In the first part, an extremely simple controller design methodology is derived by treating the effects of distributed flexibility as an uncertain term in torque about which no apriori knowledge is assumed other than a bound. The controller design methodology is validated for a single rotating flexible link manipulator modeled using ANSYS.
In the second part, a self-tuning control strategy for modeling, identification, and self-tuning control of a SISO discrete-time nonlinear system is validated. The classical recursive least squares algorithm for system identification and pole-placement technique for controller design is employed. The pseudolink concepts are used to determine on-line angular displacement of the end-effector of the flexible link manipulator modeled using ANSYS.
Finally, the third part addresses the topics of on-line system identification of an unknown nonlinear dynamical system using back-propagation neural network and the on-line self-tuning adaptive control of such systems using a separate neural network as a controller. An on-line self-tuning adaptive control output tracking architecture/law using three multi-layer back-propagation neural networks is proposed. The weight updating of the neural networks is generalized using gradient methods. The convergence of errors of the closed loop feedback system architecture is proved. The new OLSTAC scheme/architecture is applied to a single rotating flexible link manipulator as well as to a two “coupled” flexible link manipulator arm. It is demonstrated through illustrative simulations that the OLSTAC scheme/architecture is generic in the sense that it requires minimal knowledge of the unknown plant. While the proposed OLSTAC scheme is based on an assumption, Assumption SI-1, that make the sufficient condition that the unknown nonlinear/uncertain system can be separated into two nonlinear terms, one, the nonlinear term in the state, and the other, the nonlinear term representing control, it works admirably for the cases when the system is highly nonlinear and uncertain, e.g., the flexible link manipulator systems.
The signal from the accelerometer at the tip of the boring bar was used as the input signal for the neural network. The network generates an appropriate output to the peizoelectric pusher in the boring bar, providing enough damping to reduce the vibrations at the tip of the bar. The results from the open loop and closed loop systems are discussed along with the two methods used for learning in the neural network. An introduction to neural networks, especially CMAC networks is an important part of this work as is explained in the project definition and scope of this project.