NASCAR Refueling Challenges: Connie Wang Outline Background Model - PowerPoint PPT Presentation

NASCAR Refueling Challenges: Connie Wang

Outline • Background • Model Highlights • Safety and Efficiency • Proof Highlights • Conclusion The Strategy Behind a Pit Stop by Connie Wang

Background • NASCAR races • 36 total races • 34 oval tracks • .526 – 2.66 miles long • 188 – 500 laps • Refueling rules • No sensors to monitor exact gas level • 24 gallons per pit stop The Strategy Behind a Pit Stop by Connie Wang

Model Highlights • Controls • 𝑗𝑔 𝑔𝑣𝑓𝑚 > 𝑔𝑑 ∗ 𝑤 ∗ 𝑈; 𝑑𝑝𝑜𝑢𝑗𝑜𝑣𝑓; • 𝑗𝑔 𝑔𝑣𝑓𝑚 ≤ 𝑔𝑑 ∗ 𝑤 ∗ 𝑈; 𝑔𝑣𝑓𝑚 = 𝑛𝑏𝑦; • ODEs • 𝑦 5 = 𝑤 ∗ 𝑒𝑦 • 𝑧 5 = 𝑤 ∗ 𝑒𝑧 • 𝑒𝑦 5 = −𝑒𝑧 • 𝑒𝑧 5 = 𝑒𝑦 • 𝑔𝑣𝑓𝑚 5 = −𝑔𝑑 ∗ 𝑤 (linear) • 𝑔𝑣𝑓𝑚 5 = −(𝑔𝑑 ∗ 𝑤 ∗ 𝑢 + 𝑑) (quadratic) The Strategy Behind a Pit Stop by Connie Wang

Safety and Efficiency • Stay on track • 𝑦 < + 𝑧 < = 𝑠𝑏𝑒 < • Sufficient fuel • 𝑔𝑣𝑓𝑚 ≥ 0 • Do not stop unnecessarily • 𝑗𝑔 𝑔𝑣𝑓𝑚 > 𝑔𝑑 ∗ 𝑤 ∗ 𝑈; 𝑑𝑝𝑜𝑢𝑗𝑜𝑣𝑓; The Strategy Behind a Pit Stop by Connie Wang

Proof Highlights (on track) • Loop invariants • 𝑦 < + 𝑧 < = 𝑠𝑏𝑒 < • 𝑒𝑦 < + 𝑒𝑧 < = 1 • 𝑒𝑦 ∗ 𝑤 = −𝑧 • 𝑒𝑧 ∗ 𝑤 = 𝑦 • 𝑠𝑏𝑒 ≥ 0 • Differential Cuts • 𝑒𝑦 ∗ 𝑤 = −𝑧 • 𝑒𝑧 ∗ 𝑤 = 𝑦 The Strategy Behind a Pit Stop by Connie Wang

Proof Highlights (sufficient fuel) • Loop Invariants • 𝑔𝑑 > 0 • 𝑈 > 0 • 𝑔𝑣𝑓𝑚𝑗𝑜𝑗𝑢 > 𝑔𝑑 ∗ 𝑤 ∗ 𝑈 (linear) • 𝑔𝑣𝑓𝑚𝑗𝑜𝑗𝑢 > 𝑔𝑑 ∗ 𝑤 ∗ 𝑈 < + 𝑑 ∗ 𝑈 (quadratic) • 𝑛𝑏𝑦 > 𝑤𝑑 ∗ 𝑤 ∗ 𝑈 • Differential Cuts • 𝑔𝑣𝑓𝑚 = 𝑔𝑣𝑓𝑚𝑗𝑜𝑗𝑢 − 𝑔𝑑 ∗ 𝑤 ∗ 𝑈 (linear) • 𝑔𝑣𝑓𝑚 = 𝑔𝑣𝑓𝑚𝑗𝑜𝑗𝑢 − (𝑔𝑑 ∗ 𝑤 ∗ 𝑈 < + 𝑑 ∗ 𝑈) (quadratic) The Strategy Behind a Pit Stop by Connie Wang

Conclusion • Can CPS models help NASCAR teams? • Proof helps devise strategies • Use of algorithmic CPS controllers • Future work • Acceleration/deceleration • Time constraints • Multiple cars • Tire degradation The Strategy Behind a Pit Stop by Connie Wang

Thanks! The Strategy Behind a Pit Stop by Connie Wang