Automatic Control of a Dynamic System: Positioning of a Spherical Object on a Flat Surface

Controlling the value of a variable and compensating for external influences is a fundamental problem in a wide range of applications. This thesis investigates the issues of such control problems; it presents theory on control design and system modeling as well as the development of a demonstrator in the form of a ball-balancing platform to apply these concepts on.

This project’s purpose is to design a dynamic system and a state space controller that performs as well as possible with respect to response time and precision.

The purpose of the project is achieved by analyzing the dynamic problem and from it create a theoretical model. This is then used to design a state space controller in order to continuously regulate the position of a ball on the platform. The final step is to build a demonstrator which will be used to verify that the designed controller fulfills the criteria that was assigned at the beginning of the project.

The controller was tested by performing a step in the set-point with 15 millimeters. This made it possible to analyze the step response in order to determine the rise time, overshoot and the static error of the system. The result of the tests was a rise time of 0.3 seconds, with a overshoot of 4%, which fulfills the speed demands of the system. The static error had a peak of 3 millimeters offset from the set-point.

The main part of the error was caused by a hardware issue in the form of the ball not moving even though the platform is tilting. This due to irregularities on the ball’s surface as well as the resistive touchscreens cushioning effect. The static error was therefore deemed as acceptable.
Source: KTH
Author: Lagerkvist Blomqvist, Johan | Osterman, Niles

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