Analysis and design of a learning feedforward controller using Bartlet window

A learning feedforward controller (LFFC) using the Bartlet window function is proposed for a better tracking control of linear system over a finite time interval. LFFC is applied as a feedforward controller to the existing feedback controller. This paper demonstrates that using a simple window function-Bartlet (Fejer or triangular) window in signal processing, the design of a learning feedforward controller reduces to determining only two design parameters: the learning gain and the number of point in the window. Convergence analysis is presented together with a design procedure.

1. Introduction

Learning Feedforward Control (LFFC) [1]–[4], [5] can be regarded as a variant of ‘Iterative Learning Control’ (ILC) [6], [7]. ‘Iterative Learning Control’ (ILC) [6] can be considered as a value-added block to enhance the feedback control performance by capitalizing the repetitiveness of system's operation. Clearly, the purpose of introducing the ILC is to utilize the system repetitions as experience to improve the system control performance even under incomplete knowledge of the system to be controlled. While the formal mathematically rigorous analysis is initially due to [6], the basic idea can be traced back to [8] and even to [9] which is commented in [10]. A recent survey and historical note on LFFC can be found in [11] while the design procedures are summarized in [12]. Detailed literature reviews on ILC research can be found in [13], [14].