Evaluation of Numerically Developed Models of an ECB for Estimating the Braking Torque on the SkiCrosser

Sammanfattning: Cross-country skiing is a popular method of exercising that builds strength, stamina and engages the entire body. As cross-country skiing requires snow to be present, it is typically only performed during the winter, resulting in a rather limited way of exercising. The SkiCrosser is a mechanical exercising machine that solves this issue by mimicking the movement and muscle engagement found in cross country-skiing, removing the dependency of snow altogether. The resistance of the machine can be adjusted manually, requiring the user to step off the machine and pause their exercise.  To improve upon the SkiCrosser, the thesis aims to investigate the possibility of implementing an Eddy Current Brake (ECB) on the machine. An ECB consisting of a spinning conductive disc and electromagnets would allow the resistance of the SkiCrosser to be controlled electronically. The focus of the research is to determine how accurately mathematical models developed using numerical methods can estimate the braking torque of the ECB for different skiers and skiing cases on the SkiCrosser.  A case study was performed where speed data from the SkiCrosser was collected for three different skiers, skiing at different paces and resistances (skiing cases). An ECB consisting of two electromagnets and an aluminium conductive disc was developed. To accurately and repeatably simulate the human skier when testing the ECB, a test bed was constructed. The test bed allowed the speed of the ECB’s conductive disc and the current supplied to the electromagnets to be controlled. Additionally, the test bed allowed the generated braking torque to be measured. Three numerical models were developed from data gathered from the test bed, describing the ECB’s dynamics. Two of the models were grey box models, where one had a linear speed relationship and the other nonlinear. The third model was a nonlinear ARX model.   The speed data from the case study was used as a speed reference on the test bed. The ECB’s braking torque on the SkiCrosser could thus be simulated for different skiers and skiing cases. Each model’s accuracy was then determined by comparing the simulated braking torque to the model estimations.   A performance comparison of the three developed models was conducted and discussed. The aim of the comparison was to understand the model accuracies were affected by different skiing cases and skiers, as well as reveal which model provides the most accurate estimations.