Ga Charles

Design of a Gain Scheduled Flight Control System Using Bifurcation Analysis

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

BIFURCATION TAILORING VIA NEWTON FLOW-AIDED ADAPTIVE CONTROL

The aim of bifurcation tailoring is to design an appropriate control law such that the controlled system has a desired bifurcation diagram. After describing two open-loop bifurcation tailoring techniques, this paper proposes a new open-loop plus close-loop bifurcation tailoring method based on a combination of the Newton-flow algorithm and the minimal control synthesis (MCS) adaptive control strategy. This method is applied to the Duffing system as an illustrative example.

BIFURCATION TAILORING OF NONLINEAR SYSTEMS

Abstract We discuss a novel approach to control bifurcations in nonlinear systems. The aim of bifurcation tailoring is to design an appropriate control law such that the controlled system has a desired bifurcation diagram. After describing two open-loop bifurcation tailoring techniques, this paper proposes two alternative modified bifurcation tailoring methods based on the use of the Newton-flow algorithm and the so-called Minimal Control Synthesis adaptive control strategy. The novel technique is applied to the Duffing system as an illustration example.

On-line bifurcation tailoring: an application to a nonlinear aircraft model

Abstract Bifurcation tailoring is a novel control technique aimed at changing the entire bifurcation diagram of a given nonlinear system to some desired one. Bifurcation tailoring was successfully carried out on a second order nonlinear highly manoeuvrable aircraft model so as to control the angle of attack to an arbitrary prescribed bifurcation diagram under the variation of elevator. On-line feedforward scheduling was carried out using a Newton Flow method, and feedback stabilisation was provided by an adaptive control strategy known as the Minimal Control Synthesis (MCS).