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

在系统理论和自动控制领域提出的研究目标是基于基于能量的空间离散化的简单模型，为一类分布参数系统发展前馈和反馈控制设计方法。通过开发统一的、易于处理的、适用于不同类型物理系统的模型结构，本工作为非线性系统控制设计的自动化做出了贡献，这仍然是一个开放的研究领域。所考虑的一类系统的动力学是由偏微分方程系统控制的，偏微分方程可以写成基于能量的波特-哈密顿形式。在控制设计方面，处理有限维的集总参数近似模型（用非线性常微分方程系统表示）比较容易。保持空间离散化的结构产生这样的模型，它又具有波特-哈密顿形式。所考虑的一类系统的典型例子是（网络）管道或柔性机械结构中的流体流动，因为它们可以成为模块化机器人系统的一部分。缺乏一个整体的，自动化的设计过程，从建模到轨迹生成和反馈控制（不仅仅是）在port- hamilton框架内考虑的系统类别激发了研究建议。分布参数系统的前馈和反馈控制设计方法多种多样，也是基于偏微分方程，但往往局限于线性情况或提供系统特定解。为了解决研究计划中提出的关于任务建模、分析和控制的问题，将应用线性系统理论和非线性控制理论的不同方法。所使用的工具，除其他外，线性可控性和可观测性措施，非线性非最小相位系统的动态反演方法，也基于优化，以及Luenberger的基于双观测器的补偿器设计方法的端口-哈密顿自适应。在很大程度上需要借助预期结果自动解决的两个相关控制任务是非线性输电网络中工作点间瞬态轨迹生成和弹性机械臂的良好阻尼轨迹跟踪。

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.