Adaptive Control and Scaling Approach for the Emulation of Dynamic Subscale Torque Loads

National Aeronautics and Space Administration

Adaptive Control and Scaling Approach

for the Emulation of Dynamic Subscale

Torque Loads

Santino J. Bianco · Donald L. Simon NASA Glenn Research Center, Cleveland, OH, USA Dr. Elyse D. Hill Oak Ridge Associated Universities, Oak Ridge, TN, USA AIAA Science and Technology (SciTech) Forum th th January 8 – 12 , 2024 This manuscript is a joint work of employees of the National Aeronautics and Space Administration and employees of Oak Ridge Associated Universities under Contract/Grant No. 80HQTR21CA005 with the National Aeronautics and Space Administration. The United States Government may prepare derivative works, publish, or reproduce this manuscript and allow others to do so. Any publisher accepting this manuscript for publication acknowledges that the United States Government retains a non-exclusive, irrevocable, worldwide license to prepare derivative works, publish, or reproduce the published form of this manuscript, or allow others to do so, for United States government purposes.

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• Motivation • The aviation industry is pursuing electrified aircraft propulsion (EAP) due to its ability to increase engine/aircraft performance, efficiency, and operability.

• Need to replace turbomachinery during initial EAP control algorithm verification on hardware due to cost and safety risks.

• Previously published approach for replacing turbomachinery has limitations.

• Purpose • Present a modification to published emulation control approach that reduces or eliminates its limitations.

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1. Introduce original approach and discuss limitations.

2. Explain adaptive approach and prove stability.

3. Explain hardware-in-the-loop test setup to verify controller operation.

4. Show and discuss performance results.

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Full-Scale Full-Scale Hardware Turbomachinery Electro-mechanical Full-Scale EM Torque Software System EAP Fuel Flow Test Article Controller Power Rate Paper Test Article Lever Communication Signal Angle EM Turbomachinery DC Line To Inverter Power AC Line System Full-Scale Spool Speed With Turbomachinery Without Turbomachinery (HyPER) Sub-Scale Turbomachinery Representation Sub-Scale Electro-mechanical Sub-Scale EM Torque Full-Scale EM Torque EAP System Controller Power Emulation EM Torque Lever Fuel Flow Net Turbo- Angle Rate Emulation machinery Full-Scale Control Torque EM EM Inverter Turbomachinery To Model Inverter Power System Sub-Scale Spool Speed Full-Scale Spool Speed Turbomachinery is replaced and the dynamical characteristics of the system are preserved.

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• Sliding Mode Impedance Controller with Scaling (SMICS) [1]

Emulation EM Torque −1 𝑇𝑇 = 𝐽𝐽 𝐽𝐽 𝑇𝑇 + 𝑇𝑇 + 𝜂𝜂𝜂𝜂𝜂𝜂𝜂𝜂 𝜂𝜂 , 𝜙𝜙 + 𝐾𝐾 𝜂𝜂 + 𝐾𝐾 � 𝜂𝜂 𝑑𝑑 𝜂𝜂 + 𝐾𝐾 𝜂𝜂 + 𝐵𝐵 𝜔𝜔 − 𝑇𝑇 𝑀𝑀 𝑃𝑃 𝐸𝐸 𝐺𝐺 𝑃𝑃 𝐼𝐼 𝐷𝐷̇ 𝑃𝑃 𝑃𝑃 𝐺𝐺 𝐸𝐸 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑠𝑠 Plant Inertia Plant Damping Coefficient

• Lyapunov Stability Analysis

̇ 𝑉𝑉 = − 𝜂𝜂 𝜂𝜂𝜂𝜂𝜂𝜂𝜂𝜂 𝜂𝜂 , 𝜙𝜙 + 𝐾𝐾 𝜂𝜂 + 𝐾𝐾 � 𝜂𝜂 𝑑𝑑 𝜂𝜂 + 𝐾𝐾 𝜂𝜂 𝑃𝑃 𝐼𝐼 𝐷𝐷̇ • Because of red, asymptotic controller stability unable to be proven.

• Because of uncertainty in green, sliding mode control effort is

increased. Thus, chatter is increased.

Unable to prove asymptotic stability or correct for plant parameter uncertainty using original approach.

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• Adaptive Sliding Mode Impedance Controller with Scaling (ASMICS) −1 ̂ � 𝑇𝑇 = 𝐽𝐽 𝐽𝐽 � �𝑇𝑇 + 𝑇𝑇 − 𝐵𝐵 𝜔𝜔 − 𝑇𝑇 + 𝐵𝐵 𝜔𝜔 − 𝜂𝜂 sat 𝜂𝜂 , 𝜙𝜙 − 𝐾𝐾 𝜂𝜂 𝑀𝑀 𝑃𝑃 𝐸𝐸 𝐸𝐸 𝐺𝐺 𝐸𝐸 𝑃𝑃 𝐺𝐺 𝑃𝑃 𝑃𝑃 𝑃𝑃 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑢𝑢 : impedance portion ̇ 𝜂𝜂 : sliding mode portion 𝑒𝑒𝑒𝑒 • Adaptation Laws ̇̂ −1 𝐽𝐽 = −𝛾𝛾 𝜂𝜂 𝐽𝐽 � �𝑇𝑇 + 𝑇𝑇 − 𝐵𝐵 𝜔𝜔 𝑃𝑃 𝐽𝐽 𝐸𝐸 𝐺𝐺 𝐸𝐸 𝑃𝑃 𝐸𝐸 𝑃𝑃 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑠𝑠 ̇ � 𝐵𝐵 = −𝛾𝛾 𝜂𝜂 𝜔𝜔 𝑃𝑃 𝐵𝐵 𝑃𝑃 𝑃𝑃 • Lyapunov Stability Analysis ̇ 𝑉𝑉 = − 𝜂𝜂 𝜂𝜂𝜂𝜂𝜂𝜂𝜂𝜂 𝜂𝜂 , 𝜙𝜙 + 𝐾𝐾 𝜂𝜂 𝑃𝑃 • Controller stability proven due to removal of red and addition of adaptive parameters.

Adaptive approach is asymptotically stable and corrects for plant parameter uncertainty.

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• Facility: Hybrid Propulsion Emulation Rig (HyPER) [2] • Engine: Electrified Advanced Geared Turbofan 30,000 lbf thrust (AGTF30) [3] • Controller: Turbine Electrified Energy Management (TEEM) [4] Tested in a sub-scale facility configured to represent a parallel hybrid-electric turbofan propulsion system.

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Test Article Paper Test Article NASA Glenn Research Center 8 www.nasa.gov

• Sea-level static conditions.

• Nominal Tests 1. SIL – Theoretical Simulation – (a) 2. HIL – SMICS – (b) 3. HIL – ASMICS – (c) • Robustness tests with both controllers.

1. Nominal plant parameters.

2. Artificially doubled plant inertia and damping coefficient values.

Turbofan model commanded burst/chop throttle maneuver at sea-level static conditions for seven different tests.

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Legend VBV - variable bleed valve VAFN - variable area fan nozzle LS - low spool HS - high spool LPC - low pressure compressor HPC high pressure compressor HPT - high pressure turbine 𝑥𝑥 - generic variable RMSRE - root -mean-squared relative error RE - relative error Accuracy of turbofan model behavior increased. Significantly reduced controller efforts.

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SMICS ASMICS

100% change in initial plant parameter guess has little effect on ASMICS operation.

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• An adaptive emulation controller was tested and verified in a hardware-in-the-loop environment.

• Emulated mechanical loads of turbofan on a parallel hybrid electrical architecture.

• Compared against original, non-adaptive approach.

• Adaptive approach: • Asymptotically stable in the sense of Lyapunov.

• Increases turbofan model operation accuracy.

• Decreases control effort.

• Robust to significant plant parameter uncertainty.

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• People • Marcus A. Horning • Jonathan L. Kratz • Dennis E. Culley • Projects • NASA Hybrid Thermally Efficient Core (HyTEC) NASA Glenn Research Center 13 www.nasa.gov

[1] Bianco, S. J., and Simon, D. L., “Control and Scaling Approach for the Emulation of Dynamic Subscale Torque Loads,” AIAA Aviation Forum/Electric Aircraft Technologies Symposium (EATS), San Diego, CA, 2023.

[2] Buescher, H. E., Culley, D. E., Bianco, S. J., Connolly, J. W., Dimston, A. E., Saus, J. R., Theman, C. J., Hunker, K. R., Garrett, M. J., Haglage, J. M., Horning, M. A., Cha, Y. C., and Purpera, N. C., “Hybrid- Electric Aero-Propulsion Controls Laboratory: Overview and Capability,” AIAA Science and Technology (SciTech) Forum, National Harbor, MD, 2022.

[3] Chapman, J. W., and Litt, J. S., “Control Design for an Advanced Geared Turbofan Engine,” AIAA Propulsion and Energy Forum, Atlanta, GA, 2017.

[4] Kratz, J. L., Culley, D. E., and Thomas, G. L., “A Control Strategy for Turbine Electrified Energy Management,” AIAA Propulsion and Energy Forum, Indianapolis, IN, 2019.

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