- Curriculum Vitae
- pangbor2@illinois.edu
- Ph.D. Candidate in Mechanical Engineering – University of Illinois
- M.S. Mechanical Engineering – University of Illinois (August 2015)
- B.S. Mechanical Engineering – Pennsylvania State University (May 2013)
- Research Interests: Dynamic Modeling and Control, Mobile Energy Systems, Air-Conditioning and Refrigeration Systems

This research is supported by:

- The National Science Foundation Graduate Research Fellowship
- The National Science Foundation Engineering Research Center for Power Optimization of Electro-Thermal Systems (POETS)
- The Center for Integrated Thermal Management of Aerospace Vehicles (CITMAV)
- The Air Force Research Laboratory (AFRL)

**Introduction to Controls**

Presented to the Center for Power Optimization of Electro-Thermal Systems (POETS) on March 16, 2017

**Current Work**

Modern vehicles are complex systems composed of many subsystems and components that interact in a variety of energy domains and on a variety of dynamic timescales. To meet the challenges imposed by increasing power and thermal demands on these systems, it is necessary to develop comprehensive strategies that manage the routing and storage of energy system-wide. My goal is to optimize the performance, efficiency, and safety of these systems subject to increased operational requirements, supporting the successful development and deployment of the next generation of vehicle systems.

##### Graph-Based Modeling and Control of Energy Systems

This research seeks to develop a modeling and control framework that allows for the integration of energy systems with multi-domain and multi-timescale interactions. Specifically, graph-based models of thermal fluid systems are derived from conservation of mass and energy. This facilitates the control-oriented modeling of interconnected networks of energy system components, including tanks, pumps, cold plates and heat exchangers. An experimental testbed is used to demonstrate the accuracy of this modeling approach for capturing both hydrodynamic and thermodynamic behavior [7]. The dynamic models can then be embedded into hierarchical model-based control designs [6].

Fig. 1 below shows a notional example of an oriented graph, which consists of an interconnection of vertices (circled) and edges (lines). Each vertex is assigned a dynamic state representing the storage of a conserved quantity, while each edge is associated with a value representing the transfer rate of that quantity between two vertices. Conservation equations (for example, of mass or thermal energy) are then applied to develop dynamic models of the vertex states. Furthermore, each edge transfer rate is assumed to be a function of the states of the vertices adjacent to that edge and an exogenous input. Fig. 2 includes equations for several vertices and edges of the example graph.

For fluid thermal components, graphs based on conservation of mass can be developed to describe hydrodynamic relationships (pressures and mass flow rates), while graphs based on conservation of thermal energy can be developed to describe thermodynamic relationships (temperatures and thermal energy transfer rates). Once component-wise graphs have been developed, these can be programmatically assembled to create models of complete system architectures, capturing interconnections both within and between the thermal and hydraulic domains of the system.

The graph-based modeling framework has been validated with experimental data collected from a testbed constructed by members of the Alleyne Research Group. This testbed is pictured in Fig. 2.

This testbed has been designed as a “thermal fluid breadboard” to facilitate the rapid reconfiguration of component placement and interconnection. This allows many different system architectures to be represented. Comparisons of experimental data to both nonlinear and linearized graph-based models have demonstrated the ability of the proposed modeling framework to accurately describe both the hydrodynamic and thermodynamic behavior of thermal fluid systems. Several traces from such comparisons are shown in Fig. 3.

Leveraging the modeling framework for the purposes of control, ongoing work includes the development of model-based hierarchical controllers that use the hydrodynamic and thermodynamic graph-based models to robustly optimize system-wide performance and efficiency [6].

##### Model Predictive Control for Thermal Management of Aircraft

In collaboration with the Center for Integrated Thermal Management of Aerospace Vehicles (CITMAV) at Purdue University, this research seeks to meet the challenges of managing thermal energy and enforcing operational constraints for high-performance aircraft. To achieve these goals, a Model Predicative Controller (MPC) is implemented that utilizes preview of upcoming loads and disturbances to prevent temperature constraint violations. Case studies on an experimental testbed demonstrate improved performance of these proactive control approaches as compared to traditional reactive control designs [2,8].

Fig. 4 below shows the CITMAV experimental testbed, designed to be a simplified version of an aircraft fuel thermal management system (FTMS). Fig. 5 shows a schematic of the testbed. The system consists of two heat loads (high and low frequency) cooled by heat exchange with a chilled loop.

The system is modeled as a directed graph, as shown in Fig. 6, where vertices of the graph represent dynamic temperature states of the system and edges of the graph represent power flow between the vertices, capturing heat transfer via fluid flow and energy exchange with heat loads and thermal sinks. This graph-based model is then used to design a MPC for thermal management.

Fig. 7 compares the performance of the MPC (the “proactive” controller) against that of a PI controller (the “reactive” controller). In these results, the MPC receives a 30 second preview window of the upcoming low frequency heat load, representing an operational profile that may be known in advance as part of an aircraft’s mission. One can see that the proactive controller increases the mass flow rate 30 seconds prior to the onset of the first step in heat load. This is a result of the preview information received by the controller about the upcoming load, and has the effect of pre-cooling the low frequency heat load bay to prepare for the upcoming heat load, preventing a significant violation of the constraint later on. By contrast, the reactive approach does not increase the mass flow rate until after the temperature exceeds the reference, by which time it is too late to prevent significant overheating.

#### Previous Work

##### Switched-System Controllers

The dynamics of energy systems can very greatly with operating conditions. These systems can be captured in modeling by treating them as a collection of distinct operating modes, each with its own model formulation. Switching the model between these modes as a function of states and inputs allows the system to be described across a wide operational envelope. For example, the switched moving boundary modeling approach for multi-phase evaporators incorporates modes both with and without superheated flow at the refrigerant outlet as shown in Fig. 8.

Controllers for these systems can also benefit from a switched framework as shown in Fig. 9, allowing for the development of model-based control laws for each mode.

This research proposes a switched Linear Quadratic Gaussian (LQG) design to rapidly drive the system operation between modes and to perform regulation once the desired mode of operation has been achieved [3,9]. Stability analysis of the closed-loop switched system is presented, and application of the control approach in both simulation and on an experimental VCS testbed demonstrate the success of the control design.

##### Heat Exchanger Modeling with Humidity

The effects of air humidity on the performance of refrigerant-to-air heat exchangers in vapor compression systems (VCSs) are non-negligible in modeling and control design for some applications. Such applications include both those in which the ambient humidity is expected to vary greatly over time and those in which control of the air outlet humidity is desired. In this research, a control-oriented heat exchanger model is developed that captures the effects of changing inlet humidity and predicts the outlet humidity and condensate mass flow rate [10]. As shown in Fig. 10, experimental validation demonstrates that the inclusion of humidity modeling improves the accuracy of the heat exchanger model during periods of relatively rapid condensate formation (the last 2500 seconds of Fig. 10), allowing the model to capture the most salient dynamics while maintaining computational and analytical simplicity.

As shown in Fig. 11, which uses a different set of experimental data than in Fig. 10, the humidity models also accurately predict the mass of liquid condensate formed on the external surfaces of the heat exchanger.

##### Comparison of Heat Exchanger Modeling Approaches

Multi-phase heat exchangers for vapor compression systems (VCSs) are known as the most complex VCS components to model due to the highly nonlinear nature of the thermal dynamics that take place and the timescale separation between dynamics of different domains. This work compares the two most prevalent approaches used for first principles control-oriented modeling of heat exchangers, known as the finite volume (FV) and switched moving boundary (SMB) methods [4]. The goal of this work is to provide insight to members of both academia and industry into the tradeoffs associated with the choice of approach for heat exchanger modeling.

The FV approach involves discretizing the heat exchanger spatially into an arbitrary number of equally sized CVs (control volumes), as shown in Fig. 12. In the SMB approach, the heat exchanger is divided into CVs corresponding to each refrigerant phase, as shown in Fig. 13. Unlike with the FV approach, the size of volumes can vary with time as phase flow lengths change.

Fig. 14 shows simulation outputs for VCS models using both SMB and FV heat exchanger components. For the FV models, results from several different quantities of CVs are provided. These plots are superimposed over an envelope composed of the maximum and minimum values of experimental data from among five identical trials.

Fig. 15 shows the real time factor of each model, defined as the length of time taken to run the simulation divided by the length of time that is simulated. As can be seen, the SMB model has a significantly smaller RTF, and therefore less computational complexity, than any of the FV models.

After close evaluation, a nuanced view of dynamic VCS simulation emerges from this work. If simulation speed is paramount, a SMB model can perform as accurately as a highly discretized FV model while executing significantly faster. Therefore, accuracy alone is not the sole forte of the highly discretized FV model. Instead, the intended use in target application, and the need for flexibility of implementation may be the driving factors for selection of the FV model, since the added complexity of variable CV lengths in the SMB model render it more difficult to extend to various heat exchange types and geometries than the FV model.

#### Publications

**Journal **

[1] Williams, M.A., Koeln, J.P., **Pangborn, H.C.****,** and Alleyne, A.G., “Dynamical Graph Models of Aircraft Electrical, Thermal, and Turbomachinery Components,” *ASME Journal of Dynamic Systems, Measurement, and Control*, 2017. (submitted)

[2] **Pangborn, H.C.**, Hey, J.E., Deppen, T.O., Alleyne, A.G., and Fisher, T.S., “Hardware-in-the-Loop Validation of Advanced Fuel Thermal Management Control,” *Journal of Thermophysics and Heat Transfer*, 2017. [PDF]

[3] **Pangborn, H.C.** and Alleyne, A.G., “Switched Linear Control for Refrigerant Superheat Recovery in Vapor Compression Systems,” *Control Engineering Practice*, Volume 57, December 2016, Pages 142-156. [PDF]

[4]** Pangborn, H.C.**, Alleyne, A.G., and Wu, N., “A Comparison between Finite Volume and Switched Moving Boundary Approaches for Dynamic Vapor Compression System Modeling,” *International Journal of Refrigeration*, Volume 53, May 2015, Pages 101-114. [PDF]

**Conference**

[5]** Pangborn, H.C., **Koeln, J.P. and Alleyne, A.G., “Passivity and Decentralized MPC of Switched Graph-Based Power Flow Systems,” *Proc. of the 2017 Conference on Decision and Control*, December 2017. (submitted)

[6]** Pangborn, H.C.**, Williams, M.A., Koeln, J.P. and Alleyne, A.G., “Graph-Based Hierarchical Control of Thermal Fluid Power Flow Systems,” *Proc. of the 2017 American Control Conference*, May 2017. [PDF]

[7] Koeln, J.P., Williams, M.A., **Pangborn, H.C.**, and Alleyne, A.G., “Experimental Validation of Graph-Based Modeling for Thermal Fluid Power Flow Systems,” *Proc. of the ASME 2016 Dynamic Systems and Control Conference*, October 2016. [PDF]

[8] **Pangborn, H.C.**, Hey, J.E., Deppen, T.O., Alleyne, A.G., and Fisher, T.S., “Hardware-in-the-Loop Validation of Advanced Fuel Thermal Management Control,”* Proc. of the 46th AIAA Thermophysics Conference*, June 2016. [PDF]

[9] **Pangborn, H.** and Alleyne, A.G., “Switched Linear Control of Vapor Compression Systems Under Highly Transient Conditions,” *Proc. of the 2016 American Control Conference*, July 2016. [PDF]

[10]** Pangborn, H. **and Alleyne, A.G., “Dynamic Modeling of Heat Exchangers with Humidity and Condensation,” *Proc. of the ASME 2015 Dynamic Systems and Control Conference*, October 2015. [PDF]

[11]** Pangborn, H.**, Brennan, S., and Reichard, K**.**, “Development and Applications of a Robot Tracking System for NIST Test Methods,” *Systems and Information Engineering Design Symposium,* Charlottesville, VA, April 26, 2013. [PDF]

**Theses**

[12]** Pangborn, H.**, “Dynamic Modeling, Validation, and Control for Vapor Compression Systems,” *M.S. Thesis*, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, July 2015. [PDF]

[13]** Pangborn, H.,** “Development and Applications of a Robot Tracking System for NIST Test Methods,” Undergraduate Honors Thesis, Department of Mechanical and Nuclear Engineering, Penn State University, May 2013. [PDF]

Slides from the Feb. 13, 2017 Penn State Mechanical

Engineering Seminar can be downloaded here.