Engine Control by Robust State Feedback

Abstract

This chapter reviews linear multivariable theory and introduces polytopic system descriptions of plant variability. The chapter also presents various methods for MIMO state-feedback synthesis, such as: LQR, \({\mathcal{H}}_{2}\), \({\mathcal{H}}_{\infty }\) and mixed-objective optimization with regional pole placement constraints. A simplified \({\mathcal{H}}_{\infty }\) compensator synthesis method is presented for SISO systems. Matlab code and simulations using the CMAPSS nonlinear engine model are included.The purpose of this chapter is to provide an overview of robust, multivariable techniques that are directly applicable to the GTE control problem. As pointed out in Chap. 3, fixed controllers cannot be expected to preserve engine limits or to operate satisfactorily across the whole flight envelope, less so if the engine health parameters are subject to changes and unmodeled dynamics exist. However, various approaches to gain scheduling are based on a set of fixed controllers. It is therefore essential to discuss the salient features of robust multivariable control and provide practical design guidelines. The chapter assumes familiarity with the state-space pole-placement concept, at a minimum.Actual engines incorporate real-time sensing of fan and core speeds, which are the states of the dynamic model. This fact opens the doors to many techniques based on state measurement feedback, such as the linear quadratic regulator (LQR) and sliding mode control. Although most state feedback techniques admit observer-based extensions, the performance and robustness properties attained with measurement feedback are partially lost when a state estimator is introduced. A classical example of this effect is given by the performance and robustness losses associated with observer-based implementations of linear quadratic regulation. Loop transfer recovery techniques [29] aim to restore the lost performance and robustness properties. The chapter begins by introducing essential concepts such as singular values and signal and system norms and their computation using Matlab. Robustness and performance are then addressed using classical LQR theory. A characterization of the uncertain design plant, along with a corresponding formulation of the control objectives is then developed using the tools of \({\mathcal{H}}_{2}\) and \({\mathcal{H}}_{\infty }\) robust state feedback synthesis. A classical LQR controller and robust \(\mathcal{H}\)-norm based controllers are designed for the 40k-class engine, using W F, VSV, and VBV as actuators. The designs are then simulated in CMAPSS-40k.