Design of a Gain-Scheduled Flight Control System Using Bifurcation Analysis

Abstract

A method for identifying regions of instability in closed-loop systems has been developed for flight dynamics applications. This forms a novel approach in which a surface of equilibria is generated in the region of interest as the influence of the control system is increased. In this way, the creation and destruction of equilibria in the controlled system can be easily found and visualized. This systematic approach allows the stability of the closed- loop system to be directly related to that of the open loop. Results are given for a highly nonlinear aircraft model and demonstrate the power of a combined analytical and graphical approach to control system synthesis. flight dynamics model. We believe that there is great deal of poten- tial in the use of continuation methods in the design and analysis of gain-scheduled feedback control systems. They allow us to address systems with significant nonlinearity and in particular multivalued steady states. The essence of this paper is to consider the application of a gain-scheduled state feedback controller to an aircraft. Contin- uation algorithms are used for two purposes within this paper: 1) to create pseudocontinuous gain schedules throughout a wide oper- ating region and 2) to create surfaces of state equilibria that show changes in the global behavior of the system ranging from the open- loop to the closed-loop configurations. The first step in this approach is to create pseudocontinuous gain functions that satisfy the design criteria at equilibrium throughout the desired operating region of the nonlinear system. Given suf- ficient control authority, these allow the dynamic response of the desired branch of equilibria to be specified. This paper formalizes a continuation approach to gain scheduling using standard feedback control design terminology. The second step is to determine the global implications of this gain-scheduled controller. A novel approach is adopted in which three-dimensional bifurcation surfaces of equilibria are found as both the reference signal and the controller gains are varied. This powerful technique illustrates graphically the influence of the con- trol system and is shown to be invaluable in the evaluation of the global stability of the system. These bifurcation surfaces can be used to indentify undesired attractors within the closed-loop system. The creation of equilibrium surfaces in terms of the variation in control system gain is an entirely new concept in aircraft controller design and allows a tradeoff between local and more global properties of the closed-loop system. These methods are demonstrated using a highly nonlinear air- craft model, the hypothetical high angle of incidence research model (HHIRM). 8 Aircraft dynamics are complex, incorporating nonlin- earities as a result of many factors such as inertial coupling be- tween the different degrees of freedom and aerodynamic forces and moments. 9