Model-following control for the trajectory-tracking of nonlinear systems using output feedback

• Applicant: Dr. Kai Wulff
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 508065537

We consider the trajectory-tracking control problem for nonlinear systems. In this problem a controller is to be devised such that the considered process follows a user-commanded trajectory even when the process is subject to disturbances and model uncertainties. In particular we shall consider a typical scenario where the trajectory is not known a priori and is only provided during the process run-time. Therefore a suitable feedforward control cannot be computed prior to the process initialisation. For typical, state-of-the-art approaches for trajectory-tracking the desired trajectory has to fulfil certain requirements (e.g. differentiability requirements). The aim of the approach taken in this proposal is to reduce or even drop all such requirements. In view of the practical relevance, however, we shall allow the use of measurable outputs for the feedback control of the process. We consider the so-called model-following control (MFC) scheme. This well-known approach uses a closed-loop system consisting of the process model and a controller to simulate a reference system behaviour at run-time. This yields a nominal control signal that can be used as feedforward control for the process. Disturbances and model uncertainties are compensated by a second, so-called process controller. Most available studies consider a linear model in the model control loop (MCL). Our research focusses on the analysis of the MFC structure using the nominal nonlinear process dynamics in the MCL. This is a renewal proposal. This project so far produced several results underlining that using a nonlinear model in the MCL yields a significant increase of robustness compared to single-loop designs. We established that the region of attraction can be significantly increased for set-point control in various problem settings. The additional degree of freedom given by the initialization of the MCL can be utilised to increase the region of attraction, to avoid the peaking-phenomenon in high-gain control or large gains in discontinuous feedback. However, most results achieved so far consider set-point control and require some knowledge of the process states. The research for this renewal proposal shall extend these results by considering pure output feedback and tracking of arbitrary trajectories, also in presence of state or input constraints. We shall investigate stability and robustness properties of this control structure with respect to several system classes and types of perturbations applying static as well as dynamic output feedback controller designs including observer-based trajectory tracking and dynamic extension. As a benchmark for evaluating our approaches we shall use corresponding single-loop control designs with output feedback. Application and implementation of the approaches shall be verified in practical case studies.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr.-Ing. Johann Reger