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Optimal Control of Formula One Car Energy Recovery Systems
D. J. N. Limebeer with
Peter Fussey; Mehdi Masouleh; Matteo Massaro; Giacomo Perantoni; Mark Pullin; Ingrid Salisbury.
Work part funded by the Engineering and Physical Sciences Research Council
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Contents
• Thermal-Electric Energy Recovery
• Track Modelling
• Car Modelling
• Optimal Control
• Nominal Car Performance & Setting the Scene
• Brief review of 2013 KERS
• 2014 Power Unit Performance
• Power Unit Map optimisation
• Conclusions
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Powertrain
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Thermal Energy Recovery
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2014 Power Train I
Lithium Ion Battery Kinetic Energy Recovery System
Thermal Energy Recovery system Turbo-compounded
IC engine
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2014 Power Train II 1. 100 kg of fuel per race; 2. the fuel mass flow limit 100 kg/hour.
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Track Modelling
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Track as a Ribbon Frenet-Serret apparatus
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Lemniscate of Bernoulli
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Track Model I
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Track Model II
Elevation
Geodesic curvature
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Car Kinematics
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Car Modelling
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Car Modelling
• Newtonian mechanics;
• Closed kinematic suspension loops;
• Meta modelling;
• Magic Formula-type tyre;
• Aerodynamic maps;
Aerodynamics are for people
who can't build engines.
Enzo Ferrari
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Car Modelling
• Newtonian mechanics;
• Closed kinematic suspension loops;
• Magic Formula-type tyre;
• Speed-dependent aerodynamic maps;
Aerodynamics are for people who can't
build engines.
Enzo Ferrari
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Suspension System
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Suspension System
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Car Dynamics
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Partial EOM
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Tyre Model
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Aerodynamic Maps
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Optimal Control
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Optimal Control Problem
Mayer-Pontryagin Cost
EOM
TPBVP
PMP
Control Hamiltonian
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Numerical Optimal control
Discrete Mayer cost
Discrete dynamics
NLP Karush-Kuhn-Tucker (KKT) optimality conditions
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Practicalities
• Scaling important;
• Non-smooth features must be approximated;
• Singular arcs regulated
• Direct methods with Gaussian quadrature integration schemes method of choice;
• Computations use GPOPS-II, IPOpt and ma57.
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Non-smooth Features
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Optimal Car Performance
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Refined Mesh
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Speed Profile of Nominal Car
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The Racing Line; corners 10-16
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Optimal Lap of Barcelona
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Conventional 2013 KERS
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Kinetic Energy Recovery
• 2013 kinetic energy recovery systems (KERS) facilitate the capture of kinetic energy that derives from braking;
• Recovered energy can be stored for later deployment in propelling the car;
• Short-term power boost to be used under over taking.
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Conventional KERS Constraints
Cannot use engine to
recharge batteries.
Engine only
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Power Usage Bang-Bang controls
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Energy Usage
Energy Quota 400kJ
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2014 Power Train
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2014 Power Train Features
• Controls: steering, brakes, fuelling, waste gate (MGU-H), MGU-K;
• The car's energy store (ES) up to 4 MJ;
• ES-2-MGU-K up to 4MJ per lap;
• MGU-K-2-ES up to 2MJ per lap;
• MGU-K restricted to ±120 kW.
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Simulation Track - Spa
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Energy Usage (racing)
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Power Usage (racing)
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Speed Difference and Long Gravity
Down hill
Up Hill
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Power Unit Maps
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Power Unit Maps
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Energy Usage (Racing)
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Power Usage (Racing)
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Optimised 2D & 3D maps
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Conclusions & Future Work I
• Optimal control of thermal-electric power trains accomplished;
• Like-for-Like performance with 2/3 fuel consumption;
• Three-dimensionality can be important and can be studied;
• Power train maps can be parameterised and optimised;
• Fast dynamics relating to aero-suspension treated quasi-statically;
• Further progress being made in the optimal control of high-fidelity models...
Thanks for Listening