Method for LFT Calculation with High Order Parametric Systems

Linear closed loop systems are usually tested for robustness with respect to uncertain parameters using an upper Linear Fractional Transformation (LFT). This paper presents a method to calculate such a LFT for a system with a very large number (more than 300) of uncertain parameters. This is typically the case for precise control systems of drag-free satellites. Advanced Matlab toolboxes make use of symbolic manipulations. A more conventional approach is based on the interconnection of LFT representations of a single uncertainty. Both lead to memory management errors, when the number of uncertainties becomes large. With the method proposed here, these drawbacks can be avoided. It consists of two major steps. The first step reformulates the system in a matrix equation with matrix elements containing only single uncertain parameters. In a second step the LFT representation is computed from the reformulated system and then used for further μcalculations and sensitivity analyses. The basic method is explained with a simple springmass-system with five uncertain parameters. More importantly the application case of the LISA Pathfinder/ST7 control system is reported with 350 uncertain physical parameters. This LFT method can successfully support robustness analyses and thus reduce verification cost in the development process.