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Nonlinear Model Predictive Control of a Hybrid Thermal Management System

Demetrius Gulewicz, Uduak Inyang-Udoh, Trevor Bird, Neera Jain

Abstract

Model predictive control has gained popularity for its ability to satisfy constraints and guarantee robustness for certain classes of systems. However, for systems whose dynamics are characterized by a high state dimension, substantial nonlinearities, and stiffness, suitable methods for online nonlinear MPC are lacking. One example of such a system is a vehicle thermal management system (TMS) with integrated thermal energy storage (TES), also referred to as a hybrid TMS. Here, hybrid refers to the ability to achieve cooling through a conventional heat exchanger or via melting of a phase change material, or both. Given increased electrification in vehicle platforms, more stringent performance specifications are being placed on TMS, in turn requiring more advanced control methods. In this paper, we present the design and real-time implementation of a nonlinear model predictive controller with 77 states on an experimental hybrid TMS testbed. We show how, in spite of high-dimension and stiff dynamics, an explicit integration method can be obtained by linearizing the dynamics at each time step within the MPC horizon. This integration method further allows the first-order gradients to be calculated with minimal additional computational cost. Through simulated and experimental results, we demonstrate the utility of the proposed solution method and the benefits of TES for mitigating highly transient heat loads achieved by actively controlling its charging and discharging behavior.

Nonlinear Model Predictive Control of a Hybrid Thermal Management System

Abstract

Model predictive control has gained popularity for its ability to satisfy constraints and guarantee robustness for certain classes of systems. However, for systems whose dynamics are characterized by a high state dimension, substantial nonlinearities, and stiffness, suitable methods for online nonlinear MPC are lacking. One example of such a system is a vehicle thermal management system (TMS) with integrated thermal energy storage (TES), also referred to as a hybrid TMS. Here, hybrid refers to the ability to achieve cooling through a conventional heat exchanger or via melting of a phase change material, or both. Given increased electrification in vehicle platforms, more stringent performance specifications are being placed on TMS, in turn requiring more advanced control methods. In this paper, we present the design and real-time implementation of a nonlinear model predictive controller with 77 states on an experimental hybrid TMS testbed. We show how, in spite of high-dimension and stiff dynamics, an explicit integration method can be obtained by linearizing the dynamics at each time step within the MPC horizon. This integration method further allows the first-order gradients to be calculated with minimal additional computational cost. Through simulated and experimental results, we demonstrate the utility of the proposed solution method and the benefits of TES for mitigating highly transient heat loads achieved by actively controlling its charging and discharging behavior.

Paper Structure

This paper contains 20 sections, 26 equations, 14 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Control-oriented Modeling of Hybrid TMS
  3. Integration Methods Suitable for Real-Time Control
  4. Contribution
  5. System Description
  6. Hybrid TMS Model
  7. Single-phase pumped fluid loop
  8. TES Subsystem
  9. Graph-Based State-Dependent Coefficient Representation
  10. Model Predictive Controller Design
  11. NMPC Solution Method
  12. Integration of Simplified Hybrid TMS Dynamics
  13. Approximate Gradients
  14. NMPC Implementation
  15. Simulated Results
  16. ...and 5 more sections

Figures (14)

  • Figure 1: Schematic of the hybrid TMS.
  • Figure 2: Schematic showing the finite volume discretization of a single TES device into a total of 18 control volumes (3 fluid, 3 metal, and 12 PCM-metal composite).
  • Figure 3: Simulated heat load input applied to the cold plate to emulate high-power electronics.
  • Figure 4: Simulation results depicting the primary (total) mass flow rate through the system, the flow rate through the TES devices, and the cold plate wall temperature.
  • Figure 5: Front side of the hybrid TMS testbed.
  • ...and 9 more figures