Adaptive control of coupled rigid and flexible multibody systems with port-Hamiltonian structure

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The objective of the proposed research project is the development of adaptive tracking control techniques for coupled multibody systems with rigid and flexible components. The rigid components are described by nonlinear differential-algebraic equations. The flexible components are described by linear partial differential equations in one spatial dimension for a start. In the course of the project also multi-dimensional flexible subsystems will be considered, which are discretized by suitable methods. In each case, the models exhibit a port-Hamiltonian structure, and hence the physical properties (in particular, the power balance) can be captured in a mathematically rigorous way. A distinctive feature of port-Hamiltonian systems is that they are intrinsically modular, because arbitrary subsystems can be coupled via their ports. Despite these advantages, the port-Hamiltonian approach to modeling gets only little recognition in mechanics. Therefore, systematic methods for tracking control of such coupled multibody systems are still missing. In this project, first, a structural characterization of important system theoretic properties, such as input-output configurations, possible delays and the stability of the internal dynamics, will be conducted on the basis of physical considerations. Building on that, control techniques will be developed which guarantee the evolution of the tracking error within a prescribed margin. To this end, methods from funnel control and inversion-based feedforward control are combined, which led to far-reaching results for rigid multibody systems described by differential-algebraic equations in the first phase of the project. Now, in the second phase of the project, the feedforward controller will be designed for an approximation of the flexible components via coarse discretizations and combined with a funnel controller for the exact model. The latter is intended to compensate the approximation errors. Exploiting the modular construction of port-Hamiltonian systems, the possibility of a recursive feedforward control design will be investigated. For the applicability of funnel control, approaches which establish a functional relation between the original output and an alternative output that is co-located to the input will be considered. The performance and implementability of the developed methods will be constantly verified by means of selected experiments. The experiments support the selection of technically suitable controller design parameters and thus lead to a feedback between theory and practice.