Bor-Chin Chang

Optimal disturbance reduction in linear multivariable systems

This paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory. The approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation. The resulting computations are easily implemented using existing methods.

Aircraft Accident Prevention: Loss-of-Control Analysis

The majority of fatal aircraft accidents are associated with ‘loss-of-control’. Yet the notion of loss-of-control is not well-deflned in terms suitable for rigorous control systems analysis. Loss-of-control is generally associated with ∞ight outside of the normal ∞ight envelope, with nonlinear in∞uences, and with an inability of the pilot to control the aircraft. The two primary sources of nonlinearity are the intrinsic nonlinear dynamics of the aircraft and the state and control constraints within which the aircraft must operate. In this paper we examine how these nonlinearities afiect the ability to control the aircraft and how they may contribute to loss-of-control. Examples are provided using NASA’s Generic Transport Model.

Constructing linear families from parameter-dependent nonlinear dynamics

Generating families of linear models from nonlinear parameter-dependent equations requires explicit analytical characterization of the equilibrium surface. Doing so in terms of the original system parameters is generally not possible. Introducing an alternative parameterization, we propose an efficient method for computing local linear parameter-dependent families. Although local, these families can be constructed anywhere, specifically around bifurcation points where other methods fail.

Robust control systems design using H-infinity optimization theory

In this paper, we show step-by-step procedures for applying the H°° theory to robust control systems design. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H°° control theory. We will review the physical meanings of the H°° norm, explain how it relates to robustness issues, and show how to formulate H°° optimization problems, including the construction of a state-space realization of the generalized plant. An efficient algorithm is used to compute the optimal H°° norm. The controller formulas of Glover and Doyle are slightly modified and are used to construct an optimal controller without any numerical difficulty.

Fast stability checking for the convex combination of stable polynomials

A fast algorithm is proposed for checking the stability of the edges of a polytope where most of the computations involved depend on the number of vertices rather than on the number of edges. This algorithm is based on the segment lemma derived by H. Chapellat et al. (1988). Although the segment lemma is an important result on its own, no explicit algorithm was given there. Some important properties of the lemma are revealed, and it is shown how they lead to a fast algorithm. In this algorithm, the major computations involved are those of solving for the positive real roots of two polynomials with degree less than or equal to n/2 for each vertex. The computations required by the algorithm are mainly vertex-dependent, and the burden of the combinatoric explosion of the number of edges is greatly reduced. >

Multivariable control and failure accommodation in eye-head-torso target tracking

A simple eye-head-torso target tracking system is employed to demonstrate how cooperative control and failure accommodation can be achieved using the multivariable regulator and H/sub 2/ control theory. The eye, head, and torso serve as three subsystems working cooperatively to track the target as closely as possible and then readjust their positions so that the three are aligned in the same direction. The control system also has the reconfiguration capability to accommodate the failure of one or two subsystems by switching to the control law that would provide optimal performance for the remaining healthy subsystems.

Design of fault-tolerant systems for actuator failures in nonlinear systems

Controller design for actuator failures in nonlinear systems is considered. Nonlinear regulator theory is employed to address the persistent disturbance caused by jammed actuators. An example of the aircraft longitudinal flight control is used to illustrate the design procedure. It is seen that the nonlinear regulators provide a larger window of safety than their linear counterpart especially in the face of time delays needed for identification of the actuator failures.

Loss-of-Control: Perspectives on Flight Dynamics and Control of Impaired Aircraft

Loss-of-Control (LOC) is a major factor in fatal aircraft accidents. Although denitions of LOC remain vague in analytical terms, it is generally associated with a signicantly diminished capability of the pilot to control the aircraft. In previous work we considered how the ability to regulate an aircraft deteriorates around stall points. In this paper we examine how damage to control eectors impacts the capability to keep the aircraft within an acceptable envelope and to maneuver within it. We show that even when a sucient set of steady motions exist, the ability to regulate around them or transition between them can be dicult and nonintuitive, particularly for impaired aircraft.

Nonlinear Dynamics, Stability and Bifurcation in Aircraft: Simulation and Analysis Tools

In this paper we consider stability and bifurcation analysis based on nonlinear description of the aircraft dynamics to aid in the design of reconfigured controllers for actuator failure accommodation. We present the computational and visualization tools required for stability and bifurcation analysis. These tools for design, validation and verification are illustrated using a full envelope model of the F-16 aircraft. We use continuation methods to identify bifurcation points of the F-16 model in straight and level flight, for the nominal system and various single actuator failure situations. Control reconfiguration following actuator failure is formulated as a nonlinear regulator problem. This work provides a systematic way to identify the maneuverability envelope, provides an understanding of how aircraft depart from controlled flight and can contribute to the design of recovery strategies to regulate key flight parameters in the face of actuator failures.

Uncertainty Modeling for Robustness Analysis of Control Upset Prevention and Recovery Systems

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. Such systems (developed for failure detection, identification, and reconfiguration, as well as upset recovery) need to be evaluated over broad regions of the flight envelope and under extreme flight conditions, and should include various sources of uncertainty. However, formulation of linear fractional transformation (LFT) models for representing system uncertainty can be very difficult for complex parameter-dependent systems. This paper describes a preliminary LFT modeling software tool which uses a matrix-based computational approach that can be directly applied to parametric uncertainty problems involving multivariate matrix polynomial dependencies. Several examples are presented (including an F-16 at an extreme flight condition, a missile model, and a generic example with numerous crossproduct terms), and comparisons are given with other LFT modeling tools that are currently available. The LFT modeling method and preliminary software tool presented in this paper are shown to compare favorably with these methods.