Funnel MPC with application to the control of magnetic levitation systems

点击翻译按钮获取中文摘要

The objective of the proposed research project is the development, numerical implementation and analysis of the new control concept Funnel MPC (FMPC). This concept ties adaptive tracking control, learning and optimization based methods together in an innovative way.Funnel control and model predictive control (MPC) are both current research areas in control engineering and mathematical systems theory, which successfully balance theory and application. FMPC utilizes known advantages of both control strategies (e.g., compliance with output and control constraints, inherent robustness, excellent control performance) to achieve the long-term goal of a universal controller design for nonlinear systems. FMPC consists of three components:1.) In a model-based part of the controller, elements from funnel control are integrated into MPC, e.g., by incorporating the high-gain factor from the funnel controller in the construction of the stage costs. This ensures compliance with the output constraints and ultimately allows to rigorously prove recursive feasibility via an optimality argument – without (stabilizing) terminal constraints and independent of the length of the prediction horizon. 2.) MPC does not guarantee robustness in general. Hence, it is a main objective to transfer the robustness inherent to funnel control to FMPC. To this end, the control loop is extended by a model-free component via coupling with a funnel controller with respect to the prediction error of the model-based part. For this combination, robustness with respect to model uncertainties is to be proved rigorously.3.) Through a second extension of the control loop by a learning component a continuous model adaptation as well as a concomitant improvement of controller performance is achieved. For this purpose, unknown model parameters are approximated and the system state is estimated. Meanwhile, the robustified FMPC guarantees the strict satisfaction of the output constraints. Additionally, as numerical tests have shown, it induces a sufficient stimulation of the system, which ensures a high information content in the input-output data that is necessary for the learning process. This is to be characterized in a mathematically rigorous and laid out in a verifiable way by the concept of „persistency of excitation“ within the project. As a proof of concept the control of magnetic levitation trains will be considered, where a regular feedback between theory and numerical practice is intended. In levitation control a prescribed distance between vehicle suspension and guideway must be ensured. Furthermore, a robustness with respect to uncertainties (e.g., the total mass of the vehicle depending on the occupancy of the passenger area) and disturbances (e.g., wind conditions) is crucial. At the same time, a high controller performance, including travelling comfort, is desirable. Exactly those properties are unified in the innovative concept FMPC.