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This paper describes an adaptive feedforward controller to let the output of a plant with stable and unstable zeros track a time varying desired output. The dynamics of the closed loop system consisting of the plant and the feedback controller are assumed unknown or slowly varying due to changes on the plant parameters. In the control scheme proposed in this paper, the feedforward controller is adaptive while the feedback controller is fixed under the assumption that the closed loop system remains stable at all times. With a few samples of future reference input data available, the preview action of the adaptive feedforward controller cancels the phase lag caused by the closed loop dynamics and attains the zero phase error tracking performance (i.e., the plant output is in phase with any sinusoidal desired output) asymptotically.
Tsao et al. (Tue,) studied this question.