Murray Kerr

On the Existence of Stable, Causal Multipliers for Systems With Slope-Restricted Nonlinearities

The stability of a feedback interconnection of a linear time invariant (LTI) system and a slope-restricted nonlinearity is revisited. Unlike the normal treatment of this problem, in which multipliers are explicitly chosen and then stability conditions checked, this technical note derives existence conditions for a sub-class of these multipliers, namely those which are L 1 bounded, stable, causal and of order equal to the LTI part of the system. It is proved that for the single-input-single-output case, these existence conditions can be expressed as a set of linear matrix inequalities and thus can be solved efficiently with modern optimization software. Examples illustrate the effectiveness of the results.

Anti-windup compensation of rate saturation in an experimental aircraft

This paper describes the design, flight testing and accompanying analysis of two anti-windup (AW) compensators for an experimental aircraft - the German Aerospace Centers (DLR) advanced technologies testing aircraft (ATTAS). The AW compensators were designed to reduce the deleterious effects of rate-saturation of the aircrafts actuators on handling qualities. The AW compensators were flight-tested and assessed using the resulting pilot comments, in the form of handling qualities ratings (HQRs) and pilot-involved-oscillation ratings (PIORs), and flight test data. These media demonstrate that the AW compensators improved the predictability and handling of the aircraft. The results also provide an initial understanding of the relationship between the theory and design choices for AW controllers and the response of the piloted aircraft during periods of rate saturation.

AIRBUS efforts towards advanced real-time Fault Diagnosis and Fault Tolerant Control

Abstract In this article the industrial goals and objectives of the European Framework 7th project termed “REconfiguration of CONtrol in Flight for Integral Global Upset Recovery (RECONFIGURE)” are presented. Commercial aircraft fault tolerant control (FTC) strategies in the flight control system (FCS) are based on fail-safe flight control law reconfiguration which relies on upstream hardware redundancy-based robust Fault Detection and Diagnosis (FDD). This industrial state-of-practice fits well in the current certification process but it also decreases the easiness of the piloting task as soon as the system level of degradation increases. Thus, the main goal of RECONFIGURE is to research and develop aircraft FDD and FTC technologies that facilitate the automated handling of off-nominal/abnormal events and optimize the aircraft status and flight. The article details the project description of work, from industrial benchmark (fault scenarios and aircraft model) up to industrial verification and validation (V&V) activities, via advanced FDD/FTC research and development. The expected results and perspectives are also presented.

A robust anti-windup design procedure for SISO systems

A model-based anti-windup (AW) controller design approach for constrained uncertain linear single-input–single-output (SISO) systems is proposed based on quantitative feedback theory (QFT) loopshaping. The design approach explicitly incorporates uncertainty, is suitable for the solution of both the magnitude and rate saturation problems, and provides for the design of low-order AW controllers satisfying robust stability and robust performance objectives. Robust stability is enforced using absolute stability theory and generic multipliers (i.e. circle, Popov, Zames–Falb), and robust performance is enforced using linear lower-bounds on the input–output maps capturing the effects of saturation as a metric. Two detailed design examples are presented. These show that even for simple systems, certain popular AW techniques lead to compensators that may fail to ensure robust stability and performance when saturation is encountered, but that the proposed QFT design approach is able to handle both saturation and uncertainty effectively.

Flight testing of low-order anti-windup compensators for improved handling and PIO suppression

This paper presents the results of recent flight tests of several anti-windup (AW) compensators on the German Aerospace Centres (DLR) Advanced Technologies Testing Aircraft (ATTAS). The objectives of the tests were twofold: to demonstrate the potential for rigorously designed low order AW compensators to reduce the pilot-involved-oscillation (PIO) proneness of the aircraft and improve the handling qualities; and to compare a variety of low-order AW compensators to determine the importance of different design parameters. The AW compensators were assessed based on pilot handling qualities ratings (HQRs) and PIO ratings (PIORs). These ratings, and supporting pilot comments and flight data, demonstrate that the AW compensators improved the handling qualities and reduced the PIO proneness of the aircraft, albeit to different degrees. The results also provide a basic understanding of the relationship between design parameters and the response of the piloted aircraft during periods of rate saturation.

Practical approaches to low-order anti-windup compensator design: a flight control comparison

Abstract This paper considers three different methods for low-order anti-windup (AW) compensator design and compares their application to a realistic flight control problem, where the dominant actuator nonlinearity is aileron rate saturation. The compensator design methods all rigorously enforce at least local exponential stability via absolute stability results, but differ in both the construction of the AW compensator itself and the performance requirements used in the design. In particular, the paper compares a low order AW “optimal” design method in which the compensator poles and zeros are chosen by the designer and the accompanying gains synthesised optimally; a new low order method in which the optimisation procedure optimally chooses both the zeros and the gains; and a recently introduced classical design method where loopshaping is used to completely determine the gains and dynamics of the compensator. The methods are compared using a high-order nonlinear model of the lateral dynamics of an experimental aircraft, on which similar compensators have recently been flight tested.

Gain-Scheduled FDI for a Re-entry Vehicle

This paper presents the design of a gain scheduled fault detection and isolation (FDI) filter for the Hopper reusable launch vehicle (RLV). The fault scenario is that of faults in the vehicles rudder actuator and sideslip sensor during a focused 90 second period of the re- entry. Both of the considered faults strongly affect the lateral response of the vehicle, making simultaneous FDI difficult. A dynamically stable model of the Hopper RLV is considered and FDI filter design is performed on linearised models of the vehicle trimmed about the re- entry trajectory. H-infinity theory is employed for the FDI filter synthesis, with a set of LTI FDI filters designed at the trim points and then scheduled to form the gain scheduled FDI filter. The effectiveness of the LTI point-design filters and the gain-scheduled filter are determined by simulation using a tightly gain-scheduled model of the linearised vehicles open-loop response that captures the strongly parameter varying vehicle behaviour as it tracks the re-entry trajectory. The advantages of using gain-scheduled FDI filters for FDI on RLVs are highlighted via the simulations.

QFT Based Robust Control of a Single-Link Flexible Manipulator

This article presents the application of multi-input multi-output (MIMO) quantitative feedback theory (QFT) to the control of a single-link flexible manipulator. The manipulator employs an actuation scheme comprised of a DC motor that provides spatially discrete actuation and a surface bonded piezoelectric ceramic that provides spatially distributed actuation. The efficacy of the sequential MIMO QFT methodology for articulating flexible structure control is investigated using the flexible manipulator testbed, with the control system designed to achieve rapid, rest-to-rest positioning of the manipulator tip in the presence of significant parametric and non-parametric structured uncertainty. Numerical simulations and experiments are employed to validate the synthesised control system and the combined discrete-distributed actuation scheme. Conservatisms in the MIMO QFT methodology are identified and partly alleviated using recent theoretical and design improvements.

Robust Stability of Sequential Multi-input Multi-output Quantitative Feedback Theory Designs

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

ℒ 2 gain bounds for systems with slope-restricted nonlinearities

This paper proposes a new method for calculating a bound on the ℒ 2 gain of a system consisting of a linear time invariant (LTI) part and a static nonlinear part, which is odd, bounded, zero at the origin and has a restriction on its slope. The problem is posed in the IQC framework and the ℒ 2 gain bound is found by solving a set of linear matrix inequalities (LMIs). The novelty of the paper lies in the use of a recent characterisation of the multiplier for systems with slope-restricted nonlinearities. Examples illustrate the effectiveness of the results against the state-of-the-art.