Nonlinear model predictive control with Timed-Elastic-Bands

随着技术过程变得越来越复杂，对其控制和自动化的要求也在增加。因此，明确考虑过程约束（如控制和状态变量的限制）的控制概念在研究和应用中变得重要。在这种情况下，预测控制器提供了一种方法来反复解决非线性动态过程的渐退水平最优控制问题。在过去的十年中，对预测控制的数值有效实现的兴趣已经大大增加，以便使它们能够广泛应用于具有快速动态的机电系统。到目前为止，预测控制中的大多数方法都局限于最小化二次代价函数，特别是控制误差和努力。然而，这些传统的公式不适合时间最优控制任务。考虑到这些目标，该研究项目致力于开发非线性预测控制的创新方法，明确考虑状态表示和成本函数中的时间信息。本项目集中于两个中心目标：首先，将模型预测控制扩展到时间最优控制任务及其有效计算；其次，用专用的高效数值解算器逼近一般控制任务的最优控制问题。该研究计划涉及一种基于时间弹性带的高效模型预测控制新方法的概念、开发、实现和评估。通过仿真和实验对新方法和现有方法进行了比较研究，包括计算量、控制性能以及预测和闭环控制在干扰下的鲁棒性分析。

As technical processes become progressively more complex, the demands on their control and automation increase as well. Hence control concepts that explicity consider process constraints such as limitations of control and state variables gain importance in research and applications. In this context predictive controllers provide a means to repeatedly solve a receding horizon optimal control problem for nonlinear dynamic processes. Within the past decade the interest in numerical efficient realizations of predictive control has grown considerably in order to enable their widespread utilization even for mechatronic systems with fast dynamics. Until nowadays the majority of approaches in predictive control are restricted to the minimization of quadratic cost functionals, in particular control error and effort. However, these conventional formulations are not suited for time-optimal control tasks. With these objectives in mind, the research project devotes itself to the development of innovative methods for nonlinear predictive control with explicit consideration of temporal information in state representation and cost function. This project focusses on two central objectives: Firstly, extension of model predictive control to time-optimal control tasks and their efficient computation and secondly, approximation of the optimal control problem for general control tasks with dedicated efficient numeric solvers.The research programme involves the conception, development, realization and valuation of a new approach for efficient model predictive control that is based on so called Timed-Elastic-Bands. A comparative investigation among the novel approach and established methods is carried out in simulations and experiments including the analysis of computational effort, control performance as well as robustness of the prediction and closed-loop control under disturbances.