Strategy Optimization - MSXV

ASC objectives for SOV

1. to complete the American Solar Challenge base route without trailering

2. to complete as many official miles as possible

3. to complete the distance in the shortest elapsed time

Additional Constraints (From ASC2024 Regs B)

1. “The Standard Tour Day is from 9:00 am – 6:00 pm (9 hours). Actual Tour hours may be adjusted to start later or end earlier than the standard racing day based on the exact Segment distances and coordination of activities at each of the Stage/Check Points.”

2. “Solar cars must observe a maximum speed limit of 104.6 km/h (65 mph) or the posted speed limit (whichever is lower), unless further restricted by the Officials per Reg. 10.9.B.”

3. “In areas with a posted speed limit of at least 96.6 km/h (60 mph), teams shall maintain a minimum speed of 32.2 km/h (20 mph) unless trapped behind other traffic. Teams unable to maintain this speed must pull over at the next safe opportunity to resolve the issue.”

What are the outputs?

1. What speed should we drive at?

2. Should we take-on a loop?

What are the inputs to this function?

How our car consumes, captures, and stores energy: E(stored) = E(in) - E(out)

Consumption: Past consumption can be measured/logged to inform the car’s current state. Future consumption needs to be predicted to inform strategy.

Capture: Predict the amount of solar energy available in a day depending on space and time.

Storage: Is charging or discharging preferred at a given time.

Our goal?

If we can ensure the completion of the route, our secondary objective should be to maximize distance for in the fixed ~9hr time.

Strategies?

• conservative

• aggressive

Conservative Strategy

Guiding Principles

• Car without solar capture: “simple vehicle travelling at a constant speed uses less energy than it does for any other strategy with the same average speed.” [1]

• Solar car: “for a long journey, most of the time should be spent travelling at a constant speed” [1]

• Speed vs Efficiency

Procedure

• re-calculate V = d/t at some frequency and drive faster than it by some margin

Insurance

• Is this theoretically achievable? Are there situations where there is an even safer strategy?

Aggressive Strategy

Non-linear MPC - Optimal Control Theory

To-do:

1. Consumption Prediction

   1. Motors

      1. Drag force (velocity, weather)

      2. Gravitational force (slope of track)

      3. Rolling friction force (velocity, slope of track)

   2. Auxillary

Rodrigo Tiscareno Can you get me a tabular data set with the inclination, wind speed, and wind direction for all times at all locations on a given route for a single day. Location can just be a scalar value of the distance along a course.

2. Capture Prediction

   1. Weather (space, time) → Solar Irradiance (orientation) → PV efficiency

Rodrigo Tiscareno Can you get me a tabular data set with quantizing the cloud percentage for all times at all locations on a given route for a single day. Location can just be a scalar value of the distance along a course.

3. Optimization???

Bibliography

[1] Optimal energy management for solar-powered cars. (n.d.). Retrieved November 9, 2023, from https://find.library.unisa.edu.au/discovery/delivery/61USOUTHAUS_INST:ROR/12146635320001831

[2] Howlett, P., & Pudney, P. (1998). An optimal driving strategy for a solar-powered car on an undulating road. Dynamics of Continuous, Discrete and Impulsive Systems, 4.

[3] Pudney, P., & Howlett, P. (2002). Critical Speed Control of a Solar Car. Optimization and Engineering, 3, 97–107. https://doi.org/10.1023/A:1020907101234

[4] Selin, I. A., Kasatkin, I. I., Zakhlebaev, E. A., & Hemminger, O. P. (2019). Building a time-optimal power consumption strategy for a solar car. IOP Conference Series: Materials Science and Engineering, 643(1), 012004. https://doi.org/10.1088/1757-899X/643/1/012004

[5] Kirk, D. E. (2004). Optimal Control Theory: An Introduction. Dover Publications. https://books.google.ca/books?id=fCh2SAtWIdwC