- Curriculum Vitae
- Twitter: @HCPangborn
- 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: Hierarchical Control, Model Predictive Control, Mobile Electro-Thermal Systems, Vapor Compression 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.

##### Hierarchical Model Predictive Control of Aircraft Electro-Thermal Systems

Hierarchical control represents an enabling technology for the electro-thermal coordination of vehicle energy systems by employing a network of communicating controllers to coordinate behavior across multiple timescales, systems, and physical domains [1,2,10]. As shown in the example hierarchical control framework of Fig. 2, controllers in the upper control layers coordinate high-level behavior at a relatively slow update rate and communicate references down the hierarchy to be tracked by faster-updating controllers responsible for managing specific subsystems and actuators. While only three control levels are shown in the example framework of Fig. 2, more levels can be added as necessary to match the timescales present in the system.

When advance knowledge of the vehicle task and/or anticipated environmental conditions is available, proactive action can be taken to optimize operation, for example by pre-cooling thermal storage elements in advance of large heat loads, or by strategically shedding or rescheduling the operation of non-critical electrical systems when thermal limits are predicted to be exceeded.

The left plot of Fig. 3 shows a comparison of graph-based hierarchical Model Predictive Control (MPC), centralized MPC, and decentralized proportional-integral (PI) control as applied to an experimental testbed representative of an aircraft fuel thermal management system (FTMS), subject to heat loads from electrical equipment. The hierarchical controller performs significantly better in maintaining desired bounds on cold plate temperatures due to its ability to coordinate both slow and fast dynamics, including compensating for unknown disturbances and model error.

Ongoing work includes hardware-in-the-loop implementation of electro-thermal hierarchical control, in which the plant consists of a real-time simulated air bay and electrical system coupled to a physical fluid-thermal testbed, as shown in Fig. 4.

##### Stability of Decentralized Control Under Switching

In addition to the practical application of hierarchical control discussed in the previous section, my research includes the development of methods for ensuring the stability of decentralized and hierarchical controllers, including under the switching on and off of paths for energy transport within a system (i.e., edges of its graph-based model) as actuators and components switch among modes of operation [7]. This has been achieved by analyzing the passivity of systems modeled as graphs, where a common storage function can be applied to ensure that passivity is preserved under coupling between switched subsystems and in feedback connection with controllers, as shown in Fig. 5. The structure of the graph-based models allows a set of inputs and outputs to be determined that render each subsystem passive while admitting a nonlinear control-affine model representation that is applicable to a wide class of systems. MPC-based control formulations for each subsystem can then be augmented with decentralized passivity-based constraints to guarantee closed-loop stability under switching.

##### Graph-Based Dynamic Modeling of Energy Systems

To facilitate model-based hierarchical control, a dynamic graph-based modeling approach has been derived by applying the conservation of energy and mass to physical components and systems [3,11]. Coupling between system elements is succinctly embedded in the structure of interconnections of a graph, allowing awareness of this coupling to be exploited for hierarchical model-based control [1,2,10] and leveraged in formal analysis of stability and robustness under closed-loop control [7].

Fig. 6 below shows a notional example of an oriented graph, which consists of an interconnection of vertices (circled) and edges (lines). When modeling a system as a graph, capacitive elements that store energy, or mass, are represented as vertices. Paths for the transport of energy, or mass, between storage elements are represented as edges. Conservation equations are then applied to develop dynamic models of the vertex states. Graph-based models of components can be derived individually and then assembled to form complete system models. This modularity facilitates representation of a wide range of vehicle energy system scales and configurations.

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, pictured in Fig. 7, has been designed as a “thermal fluid breadboard” to facilitate the rapid reconfiguration of components, allowing 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. 8.

#### Previous Work

##### 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 Predictive 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 [4,12].

Fig. 9 below shows the CITMAV experimental testbed, designed to be a simplified version of an aircraft fuel thermal management system (FTMS). Fig. 10 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 an oriented graph, as shown in Fig. 11, 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 an MPC for thermal management.

Fig. 12 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. 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.

##### 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. 13.

Controllers for these systems can also benefit from a switched framework as shown in Fig. 14, 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 [5,13]. 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 [14]. As shown in Fig. 15, 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. 15), allowing the model to capture the most salient dynamics while maintaining computational and analytical simplicity.

As shown in Fig. 16, which uses a different set of experimental data than in Fig. 15, 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 [6]. 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. 17. In the SMB approach, the heat exchanger is divided into CVs corresponding to each refrigerant phase, as shown in Fig. 18. Unlike with the FV approach, the size of volumes can vary with time as phase flow lengths change.

Fig. 19 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. 20 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] Koeln, J.P., **Pangborn, H.C.**, Kawamura, M., Williams, M.A., and Alleyne, A.G., “Hierarchical Control of Aircraft Electro-Thermal Systems,” *IEEE Transactions on Control Systems Technology*, 2018. (submitted)

[2] **Pangborn, H.C.**, Koeln, J.P., Williams, M.A., and Alleyne, A.G., “Experimental Validation of Graph-Based Hierarchical Control for Thermal Management,” *ASME Journal of Dynamic Systems, Measurement, and Control*, 2018. [PDF]

[3] 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*, 2018. [PDF]

[4] **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]

[5] **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]

[6]** 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**

[7]** Pangborn, H.C.**,** **Koeln, J.P. and Alleyne, A.G., “Passivity and Decentralized MPC of Switched Graph-Based Power Flow Systems,” *Proc. of the 2018 American Control Conference*, June 2018. (accepted-preprint available upon request)

[8] Docimo, D.J., **Pangborn, H.C.**, and Alleyne, A.G., “Hierarchical Control for Electro-Thermal Power Management of an Electric Vehicle Powertrain,” *Proc. of the ASME 2018 Dynamic Systems and Control Conference*, 2018. (accepted-preprint available upon request)

[9] Peddada, S.R.T., Herber, D.R., **Pangborn, H.C.**, Alleyne A.G., and Allison J.T., “Optimal Flow Control and Single Split Architecture Exploration for Fluid-Based Thermal Management,” *Proc. of the 2018 ASME International Design Engineering Technical Conferences*, August 2018. (accepted-preprint available upon request)

[10]** 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]

[11] 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]

[12] **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]

[13] **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]

[14]** 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]

[15]** 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**

[16]** 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]

[17]** 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]