H-infinity loop-shaping is a design methodology in modern
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
. It combines the traditional intuition of classical control methods, such as
Bode's sensitivity integral
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter invariant systems. Let ''L'' be the loop transfer function and ''S'' be the sensitivity fun ...
, with
H-infinity optimization techniques to achieve controllers whose stability and performance properties hold despite bounded differences between the nominal plant assumed in design and the true plant encountered in practice. Essentially, the control system designer describes the desired responsiveness and noise-suppression properties by weighting the plant
transfer function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for ...
in the
frequency domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signa ...
; the resulting 'loop-shape' is then 'robustified' through optimization. Robustification usually has little effect at high and low frequencies, but the response around unity-gain crossover is adjusted to maximise the system's stability margins. H-infinity loop-shaping can be applied to multiple-input multiple-output (MIMO) systems.
H-infinity loop-shaping can be carried out using commercially available software.
H-infinity loop-shaping has been successfully deployed in industry. In 1995, R. Hyde, K. Glover and G. T. Shanks published a paper describing the successful application of the technique to a VTOL aircraft. In 2008, D. J. Auger, S. Crawshaw and S. L. Hall published another paper describing a successful application to a steerable marine radar tracker, noting that the technique had the following benefits:
* Easy to apply – commercial software handles the hard math.
* Easy to implement – standard transfer functions and state-space methods can be used.
* Plug and play – no need for re-tuning on an installation-by-installation basis.
A closely related design methodology, developed at about the same time, was based on the theory of the gap metric. It was applied in 1993 for designing controllers to dampen vibrations in large flexible structures at