This thesis evaluates two automatic control systems, PID and LQ, for the purpose of controlling the steel marble in a Brio labyrinth game. The objective has been for these automatic control strategies to bring the marble through the labyrinth and examine how well they handle this problem. A mathematical model of the problem was derived and a detailed model of the labyrinth game was established in Mathworks software Simscape to streamline the development of the structural design and control system. Based on the Simscape model, the labyrinth game was modified with hardware necessary to perform the task. Before the development of the control system commenced, tests were carried out to study the marbles movement in the two models compared with the labyrinth game. This proved that the friction in the labyrinth game is non-linear compared to the models which both showed similar behavior. The control system was then implemented to be tested and evaluated in the Simscape model as well as the labyrinth game. In the Simscape model, they both perform equally well and the PID- and LQ-controller can easily bring the marble through the labyrinth. In the labyrinth game, the LQ controller succeeds in bringing the marble through the labyrinth in 45\% of cases, while the corresponding for the PID controller is 25\%. The LQ controller was the one that generally had the best performance and was able to handle the marbles movement despite the non-linearities. The PID controller's performance was poorer, which is largely due to said non-linearities but also noise in the system, which the LQ controller is not affected as much by. The study shows that non-linearities such as friction are difficult to model. The model-based design is a good method but can be time consuming and the end result can make it difficult to motivate in many cases.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-157630 |
| Date | January 2019 |
| Creators | Nådin, Mikael, Ericsson, Kristian |
| Publisher | Linköpings universitet, Reglerteknik, Linköpings universitet, Reglerteknik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | Swedish |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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