Linear, parameter‐varying control and its application to a turbofan engine

Abstract

SUMMARYThis 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 1 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 1 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.

Development and application of sliding mode LPV fault reconstruction schemes for the ADDSAFE Benchmark

“…The core sliding mode observer consists of a model of the plant in LPV form, together with the time-varying observer gain G l (ρ) and the fixed gain G n given in (11). The observer block also contains a set of 5 integrators for estimating the states to provide the output error signals e y (t) used in the observer 'feedback' calculations.…”

“…The convenience of directly applying and extending linear techniques in an LPV framework, in order to deal with a wide range of operating conditions, is appealing. In certain situations, an LPV design is more applicable than direct nonlinear approaches due to complicated modelling issues [11]. With the development of generalized methods for generating LPV models from a set of LTI systems, such as the recently proposed method in [12], LPV design has become more appealing.…”

Polynomial LPV Synthesis Applied to Turbofan Engines

“…In the latter category we can find linear parametervarying (LPV) controller design via convex optimization over linear matrix inequalities (LMI), a methodology which has found various applications especially in the aerospace industry. In particular, as shown recently in (Balas, 2002) or (Bruzelius, 2004) these techniques can succesfully be applied to control aircraft turbofan engines, which are characterized by a strong sensitivity of the system dynamics with respect to the flight envelope (power lever angle, aircraft speed, altitude) or the environment (inlet pressure, temperature).…”

Application of model-based LPV actuator fault estimation for an industrial benchmark

“…Recently, the application of linear parameter varying (LPV) concepts to system modelling, control and FDD have also received much attention (Balas, 2002;Bokor & Balas, 2004;Henry, 2008;Sato, 2010;Wei & Verhaegen, 2011a;Hecker & Pfifer, 2014;Alwi & Edwards, 2014;Henry et al, 2014;Varga & Ossmann, 2014;Vanek et al, 2014;Chen et al, 2016;Rodonto et al, 2015;Ossmann & Varga, 2015;Rotondo et al, 2015;Alwi et al, 2015). Nevertheless, the technical demands of model-based FDD, especially for the FDD problem based on using LPV, are still quite limited and restrictive in the aerospace industry (Zolghadri, 2012).…”