On the Robustness of Adaptive Nonlinear Model Predictive Cruise Control O. Santin1, J. Beran1, O. Mikuláš1, J. Pekar1, J. Michelini2, S. Szwabowski2, S. Mohan2, D. Filev2, J. Jing3, U. Ozguner3 1
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Content Introduction Algorithm High-level Overview Robustness Simulation Study Road Grade Accuracy Impact Analysis Road Grade Phase Error Correction Algorithm Conclusion
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Project History Adaptive Nonlinear Model Predictive Controller (ANLMPC) Project History SAE 2017-01-0090
SAE 2016-01-0155 * • • • • •
Lincoln MKT Nonlinear MPC in PCM 23 kB ROM, 59 kB RAM Model Adaptation (RLS) 0.6-2.4% FE Benefit
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Lincoln MKT + 1600 kg trailer Downshifting Avoidance 24 kB ROM, 6 kB RAM Constrained + Dead-zone RLS 6.3-8.8% FE Benefit
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Ford F-150 + trailer Robustness Study Grade Phase Error Correction Up to 11% FE Benefit (4500 kg trailer)
*https://cars.usnews.com/ ** https://ford.com/ SAE INTERNATIONAL
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MPC: Model Predictive Control PCC: Predictive Cruise Controller
Introduction # passengers, fuel type, Trailer mass & drag
Weather Conditions
Ford F-150
GPS Location Inaccuracy
Grade Map Inaccuracies
Goal: Evaluation of robustness of MPC based PCC SAE INTERNATIONAL
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Real grade Maps grade 4
Algorithm High-level Overview Slow changes (drag, rolling resistance, mass, bias/scale in grade, fuel type)
Fast changes (e.g. head wind)
Grade phase offset
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Robustness Simulation Study - Multipliers Fuel Type (octane number)
Weight
Aerodynamic Drag
Grade
Tire Pressure • •
Ford F-150 Model Baseline: ACC controller
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Test Road I94 M39 US12
Length [miles] 11 12 8.5
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Road grade [%] (-2.0, 2.5) (-3.3, 3.8) (-5.5, 5.5)
Real grade Maps grade
Speed [mph] (61, 69) (51, 59) (46, 54)
limits
6
Weight
Aero
Weight
Aero
MPG benefit [%] MPG benefit [%]
US12
I94
Robustness Simulation Study - Results
Grade Tire Press Fuel (octane) Fuel effect • Low octane + ACC higher torque spark timing further from MBT higher fuel Aero effect • Depends on grade Grade Tire Press Fuel (octane) symmetricity (uphill / downhill sections) • US12 closes to grade symmetricity (positive avg.) Grade effect • +/- Avg. grade -/+ FE benefit
Baseline: ACC controller (no preview utilization) with the same average speed SAE INTERNATIONAL
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Motivation for Road Grade Error Study
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In-vehicle data: • grade phase error Δd • control performance.
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Robustness improvement a grade correction method is developed.
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Road Grade Accuracy Impact Analysis • Road Grade Preview Errors 𝜙𝐵 𝑡 = 𝜸𝜙 𝑑 + 𝜟𝒅 + 𝜙𝐵𝑖𝑎𝑠 ,
Location Inaccuracy Grade Map
• Handled by Adaptation of Model Parameters (RLS) 𝑑𝑣(𝑇, 𝑣, 𝜙ሻ Scale / Bias = 𝛽1 𝑇 + 𝛽2 𝑣 2 + 𝛽3 𝜙𝐵 + 𝛽4 𝑑𝑡 error 𝑔 • Scale Error: 𝛽3 = − 100𝜸
• Bias Error: 𝛽4 = 𝛽4 𝑛𝑜𝑚 + 𝛽3 𝜙𝐵𝑖𝑎𝑠 • Phase Error: Not possible to separate the effect SAE INTERNATIONAL
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MPH benefit [%]
𝑣ሶ = 𝛽1 𝑇 + 𝛽2 𝑣 2 + 𝛽3 𝜙𝐵 + 𝛽4
Model Parameters for 𝜟𝒅
𝜟𝒅 Grade Phase Error [m]
𝛽3
MPH benefit [%]
𝜙𝐵𝑖𝑎𝑠 Grade Bias Error [%]
MPH benefit [%]
𝛽2
𝜸 Grade Scale Error [-]
MPG benefit [%]
MPG benefit [%]
MPG benefit [%]
Road Grade Accuracy Impact Analysis – Results*
𝜟𝒅 = 0 m 𝜟𝒅 = -15 m 𝜟𝒅 = -10 m 𝜟𝒅 = 10 m 𝜟𝒅 = 15 m
Large Sensitivity to Phase Error
*Ford F-150 + 10,000lbs trailer, baseline is ACC controller, US12 road (+/-5.5 %) SAE INTERNATIONAL
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𝜙𝐵 𝑡 = 𝜸𝜙 𝑑 + 𝜟𝒅 + 𝝓𝑩𝒊𝒂𝒔 , 10
Road Grade Phase Error Correction Algorithm • • • • • •
Method basis: Minimizing residuals in model representation Grade Error: 𝜙𝑒 𝑘, Δ𝑑 = 𝜙 𝑘 − 𝜙෨ 𝑘, Δ𝑑 Vehicle acceleration 𝑎𝑘 = 𝛽1 𝑇k + 𝛽2 𝑣𝑘2 + 𝛽3 𝜙(𝑘ሻ + 𝛽4 𝑎ොk (Δ𝑑ሻ = 𝛽1 𝑇k + 𝛽2 𝑣𝑘2 + 𝛽3 𝜙෨ k, Δ𝑑 + 𝛽4 Predicted acceleration Error in predicted acceleration ek (Δ𝑑ሻ = 𝑎k − 𝑎ො𝑘 (Δ𝑑ሻ Implementation: Collect backward looking vector of acceleration errors 𝐞𝐤 (Δdሻ = [𝑒𝑘 , 𝑒𝑘−1 , 𝑒𝑘−2 , ⋯ , 𝑒𝑘−𝑁𝑝 ]′
• Solve the optimization problem min 𝐞𝐤 (Δ𝑑ሻ
2
Δ𝑑
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Road Grade Phase Error Correction Algorithm • Task Flow Diagram
𝛽 1,⋯,4 ,𝑘−1
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Road Grade Phase Error Correction Algorithm - Results
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20m grade phase delay
MPH
MPG
Gear Shifts
Fuel Saving
With
49.21
16.20
38
10.46%
Without
48.66
15.57
120
6.13% 12
Conclusion • Simulation study for Ford F-150 vehicle • Achievable FE benefit up to 11% (10000lbs trailer) • Positive impact from vehicle mass • Grade and Aerodynamic drag depends on symmetricity of the road grade profile • Road Grade Inaccuracies • Offset and scale error handled by RLS • Phase error handled by the iterative estimation of the phase lag
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Thank you Ondrej Santin –
[email protected] Shankar Mohan –
[email protected]
M39 (~+/-3.5%)
I94 (~+/-2.5%)
Bias Error
Scale Error
US12 (~+/-5.5%)
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M39 (~+/-3.5%)
I94 (~+/-2.5%)
Phase Error Comp.
Phase Error
US12 (~+/-5.5%)
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