Feedforward and feedback control of distributed-parameter systems based on discretized port-Hamiltonian models

• Applicant: Privatdozent Dr.-Ing. Paul Kotyczka, since 9/2017
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2015 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 260049780

The goal of the proposed research in the field of systems theory and automatic control is the development of feedforward and feedback control design methods for a class of distributed-parameter systems, based on simple models which result from an energy based spatial discretization. By exploiting the unified, easy to handle model structure which is valid for different types of physical systems, this work represents a contribution to the automation of control design for nonlinear systems, which is still an open field of research.The dynamics of the considered class of systems is governed by systems of partial differential equations which can be written in the energy based port-Hamiltonian form. In terms of control design it is easier to deal with finite-dimensional, lumped-parameter approximation models, expressed as systems of nonlinear ordinary differential equations. The structure preserving spatial discretization yields such models which again have a port-Hamiltonian form. Typical examples for the considered class of systems are fluidic flows in (networks of) pipelines or flexible mechanical structures, as they can be part of modular robotic systems.The lack of a holistic, automatable design procedure, from modeling to trajectory generation and feedback control (not only) for the considered class of systems within the port-Hamiltonian framework motivates the research proposal. There exist a variety of feedforward and feedback control design methods for distributed-parameter systems, also based on the partial differential equations, yet they are often restricted to the linear case or provide system specific solutions.To solve the problems which are formulated in the research proposal concerning the tasks modeling, analysis and control, different methods from linear systems theory and nonlinear control theory will be applied. The tools which are used are, among others, linear controllability and observability measures, methods for the dynamic inversion of nonlinear non-minimumphase systems, also based on optimization, as well as a port-Hamiltonian adaptation of Luenberger's approach for dual observer-based compensator design.Two relevant control tasks which shall be, to a large extent, automatically solved with the help of the intended results are trajectory generation for transients between operation points in nonlinear transmission networks and well-damped trajectory tracking of elastic robot arms.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Dr.-Ing. Boris Lohmann, from 2/2016 until 8/2017