Design Examples: Adaptive Tracking Control in the Presence of Input Constraints for a Fighter Aircraft and a Generic Missile

Abstract

Two flight control related examples of adaptive autopilot design in the presence of actuator constraints are presented. The demonstrated methodology maintains closed-loop stability by changing guidance commands on-line. In addition, the method is capable of avoiding control saturation at all times, if required. Introduction During the past decade control design in the presence of input saturation has attracted a vast amount of research effort (for chronological bibliography see Ref.). This issue is especially challenging in adaptive systems, because continued adaptation during input saturation may easily lead to instability. In order to overcome the undesirable/destabilizing effects of control saturation during the adaptation process, an adaptive modification (proportional to control deficiency) to both the tracking error and the reference model dynamics was proposed by Monopoli in Ref. but without any formal proof of stability. In the PCH method of Johnson and Calise a fixed gain adjustment (proportional to control deficiency) to the reference model was introduced. Adaptive control with amplitude saturation for linear systems was addressed in Ref. Refs. consider both amplitude and rate saturation for nonlinear systems without explicit construction of the domain of attraction. ∗Graduate Research Assistant, Member AIAA †Associate Professor, Senior Member, AIAA ‡The Boeing Company, Technical Fellow, Huntington Beach, CA, Associate Fellow, AIAA Copyright c © 2005 by Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. The motivation and significance of the much needed design methods for adaptive control in the presence of input constraints can be illustrated by the aerospace applications, such as control of an unmanned aircraft, whose nominal flight control system is retrofitted with an adaptive element in order to track the guidance commands in the presence of failures and environmental uncertainties. If an unknown and/or undetected failure occurs (caused by a battle damage or a control surface malfunction), then, in spite of the failure, the guidance system would continue issuing its commands that may no longer be achievable by the aircraft. As a consequence, the required control effort will quickly saturate the aircraft surfaces while striving to maintain the “healthy” vehicle tracking performance, and subsequently will de-stabilize the aircraft. This situation may quickly become flight critical due to the fact that most of today’s high performance aircraft are open-loop unstable. Some earlier methods suggested stopping the adaptation during the saturation periods, and reverting back to the nominal controller. Alternative methodologies proposed adaptive scaling of the reference command (guidance) for preventing instabilities and failures of this type. In Ref., we extended the idea of adaptive scaling of the reference command and proposed a direct model reference adaptive control framework (MRAC) that yields stable adaptation in the presence of input constraints. The novel design approach is termed “Positive μ-modification”, or simply “μ-mod”, where the free design parameter μ defines a convex combination of the classical linear in parameters adaptive control and a modified saturation bound. With this parameterization, the control deficiency can be reduced to ensure that the control signal will never incur saturation. This is crucial for preventing structural mode interaction problems during the periods of control saturation. In this paper, we first present an overview of the the μ-modification based control design and we