Adaptive Control for a Physics-Informed Model of a Thermal Energy Distribution System: Qualitative Analysis

TL;DR

This paper develops an adaptive-control framework for linear, fully observable systems and applies it to a glycol heat exchanger within a Thermal Energy Distribution System (TEDS) at INL, addressing uncertainties in integrated energy systems. By leveraging a model-reference adaptive control structure with Lyapunov-based guarantees, the work achieves convergence of the tracking error $e(t)$ and bounded parameter error $\tilde{\theta}$, even under matched nonlinearities. The Experimental section demonstrates that AC can significantly reduce tracking errors (MAE and ITAE) relative to a nominal LQR under 50% perturbations, with modest online computational burden; explicitly accounting for matched disturbances yields additional gains for certain outputs. These results establish AC as a principled, interpretable, real-time control option for complex IES like GHXs, and lay groundwork for extending the framework to partially observable and nonlinear dynamics, as well as integration with complementary model-form correction methods.

Abstract

Integrated energy systems (IES) are complex heterogeneous architectures that typically encompass power sources, hydrogen electrolyzers, energy storage, and heat exchangers. This integration is achieved through operating control strategy optimization. However, the lack of physical understanding as to how these systems evolve over time introduces uncertainties that hinder reliable application thereof. Techniques that can accommodate such uncertainties are fundamental for ensuring proper operation of these systems. Unfortunately, no unifying methodology exists for accommodating uncertainties in this regard. That being said, adaptive control (AC) is a discipline that may allow for accommodating such uncertainties in real-time. In the present work, we derive an AC formulation for linear systems in which all states are observable and apply it to the control of a glycol heat exchanger (GHX) in an IES. Based on prior research in which we quantified the uncertainties of the GHXs system dynamics, we introduced an error of 50% on four terms of the nominal model. In the case where a linear quadratic regulator is used as the nominal control for the reference system, we found that employing AC can reduce the mean absolute error and integral time absolute error by a factor of 30%-75%. This reduction is achieved with minimal computing overhead and control infrastructure, thus underscoring the strength of AC. However, the control effort induced is significant, therefore warranting further study in order to estimate its impact on a physical system. To address further challenges, including partially observable and non-linear dynamics, enhancements of the linear formulation are currently being developed.

Figures (4)

• Figure 1: Simplified TEDS and control systems. Though a model of TES was also developed, the model form error was too large, necessitating that a GP correction be added, which is why we have omitted it from this study.
• Figure 2: Performance of the SINDyC model on the GHX experiment for (A) $\dot{m}_{ghx,bypass}$ and (B) $Q_{ghx}$. Five hundred equally spaced data points and a polynomial of order 2 were used to obtain the filtered experimental trajectories (red dashed curves).
• Figure 3: Comparison of the LQR controllers in the presence of uncertainties, both with and without correction from AC: $\theta_{l,r} = 0$ ((A) and (B)) and $\theta_{l,r} = 1.5$ ((C) and (D)).
• Figure 4: CE and MAE as a function of the multiplier for the case without matched disturbances (blue) and that with matched disturbances (orange). The MAEs and CEs are normalized to the MAE and CE of the nominal case (i.e., LQR applied to the reference system), respectively. Dashed lines are added to help visualize the MAE and CE for the case studied in Figure \ref{['fig:ghxall']}.