Constrained Mechanical Systems in Descriptor form: Identification, Simulation and Control

The subject of constrained controlled mechanical (“mechatronic”) systems in descriptor form is a field of current research in mechanical engineering, control theory and applied mathematics. It is essentially based on the progress in numerical mathematics on the solution of differential-algebraic equations, cf. [1–3] and on the developments in control theory on singular (or descriptor) systems, cf. [4–6]. In mechanics the investigation of constrained mechanical systems is a well-known problem, particular in the case of nonholonomic systems [7,8]. First relations between mechanical and numerical approaches were established by Baumgarte [9] in 1972 and more recently by Nikravesh [10] and Fuhrer [11], stimulating a lot of research work on the simulation of mechanical constrained systems, e.g. [12,13].

[1]  I. Neĭmark,et al.  Dynamics of Nonholonomic Systems , 1972 .

[2]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[3]  Parviz E. Nikravesh,et al.  Some Methods for Dynamic Analysis of Constrained Mechanical Systems: A Survey , 1984 .

[4]  C Fuhrer.  ON THE DESCRIPTION OF CONSTRAINED MECHANICAL SYSTEMS BY DIFFERENTIAL ALGEBRAIC EQUATIONS , 1985 .

[5]  A. Laub,et al.  The linear-quadratic optimal regulator for descriptor systems , 1987 .

[6]  Ernst Hairer,et al.  The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

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

[8]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[9]  P. Rentrop,et al.  Differential-algebraic Equations in Vehicle System Dynamics , 1991 .

[10]  B. Leimkuhler,et al.  Numerical solution of differential-algebraic equations for constrained mechanical motion , 1991 .

[11]  V. Mehrmann.  The Autonomous Linear Quadratic Control Problem , 1991 .

[12]  Peter C. Müller,et al.  Comparison of Descriptor Models and Reduced Dynamic Models for Constrained Robots , 1991 .

[13]  W. Kortüm,et al.  Multibody Dynamics Software and Numerical Simulation of High-Speed Vehicles , 1992 .

[14]  Ming Hou,et al.  Beobachter für lineare Deskriptor-Systeme mit unbekannten Eingängen/ Observer for linear descriptor systems with unknown inputs , 1992 .

[15]  W. Kortüm.  Software zur Modellbildung und Simulation der Dynamik mechatronischer Systeme , 1992 .

[16]  P. C. Müller,et al.  Control Analysis and Synthesis of Linear Mechanical Descriptor Systems , 1993 .

[17]  Peter C. Müller,et al.  A Parameter Estimation Method for Multibody Systems with Constraints , 1993 .

[18]  Willi Kortüm,et al.  Parameter Identification of Nonlinear Descriptor Systems , 1993 .

[19]  P. Rentrop,et al.  The Drazin inverse in multibody system dynamics , 1993 .

[20]  P. Rentrop,et al.  An Extended Descriptor Form for the Simulation of Constrained Mechanical Systems , 1993 .