Servomechanism for periodic reference input: Discrete wavelet transform-based repetitive controller

Abstract

The presented work explored the possibility of developing a discrete wavelet transform-based repetitive control (DWTRC) strategy along with a proportional controller for a liquid level system (LLS) to track a periodic reference signal. The modified DWTRC with a P control system is a type of servo mechanism, effective for periodic reference input. The entire effort derives from two distinct parts. First, the tracking performance and stability measure of the system with inclusion of a repetitive controller (RC) in presence of P controller that has been studied and compared with conventional P and PI controllers in both time and frequency domains, subjected to periodic command to establish the usefulness of the former. The most obvious disadvantage of the RC with P control is the requirement of large memory for the presence of RC, and the memory requirement linearly increases with both repetition time and sampling frequency. Second, to overcome this difficulty, deployment of the discrete wavelet transform (DWT) in the RC loop is done to reduce the problem of memory requirement, and ensures efficient and high-speed computation due to the filtering and data reduction property of DWT. Finally, the effectiveness of DWTRC is validated through saving memory and optimizing the tracking error with variation of the wavelet order and its decomposition level.