ACTIVE SUSPENSION , 1990 .

[30]  M. Kreĭn,et al.  Introduction to the theory of linear nonselfadjoint operators , 1969 .

[31]  K. Glover,et al.  Robust stabilization of normalized coprime factor plant descriptions with H/sub infinity /-bounded uncertainty , 1989 .

[32]  E. Davison,et al.  Pointwise gap metrics on transfer matrices , 1992 .

[33]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[34]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[35]  I. M. Glazman,et al.  Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form , 1974 .

[36]  Masao Nagai,et al.  Analysis and Design of Active Suspensions by H∽ Robust Control Theory , 1992 .

[37]  M. Vidyasagar.  Control System Synthesis : A Factorization Approach , 1988 .

[38]  Keith Glover,et al.  The application of scheduled H∞ controllers to a VSTOL aircraft , 1993, IEEE Trans. Autom. Control..

[39]  Vladimír Kucera.  Algebraic theory of discrete optimal control for multivariable systems [I.] , 1974, Kybernetika.

[40]  Anders Lindquist,et al.  Modelling, identification and robust control , 1986 .