System identification of a mathematical model to predict cycling power

Here we present a mathematical model that predicts the mechanical power of outdoor cycling measured in the crank arm. We derive this model from first principles to prescribe mechanical power as a function of speed and acceleration, which are described by a combination of cadence and gear ratio. In outdoor experiments, we provide subjects with a range of prescribed cadences and measure the underlying power output. We use this data to parameterize the model using non-linear regression. With this model we will design a high-performance feedback controller, that accurately controls the power in cycling by commanding cadence.