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Optimal Control of Dynamical Systems: Calculating Input Data for Multibody System Simulation

: Burger, M.

München: Verlag Dr. Hut, 2011, 148 S.
Zugl.: Kaiserslautern, TU, Diss., 2011
ISBN: 978-3-8439-0233-5
Fraunhofer ITWM ()

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 differential-algebraic equations (DDAEs), i.e., differential-algebraic equations that include the definition of an input- or control quantity and, additionally, certain time-delays 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 time-delays 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 solution-operator and an input-output-operator, that maps a specific input to the corresponding output, is defined and investigated in a functional-analytic context. The control problem is formulated precisely as the task to invert the input-output-operator. The solvability and the so-called method of control-constraints are studied.

Moreover, a more general optimal control problem is also considered and analyzed in the functional-analytic 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 full-vehicle 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 tire-surrogate model is introduced, which can be used to derive a virtual road profile, provided that measured wheel-forces and torques as well as full-vehicle model of the measurement vehicle are available. The derived and computed road profile has a certain invariance-property. That is, it can be used as input for the simulation of full-vehicle models that are different from the measurement vehicle and for which no measured quantities are available.