| Presented here is a study of a flexible link robotic manipulator being controlled using radial basis function neural networks (RBFNNs). Included within is the mathematical derivation of a flexible link model using the Lagrange equations coupled with the modal expansion method. Through simulation on different control schemes, a final controller was derived. By using the equations that simulate the link's behavior, known voltages were inputted to the link and the steady state velocity responses were recorded. This data set is then subdivided into smaller data sets that are used to train multiple RBFNNs. These RBFNNs are used in the forward path, as a direct controller. The result is a set of small, quick, and accurate NNs that train easily. The controller is simulated on multiple paths that are both continuous and discontinuous in both position and velocity. The paths are similar to desired trajectories that would be used in a real industrial setting. Finally, the controller is tested in the presence of differing types of noise to simulate industrial noise that would be present in a real factory setting. The variation in types and magnitude of the noise are investigated to determine an operating range for the controller. As a result of this research, a practical controller design was successfully generated and simulated. The controller design incorporates multiple RBFNNs in the forward path to collectively act as a direct controller. The NNs are not updated on-line to speed up the update rate of the controller. The controller is feasible for implementation in a factory setting. The controller is simulated on a complex and real world link that is used in industry today and proven effective. The simulated controller remains accurate even when discontinuities in the desired path position and velocity are present. Due to the static nature of this controller, simulation investigations suggest that it remains very stable even in the face of differing types and levels of noise. |
