Speaker
Description
This talk investigates the asymptotic energy conversion efficiency of two-port port-Hamiltonian systems operating under supplied power limits and storage constraints. The extracted energy at the output port is defined as $ E(T) \doteq -\int_0^T y_2^\top(t)u_2(t)\,dt, $ and the corresponding normalized efficiency is $\eta_E(T) \doteq \frac{E(T)}{T\bar p}.$ Lower and upper bounds are derived for the asymptotic optimal efficiency $\limsup_{T\to\infty}\eta_E^\star(T)$ by investigating optimal cyclic operation.
The framework is further specialized to port-Hamiltonian systems with a block-diagonal structure, in which the supply and extraction ports are geometrically decoupled. For this class of systems, we derive a Carnot-type upper bound on the achievable asymptotic efficiency, $ \limsup_{T\to\infty}\eta_E^\star(T) \le \eta_{\mathrm{Carnot}}= 1-\frac{\underline H_{x_1}}{\bar H_{x_1}},$ which generalizes the classical thermodynamic efficiency bound for heat engines. Numerical illustrations are provided for both linear and nonlinear systems.
[1] van der Schaft, A. and Jeltsema, D. (2021). On energy conversion in port-hamiltonian systems. In 2021 60th IEEE Conference on Decision and Control (CDC), 2421–2427.
doi:10.1109/CDC45484.2021.9683292.
[2] van der Schaft, A. and Jeltsema, D. (2022). Limits to energy conversion. IEEE Transactions on Automatic Control, 67(1), 532–538. doi:10.1109/TAC.2021.3075652.
[3] Philipp, F.M., Schaller, M., Worthmann, K., Faulwasser, T., and Maschke, B. (2024). Optimal control of port-Hamiltonian systems: energy, entropy, and exergy. Systems & Control Letters, 194, 105942. doi: 10.1016/j.sysconle.2024.105942