Adaptive Zero Phase Error Tracking Algorithm for Digital Control

Abstract

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.

Nonminimum phase adaptive inverse control for settle performance applications

“…We rely on a recursive least squares (RLS) parameter es-timation algorithm to estimate the closed-loop dynamics, and then use the zero-order Taylor series approximate inversion technique from (11) to synthesise an inverse system. Similar approaches have been taken in [22]- [24].…”

“…In [22] and [23], the ZPETC approximate inverse technique is used to synthesize an adaptive inverse for tracking, not settle performance, applications.…”

Tracking control and active disturbance rejection with application to noncircular machining

“…When the controlled plant is poorly known and is subject to uncertainties and variations, the tracking controller must have adequate adapting or learning capability so that an acceptable level of tracking performance is maintained. Hence, various solutions have been developed to improve the robustness of the feed-forward controller and the repetitive controller [1,2,[10][11][12][13][14]. Moreover, a FTS using the fuzzy proportional, integral, derivative (PID) controller has been proposed by Liu et al [15], in which the control parameters were continuously updated based on the position error and its varying rate to face the variations.…”

Adaptive inverse control for settling performance improvements

“…We rely on a recursive least squares (RLS) parameter estimation algorithm to estimate the closed-loop dynamics, and then use the inversion technique from II-B to synthesise an inverse system. A similar approach has been taken in [21], although the authors use a different inversion procedure designed for accurate tracking instead of settling performance.…”