String Stability of a Linear Formation Flight Control Systems

String stability analysis of an autonomous formation flight system was performed using linear and nonlinear simulations. String stability is a measure of how position errors propagate from one vehicle to another in a cascaded system. In the formation flight system considered here, each ith aircraft uses information from itself and the preceding ((i-1)th) aircraft to track a commanded relative position. A possible solution for meeting performance requirements with such a system is to allow string instability. This paper explores two results of string instability and outlines analysis techniques for string unstable systems. The three analysis techniques presented here are: linear, nonlinear formation performance, and ride quality. The linear technique was developed from a worst-case scenario and could be applied to the design of a string unstable controller. The nonlinear formation performance and ride quality analysis techniques both use nonlinear formation simulation. Three of the four formation-controller gain-sets analyzed in this paper were limited more by ride quality than by performance. Formations of up to seven aircraft in a cascaded formation could be used in the presence of light gusts with this string unstable system. 1 American Institute of Aero *Aerospace Engineer †Aerospace Engineer ‡Aerospace Engineer §Aerospace Engineer Copyright  2002 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner. Note that use of trade names or names of manufacturers in this document does not constitute an official endorsement of such products or manufacturers, either expressed or implied, by the National Aeronautics and Space Administration. Nomenclature Acronyms 6-DOF six degrees-of-freedom AFF Autonomous Formation Flight BIBO bounded input, bounded output DFRC Dryden Flight Research Center (Edwards Air Force Base, California) F/A-18 twin-engine jet fighter aircraft (Boeing, USA) GPS Global Positioning System ISO International Organization for Standardization MSDV motion sickness dose value, (m/sec)1.5 NASA National Aeronautics and Space Administration (Washington, D. C.) PID proportional-plus-integral-plus-derivative PSD Power Spectral Density SISO single input, single output Symbols amp amplitude of oscillation (peak value) aw frequency-weighted acceleration, m/s 2