Hermite Interpolation for Energy-based Discrete-Time Control (HermInE)

• Applicant: Privatdozent Dr.-Ing. Paul Kotyczka
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 543741503

Energy- and passivity-based designs have been developed and successfully applied in many areas of control engineering, e.g., in the context of robotics, or exploiting the port-Hamiltonian (PH) system representation. While structure-preserving discretization and discrete-time control have recently gained attention in the PH community, the state of the art in this energy-based context lacks a systematic framework for design and implementation of discrete-time controls and observers for nonlinear sampled systems based on numerical models with higher derivatives and Hermite interpolation. This includes the interconnection of discrete-time models of finite- and infinite-dimensional systems for simulation and energy-based control. The methods developed in HermInE are particularly useful for control systems at a low sampling rate compared to the system dynamics (e.g., due to hardware or communication constraints), in conjunction with the possibility of signal shaping at the actuators and generalized (over-)sampling at the sensing devices. In the proposed project, we (a) extend our previous results towards sampled control implementation with continuous or differentiable inputs, based on Hermite-Obreschkoff methods. This is motivated by actuator constraints, e.g., in sluice gates, or the need to avoid sharp controls. We (b) discuss the implementation of linear observers using the corresponding implicit models. (c) Nonlinear observers for these models have the structure of moving horizon estimators (MHE). We study the use of inter-sample measurements to robustify the estimation and exploit efficient numerical methods, well developed in real-time model predictive control (MPC). We (d) propose the according class of discrete-time port-Hamiltonian (PH) systems, and (e) study their energy-consistent interconnections for (co-)simulation. (f) The Control by Interconnection (CbI) technique is translated to discrete time, and extended in a port-thermodynamic sense, with an appropriate splitting according to reversible-irreversible energy conversions. (g) For hyperbolic systems in one spatial dimension, combinations of spatial and temporal Hermite discretizations are elaborated. The applicability of the developed methods is (h) assessed and quantified with simulation models and lab experiments from mechatronics, robotics, and hydrodynamics. The systematic use of Hermite interpolation methods as model basis for sampled control design with analytic, in particular energy-based methods, and state estimation, as well as the clarification of discrete-time interconnections of PH systems, are the key topics and novel contributions to nonlinear discrete-time control theory of HermInE.

• DFG Programme: Research Grants