Modelling and control of mechatronic systems by the descriptor approach

In recent years, the analysis and synthesis of control systems in a descriptor form has been established. The general description of dynamical systems by differential-algebraic equations (DAE) is important for many applications in various disciplines, but particularly in mechatronics. In this contribution, the pros and cons of the modelling of mechatronic systems by differential-algebraic equations are discussed with application of subsystem modelling. Additionally, the actual state of the art simulation, analysis and design of descriptor systems are presented.

[1]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[2]  C. W. Gear,et al.  Simultaneous Numerical Solution of Differential-Algebraic Equations , 1971 .

[3]  Suresh P. Sethi,et al.  A Survey of the Maximum Principles for Optimal Control Problems with State Constraints , 1995, SIAM Rev..

[4]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[5]  A. V. Dmitruk,et al.  Maximum principle for the general optimal control problem with phase and regular mixed constraints , 1993 .

[6]  P. Müller.  Optimal control of proper and nonproper descriptor systems , 2003 .

[7]  Martin Arnold,et al.  Zur Theorie und zur numerischen Lösung von Anfangswertproblemen für differentiell-algebraische Systeme von höherem Index , 1998 .

[8]  K. Takaba,et al.  H_∞ control for descriptor systems:A J-spectral factorization approach , 1994 .

[9]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

[10]  P. C. Müller,et al.  Stability and optimal control of nonlinear descriptor systems: a survey , 1998 .

[11]  W Kampowsky,et al.  CLASSIFICATION AND NUMERICAL SIMULATION OF ELECTRIC CIRCUITS , 1992 .

[12]  P. M̈uller.  Linear-Quadratic Optimal Control of Non-Proper Descriptor Systems , 2000 .

[13]  Alan J. Laub,et al.  The linear-quadratic optimal regulator for descriptor systems , 1985, 1985 24th IEEE Conference on Decision and Control.

[14]  François Delebecque,et al.  Nonlinear Descriptor Systems , 1999 .

[15]  W. E. Schmitendorf,et al.  Analytical dynamics of discrete systems , 1977 .

[16]  Gianna Stefani,et al.  Optimality Conditions for a Constrained Control Problem , 1996 .

[17]  F. Lewis.  A survey of linear singular systems , 1986 .

[18]  D. Cobb,et al.  Descriptor variable systems and optimal state regulation , 1983 .

[19]  P. Funk,et al.  Variationsrechnung und ihre Anwendung in Physik und Technik , 1962 .

[20]  P. C. Müller.  Verallgemeinerte Luenberger‐Beobachter für lineare Deskriptorsysteme , 1999 .

[21]  Peter C. Müller,et al.  Stability of Linear Mechanical Systems With Holonomic Constraints , 1993 .

[22]  Izumi Masubuchi,et al.  PII: S0005-1098(96)00193-8 , 2003 .

[23]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[24]  Edmond A. Jonckheere,et al.  Variational calculus for descriptor problems , 1988 .

[25]  L. Petzold.  A description of dassl: a differential/algebraic system solver , 1982 .

[26]  P. Müller.  Linear control design of linear descriptor systems , 1999 .