Nested feedback systems : analysis and design within an H∞-loopshaping framework

• Main Author: Halsey, K.
• Published: University of Cambridge 2002
• Subjects: 530.1
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603601

There are two principle problems to address. Firstly, there is a greater degree of freedom in model approximation within the context on an inner-loop, as something less than closed-loop stability on C⁺ is required. The standard notions which under-pin the <i>H</i>_∞-loopshaping framework, such as coprime factor and graph representations, readily generalise to connected subsets of C. However, to assess the fitness of any candidate approximation regarding inner-loop design we require a generalisation of the <i>v</i>-gap metric. This is obtained by removing the artificial dependence upon the existence of normalised coprime factorisations and working instead with a pointwise normalisation on the boundary. Secondly, we desire a means of synthesising a controller with a nested structure, that preserves the robustness guarantees associated with the conventional case. On the occasion that the inner-loop is implemented in observer form, we obtain a simple inequality relating the stability margins associated with a 2-loop nested feedback system. The guarantee this provides for the sequential approach to design is too weak to be of use. Two new methods are therefore developed which exploit the inequality to achieve a robustness guarantee. To complete this work, the generalised <i>v</i>-gap and a rigorous approach to nested feedback system synthesis are both applied to the design of a full flight control system for the USAF Have Dash II air-air missile.