Feedforward learning control with application to trajectory tracking of a flexible beam

A simple approach to the feedforward compensation in the tip-tracking control of flexible beam is presented. The approach is based on probing the system with a finite number of independent input signals and then fitting the corresponding output signals to a desired output trajectory. Since neither the dynamic model nor the full state of the beam is required, and the method applies to the tracking of a fixed, finite time output trajectory, the scheme is considered as a learning control strategy. Due to the assumed linearity, this problem is transformed into a standard least square problem. Controller saturation can be incorporated, resulting in a constrained-least-squares problem. The basic method has also been generalized to linear time-varying systems and nonlinear systems. Experimental and simulation results are presented to demonstrate the overall viability