Single-Parameter Adaptation for Acquisition and Tracking

An adaptive regulator with a smoothly variable high-order linear response controlled by a single real parameter, or a regulator including a single nonlinear element, is employed in an acquisition-tracking system. The requirement for good tracking is not compromised by the requirement for fast acquisition, and vice versa. The minimum phase character of the return ratio is preserved in a robust manner. Using intermediate design requirement simplifies the design procedure. A nonlinear static function is used as t h e exponent of a link transfer function. The transition between t h e modes is smooth and rapid. The transient responses are fast and without substantial overshoots. 1. Acquisition and tracking Acquisition and tracking systems, like those used in homing missiles, are designed to operate in two modes: acquisition mode when the error is initially large and gradually diminish, and tracking mode when the error is maintained small. An example of the acquisitiodtracking type is a homing control system for pointing a spacecraft-mounted camera, in which a rapid retargeting maneuver is followed by a slow precise scanning pattern to form a mosaic image. Another example is clock acquisition in the phase-locked loops of telecommunication systems and frequency synthesizers. Since optimizing of an LTI controller for the purpose of acquisition and for the purpose of tracking results in quite different systems, performance of LTI controllers cannot be best both for acquisition and tracking, and the controller design involves some compromises. The trade-offs can be better resolved in nonlinear and LTV controllers. Some of industrial acquisitiodtracking controllers are very sophisticated (like those for some hard disk drives) and are designed by teams of advanced level professionals. However, large investments in the control design not always can be justified, and many practical acquisitiodtracking *Members Technical Staff, Member AIAA tSenior Research Scientist, Associate Fellow AIAA Aeronautics and Astronautics, Inc. All rights reserved. Copyright