Characteristic models and adaptive iterative learning control of linear servo systems

This paper presents characteristic models of linear servo-systems and a characteristic-model based adaptive iterative learning control scheme. The system undertaken is shown to be a sixth order linear time invariant system, when utilizing the "i
d
=0" control strategy. The characteristic models from first-order to third-order are obtained, where the characteristic parameters are both time-varying and iteration-dependent. The least squares iterative learning algorithm with a forgetting factor is introduced to estimate the unknowns, and a saturated adaptive iterative learning controller is given, based on the LQ optimal control method, to realize that the system's outputs completely follow the desired trajectory over the entire interval. Numerical results are presented to verify effectiveness of the proposed learning control scheme.