Ball and plate balancing control systems are commonly studied due to the complex dynamics associated with the instability of the system in open-loop. For simplicity, mathematical models describing the ball and plate dynamics are often linearized and the effects of complex motion are assumed to be negligible. These assumptions are rarely backed with evidence or explanations validating the simplified form of the dynamical equations of motion. This thesis focuses on developing a nonlinear model that more accurately defines the dynamics of the system, in order to quantify the error of linear and nonlinear models when compared to a Simscape physical system model. To develop the nonlinear model, this thesis considers both Newton-Euler and Lagrangian modeling methods and applies the method best suited for the ball and plate system. A linear state-feedback controller is developed to compare the stable responses of each system model. The response of each plant model in open-loop and closed-loop configurations subject to different inputs, initial conditions, and disturbances are simulated in the Simulink environment.
When compared to the physical system, there was less error from the nonlinear model than from the linear model for both initial condition and disturbance responses. The differences in error were as high as 2% compared to 10% for the nonlinear and linear models, respectively. These results show that there are significant differences associated with model simplification. To optimize the performance, it may be advantageous to utilize a nonlinear model, however, the linearized model is still valid to be used in certain applications due to its stable response behavior.
| Identifer | oai:union.ndltd.org:CALPOLY/oai:digitalcommons.calpoly.edu:theses-3936 |
| Date | 01 August 2021 |
| Creators | Richter, Zachary |
| Publisher | DigitalCommons@CalPoly |
| Source Sets | California Polytechnic State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Master's Theses |
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