Feedforward and Feedback Control of Distributed-Parameter Systems Based on Discretized Port-Hamiltonian Models

DFG Ko 4750/1-1, 2015 - 2019

The goal of the research project was the development and application of automatable methods for control design of 1D hyperbolic distributed parameter systems based on spatial discretizations that preserve the port-Hamiltonian (PH) structure of the system description.

A modular three-axis lab manipulator with industrial (PLC) control hardware was developed and constructed for experimental validation of the design approaches. The fast point-to-point motion of a flexible beam, modeled under the Timoshenko assumptions, served as a test case. The combination of port-based modeling, geometric pseudo-spectral discretization and structure-preserving model order reduction allowed to establish relatively low-order PH control models, which were exploited in a two-degrees-of-freedom controller structure. The precise inversion-based feedforward controller was complemented by (disturbance) observer-based LQR control of the tracking error, which showed impressive performance. Finally, the communication delays in the PLC were identified and considered in the discrete-time control model.

The project results, including the experimental setup, are the basis for continuing works on the geometric modeling and control of flexible robots.

Doctoral researcher: Mei Wang

Link: gepris.dfg.de/gepris/projekt/260049780

Identification and Control for Pneumatic Systems

PhD project (2014 - 2019)

Partial differential equations can be used to characterize systems whose parameters depend not only on time but on a spatial variable as well. Such systems include all kinds of transport and diffusion phenomena as they arise for example in the movement of beams or in air flowing through a tube. Firstly, research is dedicated to a new approach for the identification of parameters in linear partial differential equations. Based on the thereupon parameterized model, secondly, model-based control techniques are applied to achieve a desired dynamic behavior of the distributed parameter system. Currently, research interests are focused on a pneumatic line with nonlinear friction.

Doctoral researcher: Richard Kern

Dissertation: “Design and Experimental Validation of Output Feedback Tracking Controllers for a Pneumatic System with Distributed Parameters” 

Easy-to-Implement Energy-Based Control Design for Systems of Conservation Laws

655204 - EasyEBC - H2020-MSCA-IF-2014, 2015 - 2017

“Secure, clean and efficient energy as well as resource efficiency are major societal challenges formulated in the EU Horizon 2020 Framework Programme. Many subsystems in energy, production and process industries are systems of conservation laws and their efficient operation relies on precise modelling and feasible control design. The port-Hamiltonian approach, developed in a vibrant European research community with the project supervisor as one of the leading figures, uses energy as the key argument for modelling and control of interconnected, nonlinear multi-physics systems, including systems of conservation laws.

The aim of EasyEBC is to develop easy-to-handle energy-based control design procedures for nonlinear systems of conservation laws in the port-Hamiltonian framework. Linear and nonlinear methods from mathematical control theory of finite- and infinite-dimensional systems will be applied for analysis and control synthesis, e.g. semi-group theory, discretization techniques, and energy shaping. The mathematics will be masked behind a user-friendly frontend that offers transparent tuning criteria for the closed-loop dynamics. Bridging the gap between mathematical complexity and easy applicability of the design tools is the main challenge of the project.”

The Marie-Skłodowska Curie-Fellowship was carried out at Laboratoire d’Automatique et de Génie des Procédés (LAGEP), Université Claude Bernard Lyon 1, UMR 5007 CNRS.

Fellow: Paul Kotyczka

Supervisor: Bernhard Maschke

Link: https://cordis.europa.eu/project/id/655204

Geometric Modeling, Discretization and Control of Mechanical Systems

mit Prof. Ravi Banavar, IIT-Bombay (DAAD-DST Indien 57085640, 2014-2016)

“The overall scientific goal of this joint project is to promote the development and application of nonlinear control techniques for mechanical systems based on a differential geometric modeling perspective. Two main directions of research will be pursued, according to the expertise and current topics at the participating institutions (see also the field on complementarity of the research programs):

1. The first focus is the development of controllers for mechanical systems evolving on nonlinear manifolds within the framework of geometric mechanics.

2. The second aspect is the control of flexible mechanical systems which are represented in a (discretized) port-Hamiltonian form. The latter is a geometric system description based on Dirac structures which generalize the Poisson structures from geometric mechanics.”

Participants: Sergio Delgado, Philipp Niermeyer, Paul Kotyczka (TUM), Sneha Gajbhiye, Megha Trivedi, Ravi Banavar (IIT Mumbai)

Control of Underactuated Mechanical Systems

PhD project (2011 - 2016)

Passivity based control of underactuated mechanical systems. The application of energy / passivity based methods for the stabilization of underactuated mechanical systems is often hampered by a dissipation condition, which does not allow physical damping in the passive degrees of freedom. In the framework of the IDA-PBC method we presented a solution for this problem by introducing a generalized formulation of the assignable closed-loop energy. Besides the problem of dissipation we are working on different application aspects of IDA-PBC or the Controlled Lagrangians method. Geometric methods for the control of mechanical systems. The notions and tools from differential geometry allow a very compact notation of the dynamics of mechanical systems. Together with the group of Prof. Ravi Banavar at IIT Mumbai we are working on energy based controllers for nonholonomic mechanical systems which are based on a coordinate free representation.

Doctoral researcher: Sergio Delgado-Londono

Dissertation: “Total Energy Shaping for Underactuated Mechanical Systems: Dissipation and Nonholonomic Constraints” 

Passivity-Based Control of Switching Nonlinear Systems

(DFG Lo 408/14-1, 2010 - 2013)

Passivity based control of switching systems. Dynamical systems can exhibit different types of switching behaviors and stabilization of the single switching situations is not sufficient for stability of the switched system. The focus of this project was the development of a passivity based methods for feedback controller design, adapting the well-known IDA-PBC approach. A key feature is a systematic procedure for the construction of positive (semi-)definite closed-loop dissipation matrices.

Estimation of domains of attraction. In energy based methods, the domain of attraction of an equilibrium can be, rather naturally, estimated through the level surfaces of the closed-loop energy function. Different numerical methods have been developed to obtain quantitative measures which can be used as cost functionals in controller optimization.

Doctoral Researcher: Tobias Kloiber

Dissertation: “Constructive Passivity-Based Control of Smooth and Switched Nonlinear Systems”

Parameterization of Passivity Based Controller Design

PhD project (2006 - 2010)

The IDA-PBC method is a very appealing approach to design feedback controllers for nonlinear systems which provides by construction a Lyapunov function for the closed-loop equilibrium. A major difficulty in the method is the choice of design parameters, which in general have an intransparent effect on the achievable closed-loop dynamics. The method of Local Linear Dynamics Assignment helps to find reasonable values of the design parameters by solving a simple system of linear equations. This parameterization guarantees prespecified local dynamic behavior and makes the IDA-PBC design procedure is more sytematic. By the way, a tedious definiteness check can be omitted.

Doctoral researcher: Paul Kotyczka

Dissertation: “Transparent Dynamics Assignment with Nonlinear Passivity-Based State Feedback Control” (in German)

Structure Preserving Model Order Reduction of Port-Hamiltonian Systems

Preserving system properties like stability or passivity is an important goal of model order reduction methods. It has been shown that with Krylov subspace methods high order linear systems can be reduced, preserving their port-Hamiltonian structure by using standard tools like the Arnoldi algorithm.

Doctoral Researcher: Thomas Wolf (MORLab)