title: Linear, parameter-varying control and its application to a turbofan engine
abstract: This paper describes application of parameter-dependent control design methods to a turbofan engine. Parameter-dependent systems are linear systems, whose state-space descriptions are known functions of time-varying parameters. The time variation of each of the parameters is not known in advance, but is assumed to be measurable in real-time. Three linear, parameter-varying (LPV) approaches to control design are discussed. The first method is based on linear fractional transformations which relies on the small gain theorem for bounds on performance and robustness. The other methods make use of either a single (SQLF) or parameter-dependent (PDQLF) quadratic Lyapunov function to bound the achievable level of performance. The latter two techniques are used to synthesize controllers for a high-performance turbofan engine. A LPV model of the turbofan engine is constructed from Jacobian linearizations at fixed power codes for control design. The control problem is formulated as a model matching problem in the H/sub infinity / and LPV framework. The objective is decoupled command response of the closed-loop system to pressure and rotor speed requests. The performance of linear, H/sub infinity / point designs are compared with the SQLF and PDQLF controllers. Nonlinear simulations indicate that the controller synthesized using the SQLF approach is slightly more conservative than the PDQLF controller. Nonlinear simulations with the SQLF and PDQLF controllers show very robust designs that achieve all desired performance objectives
keyphrases: turbofan engine parameter-dependent control design methods state-space descriptions time-varying parameters linear fractional transformations small gain theorem Jacobian linearizations model matching problem decoupled command response closed-loop system nonlinear simulations very robust designs linear parameter-varying control performance bounds robustness bounds single quadratic Lyapunov function parameter-dependent quadratic Lyapunov function H/sub infinity / framework