Session 61-GNC-34 of GNCC'99, August 1999.

Robust H-infinity flight control: design, analysis, and flight testing experience

Organised by: G. Papageorgiou, M. Cantoni and K. Glover

Outline

H-infinity loop shaping was proposed by McFarlane and Glover in the late eighties. Since then, much work has been done to develop H-infinity loop shaping into a powerful design tool. It has been shown that H-infinity loop shaping can systematically deal with multi-input multi-output plants, plants with nonlinear and/or parameter-dependent dynamics, and uncertainty in the mathematical model of the plant used for the controller design. The designer can also build many of the control system specifications into the cost function used for the controller synthesis. H-infinity loop shaping has been successfully used to design controllers for the Vectored thrust Aircraft Advanced flight Control (VAAC) Harrier, the Bell 205 fly-by-wire/variable stability helicopter, and a wind tunnel model used for high angle of attack active control experiments. All controllers have been flight tested, and have performed extremely well.

The first part of the invited session gives an overview of H-infinity loop shaping. H-infinity loop shaping is motivated, by motivating H-infinity control, and reviewing the controller specifications which are common to most control system design problems. The design of a continuous time H-infinity loop shaping controller for a linear time-invariant (LTI) plant model is detailed. To this end, weight selection, the closed loop guarantees that the H-infinity loop shaping controller provides, the significance of the stability margin, the suggested design procedure and a particular design philosophy are discussed in some detail. Also, H-infinity loop shaping is compared with other robust control system design methods, and the design method currently used in the United Kingdom (UK) aerospace industry.

The second part of the invited session presents two extensions/variants of H-infinity loop shaping. Firstly, the H-infinity loop shaping setup is modified to include an ideal reference model. The solution of the resulting constrained optimisation problem and the closed loop guarantees provided by the now two degrees-of-freedom controller are discussed in some detail. Secondly, it is shown that H-infinity loop shaping extends naturally to plants with linear parameter-varying (LPV) dynamics. The design of a robust LPV controller for an LPV plant model using H-infinity loop shaping, is discussed with respect to designing a robust gain scheduled controller for the longitudinal dynamics of an aircraft. The applicability of H-infinity loop shaping to aerospace control problems is illustrated by designing H-infinity loop shaping controllers for two challenging real plants. In this part of the invited session, H-infinity loop shaping is used to design a two degrees-of-freedom LTI controller for the Bell 205 fly-by-wire/variable stability helicopter.

In the third part of the invited session the nu-gap metric is introduced. The nu-gap metric is a measure of the distance between systems in terms of how different they are to control using feedback. It is a natural dual to the stability margin associated with the H-infinity loop shaping framework, and it has a clear frequency domain interpretation. In fact, it can be interpreted as a point-wise distance between the frequency responses of systems, provided a mild condition is satisfied. This allows one to identify frequency regions that dominate the difference between plants in a feedback sense, which is particularly powerful from the perspective of design.

The fourth and last part of the invited session presents a gain scheduled controller designed for the VAAC Harrier. The gain scheduled controller is based on a number of LTI H-infinity loop shaping controllers and was first flight tested in December 1993.