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

在系统论和自动控制领域的研究目标是发展一类分布参数系统的前馈和反馈控制设计方法，该方法基于基于能量的空间离散化的简单模型。通过利用适用于不同类型物理系统的统一、易操作的模型结构，这项工作代表了对非线性系统控制设计自动化的贡献，非线性系统的控制设计仍然是一个开放的研究领域。在控制设计方面，更容易处理用非线性常微分方程组表示的有限维集中参数近似模型。保持空间离散化的结构产生了这样的模型，它同样具有端口-哈密顿形式。这类系统的典型例子是管道或柔性机械结构中的流体流动，因为它们可以是模块化机器人系统的一部分。在波特-哈密顿框架内，对于这类系统，缺乏从建模到轨迹生成和反馈控制的整体、自动化的设计过程，这促使了研究提案的提出。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组，但它们往往局限于线性情况或提供系统特有的解决方案，为了解决研究方案中提出的任务建模、分析和控制问题，将应用线性系统理论和非线性控制理论的不同方法。所使用的工具包括线性可控性和能观性度量、同样基于最优化的非线性非最小相位系统的动态逆方法，以及Luenberger的基于双重观测器的补偿器设计的端口-哈密顿自适应方法。两个相关的控制任务将在很大程度上借助预期的结果自动解决：非线性传输网络中操作点之间的暂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.