1. Laboratoire d’Automatique SECTION DE Génie mécanique Angle Estimation in a PWM Stepper Motor Driver by Kalman Filtering Author Hamed Shisheh Foroush Supervisors Dr. Mark Butcher (CERN) MER. Dr. Alireza Karimi (EPFL) Acknowledgements MER. Dr. Alireza Karimi (EPFL) Dr. Alessandro Masi (CERN) Motivation & Objectives Collimators are the mechanisms installed around the 27 km Large Hadron Collider (LHC) circuit. They have to protect the accelerator components, particularly the superconducting magnets, from uncontrolled beam losses. The main components of the collimators are jaws and stepper motors. The jaws are to perform the protection responsibility of the collimators, thus in order to position them, the stepper motors have been used. Nonetheless, the positioning of these blocks have to be performed with very high accuracy (±10 μm), so the stepper motors’ angular position has to be controlled. In fact, each motor’s controller is implemented in a driver which cannot be installed in the proximity of the motors because of the high level of radiation around the motors; instead they are located in radioactive free zones several hundred meters away from them and are connected to them by long cables. This point prohibits us to use the sensor-based approaches for the angular position measurement of the stepper motors. Amongst the different sensorless approaches, the Kalman filtering has been selected. Therefore, the main objective is to develop a methodology in order to implement the Kalman filtering to perform the angular position estimation of the stepper motor, despite existence of long cables, in order then to be used in the feedback line of the closed-loop controller. In this type, the cable is modelled as a transfer function demonstrates the cable representative circuit, this transfer function is so-called Gest(s). Cable Model, Type I Cable Model, Type II Methodology Cable Models Overview Results & Conclusions Since the main characteristic of the cable is capacitive, therefore, it has been theoretically proved that the cable can be modelled as a moving averaging filter. Monte-Carlo Simulation Results: By running the Monte-Carlo simulation for the variety of noise realizations, in order to check the functionality of the Kalman filtering installed on the different cable models, it is concluded that there is no significance difference between the different cable models and thus the simpler one will be employed in the practical setup. The variety of approximations for the cable dynamics has been verified. Hence, the cable’s representative circuit is derived and used to model its dynamics. The investigated methodology considers the dynamics of the cable and the Kalman filtering as two separate modules. Therefore, the measured driver-side data are mapped to the motor- side data by passing through the cable model module. The Extended Kalman Filter module, then, estimates the angular position of the stepper motor. Practical Results: Concluded from the simulations, in the practical domain, the moving averaging filter has been exploited to model the cable dynamics along with the Extended Kalman Filter module in order to estimate the angular position of the stepper motor. Then, to find out the performance of the implemented structure, the angular position estimation and measurement are compared.