25 November : PhD defence of Wilfried Gilbert.
Titre :  Polynomial LPV Synthesis applied to turbofan engine control
Abstract : In the framework of the collaboration between LAAS and the manufacturer of aircraft and space engines Snecma, it has been proposed to elaborate advanced control laws for turbofan engines. Turbofan engines are characterized by a strong sensitivity of the system dynamics with respect to some parameters in the flight envelope. Control laws must explicitly take into account these variations. With this aim, the turbofan engine modeling is based on Linear Parameter Varying (LPV) formalism. The synthesis technique developed in this thesis, the polynomial approach, is also addressed with this formalism. 
Results on polynomial fixed order controller design are extended to LPV control with guaranteed stability and H∞ performance over the whole scheduling parameter range. Salient features of the approach are (a) the use of polynomials as modeling objects ; (b) the use of flexible LMI conditions allowing polynomial dependence of the open-loop system and controller transfer functions in the scheduling parameters ; (c) the synthesis of controllers with order and structure fixed a priori, and independantly of the order and structure of the open-loop system. The synthesis procedure is integrated into the ATOL framework developed by Snecma to systematically design reduced complexity control laws for aircraft turbofan engines. 
The polynomial approach is applied to control a turbofan engine equipping a military aircraft. First, SISO transfers are treated, then multivariable models, more difficult to deal with numerically, are considered. In both cases, the simulations are comparable to the ones obtained with the current control law applied by Snecma. 
The development of generic tools has been emphasized throughout the thesis. The integration of modeling and synthesis modules to ATOL makes the application of the polynomial approach possible for any other type of aircraft engines.