Paper · Control Systems
PaceGuide
Intelligent race pacing via GPS-based control systems — designing the feedback loop that tells a runner to speed up, ease off, or hold.
- Institution
- George Mason University
- Department
- Systems Engineering & Operations Research
- Tooling
- MATLAB / Simulink
- Length
- 9 pages, 30 figures
Abstract
Elite marathoners get a pace car. Eliud Kipchoge’s sub-two-hour attempt was held to schedule by a vehicle driving a precise, unwavering speed. Everyone else glances at a watch and does mental arithmetic mid-race — which is why recreational pacing falls apart.
This paper builds that pace car into a GPS smart watch. The system reads position, derives velocity, compares it against the target, and returns one of three instructions: faster, slower, or maintain. Four progressive Simulink models take it from an idealized proportional controller to one that survives discrete sampling and noisy GPS fixes.
The finding that matters: velocity feedback alone always leaves a residual distance error, because small speed deviations integrate into meters of shortfall over an hour. Adding a position-error integrator closes that gap — the tuned dual-input controller lands on 10 km at exactly 3600 seconds.
Four Models
Each model keeps the previous one’s structure and removes one convenient assumption, so the cost of every real-world constraint can be read off in meters.
Proportional Control
Instantaneous velocity feedback with gain K. Sweeping K = 0.1, 1, and 6 exposes the trade between responsiveness and stability.
K = 1 finishes 3 m short; K = 0.1 falls 28 m short.
Discrete-Time Sampling
Velocity is no longer known instantly — it is differenced from positions sampled every Δt. Tested at Δt = 1 s, 4 s, and 10 s.
Δt = 10 s costs 13 m of the 10 km target.
GPS Measurement Error
Zero-mean Gaussian noise (σ = 2 m) is injected into each position fix, so the derived velocity inherits sensor uncertainty.
Noise amplifies as Δt shrinks — smaller windows are worse.
Dual-Input Control
A third-order controller adds an integral position term (Ki) on top of velocity gain (Kp) to correct accumulated drift, not just instantaneous speed.
Ki = 1.5 × 10⁻⁵ hits 5 km at 1800 s and 10 km at 3600 s exactly.
Simulation Parameters
10 km
Race distance
60 min
Target finish
2.778 m/s
Target pace
σ = 2 m
GPS error
Authors
- Hocine FilaliSimulink models, Model 4 analysis, conclusion
- Amr HamzaModel 1 and Model 2 analysis
- Adewale Adekambi— meAbstract, introduction and background, Model 3 analysis
Read the full paper
Nine pages covering the block diagrams, governing equations, and simulation output for all four models.
PaceGuide.pdf