Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Optimal Control of Dynamical Systems: Calculating Input Data for Multibody System Simulation
 München: Verlag Dr. Hut, 2011, 148 S. Zugl.: Kaiserslautern, TU, Diss., 2011 ISBN: 9783843902335 

 Englisch 
 Dissertation 
 Fraunhofer ITWM () 
Abstract
In order to simulate a mechanical multibody system, input data is needed that describes properly the interface between the considered system and the exterior environment. However, such suitable input data is often not available, whereas inner quantities of the mechanical system are often known from measurement. This leads to the following task: Calculate an input or control quantity for the mechanical system such that the corresponding system outputs are as close as possible to given reference outputs.
In this thesis, general dynamical systems are considered that are described by controlled delay differentialalgebraic equations (DDAEs), i.e., differentialalgebraic equations that include the definition of an input or control quantity and, additionally, certain timedelays both in the state variables and in the control quantities are allowed. The equations of motion of a mechanical multibody system can be seen as a special case. The timedelays are considered to model, e.g., a virtual road profile that enters a vehicle model at different points.
The previously stated problem is formulated and analyzed as a mathematical control problem. To this end, a solutionoperator and an inputoutputoperator, that maps a specific input to the corresponding output, is defined and investigated in a functionalanalytic context. The control problem is formulated precisely as the task to invert the inputoutputoperator. The solvability and the socalled method of controlconstraints are studied.
Moreover, a more general optimal control problem is also considered and analyzed in the functionalanalytic context. Local minimum principles and necessary optimality conditions for delay DAE optimal control problems are derived and proved.
A main application is the calculation of a virtual road profile for fullvehicle multibody system simulation. For this application, a special subsystem approach is introduced that allows to restrict the control problem to a certain subsystem of moderate complexity: a specific tiresurrogate model is introduced, which can be used to derive a virtual road profile, provided that measured wheelforces and torques as well as fullvehicle model of the measurement vehicle are available. The derived and computed road profile has a certain invarianceproperty. That is, it can be used as input for the simulation of fullvehicle models that are different from the measurement vehicle and for which no measured quantities are available.