Using Linear Fractional Transformations for Clearance of Flight Control Laws
Independent thesis Basic level (professional degree)Student thesisAlternative title
Klarering av Styrlagar för Flygplan med hjälp av Linjära Rationella Transformationer (Swedish)
Flight Control Systems are often designed in linearization points over a flight envelope and it must be proven to clearance authorities that the system works for different parameter variations and failures all over this envelope.
In this thesis µ-analysis is tried as a complement for linear analysis in the frequency plane. Using this method stability can be guaranteed for all static parameter combinations modelled and linear criteria such as phase and gain margins and most unstable eigenvalue can be included in the analysis. A way of including bounds on the parameter variations using parameter dependent Lyapunov functions is also tried.
To perform µ-analysis the system must be described as a Linear Fractional Transformation (LFT). This is a way of reformulating a parameter dependent system description as an interconnection of a nominal linear time invariant system and a structured parameter block.
A linear and a rational approximation of the system are used to make LFTs. These methods are compared. Four algorithms for calculation of the upper and lower bounds of µ are evaluated. The methods are tried on VEGAS, a SAAB research aircraft model.
µ-analysis works quite well for linear clearance. The rational approximation LFT gives best results and can be cleared for the criteria mentioned above. A combination of the algorithms is used for best results. When the Lyapunov based method is used the size of the problem grows quite fast and, due to numerical problems, stability can only be guaranteed for a reduced model.
Place, publisher, year, edition, pages
Institutionen för systemteknik , 2003. , 96 p.
Reglerteknik, Linear Fractional Transformation, LFT, Structured Singular Value, SSV, Linear Matrix Inequality, LMI, µ-analysis, Lyapunov function, Flight Clearance, Stability Margin
IdentifiersURN: urn:nbn:se:liu:diva-2041OAI: oai:DiVA.org:liu-2041DiVA: diva2:19369