Linear-quadratic Gaussian with loop-transfer recovery methodology for the F-100 engine

Abstract

The design of a multivariable feedback control system for the F-100 turbofan jet engine is a challenging task for control engineers. This paper employs a linearized model of the F-100 engine to demonstrate the use of the newly developed linear-quadratic Gaussian with loop-transfer recovery design methodology that adopts an in- tegrated frequency and time-domain approach to multivariable feedback control synthesis so as to meet stability robustness, command following, and disturbance rejection specifications. ODERN turbofan jet engines represent an important multiple-input/multiple-output (MIMO) control ap- plication area since the dynamic coordination of fuel flow and several engine geometry variables can lead to improved performance and efficiency, while maintaining safe fan and compression stall margins. Indeed, the MIMO feedback con- trol of turbofan and turboshaft engine has received a great deal of attention in the past few years.18 The F-100 turbofan engine was used as a main design exam- ple for which different MIMO control methodologies were employed. The so-called linear-quadratic-regulator (LQR) ap- proach9'10 was the basis of engineering designs and evaluations14 that required the feedback of several F-100 state variables. In the past five years significant advances have been made in integrating time-domain optimization-based approaches (such as LQR and linear-quadratic Gaussian (LQG)) with fre- quency domain approaches. Such an integrated frequency- domain and state-space approach to MIMO control systems design was pioneered by Stein and his colleagues1114 and has culminated to the so-called linear-quadratic Gaussian with loop-transfer recovery (LQG/LTR) methodology for MIMO feedback control synthesis. The primary objective of this paper is to illustrate the LQG/LTR design methodology using a four-input/fou r- output linear model of the F-100 engine. Specifically, we stress how MIMO command following and disturbance rejection performance specifications, as well as stability robustness specifications are naturally posed in the frequency domain us- ing the singular values of suitably defined loop-transfer matrices. Then, we demonstrate how the LQG/LTR design procedure is used to meet the posed specifications. Further-