Optimizing motion paths with respect to the needs of the application

Sammanfattning: A method for optimizing motion path definitions for servo unit motors of Tetra Pak’s packaging machines using optimal control is chosen, described and tested. Tetra Pak’s packaging machines are characterized by the use of servo motors to control repetitive actions that are repeated in cycles. When developing new packaging machines the motion path of the servo motor is always optimized in some way, usually to complete a cycle of actions as fast as possible. While there is usually a need to maintain a specific position, velocity or acceleration at a few points along the cycle, there is often flexibility in where these points are located in time and in how the motion path is defined in-between these points. Finding an optimal path is time consuming with current methods employed by Tetra Pak and this thesis will focus on a way of using optimal control theory to find a motion path that is optimized according to the specific needs and limitations of the application. A common need is to perform a cycle as fast as possible, while adhering to a servo motor’s limitations on torque. The optimization method needs to optimize the path with respect to the needs of the application as well as the limitations of the mechanical system and the servo motor, and as such a significant part of the thesis concerns the problem definition and modelling of the mechanical system. As well as providing a method for optimizing motion paths, this thesis will in detail describe an example where a mechanical system will move a mass up and down as fast as possible, while adhering to a servo motor’s limits on torque and speed. The optimization method is implemented for the specific example outlined in this thesis to show that this is a viable way for Tetra Pak to design motion paths. The final result of this thesis is the definition of the optimization method used and the results of this method when optimizing the motion path for the described example. The goal of the method is to be able to be used in a wide variety of different scenarios within Tetra Pak’s research and development, and as such it is constructed to be a generic method that can handle different mechanical systems as well as different aspects to be optimized. While the method is constructed to be generic, designing a workflow for using this method for other scenarios than the example outlined as well as integrating this method into Tetra Pak’s current workflow is left for future research.