Model-following control for the trajectory-tracking control of nonlinear systems

• 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

In the proposed project 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 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 and applications of such approach consider linear systems or use a linear approximation of the process dynamics in the model control loop.In the proposed project we shall consider nonlinear systems in Byrnes-Isidori form, representing a large class of nonlinear systems. This normal form allows to distinguish between the so-called internal and external dynamics. Using the nonlinear model in the model control loop, we can generate a pair of control and output signals that is a solution of the nominal nonlinear dynamics also in case when the originally desired trajectory does not fulfill this requirement. Furthermore, we have full state information available for control in the model control loop. In this way we have more flexibility for shaping the dynamics of the model control loop, e.g. the internal dynamics can be directly influenced. Such manipulation is (to a certain extend) contained in the generated feedforward control that is applied to the process. The process controller that relies on measurable outputs only benefits from such feedforward control.The proposal aims at the impact of such approach with respect to robustness and systematic manipulation of the internal dynamics. While the focus lies on the theoretical and structural investigation of the approach, some typical applications shall be considered in order to underline practical aspects to be considered and to obtain quantitative results. Furthermore, the obtained results shall be implemented on experimental test-rigs available at the group's laboratory for experimental validation.

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