Actuator Placement for Active Surge Control in a Multi-Stage Axial Compressor

Abstract

This paper describes an actuator placement methodology for the active control of purely one-dimensional instabilities of a seven-stage axial compressor using an air bleeding strategy. In this theoretical study, using stage-by-stage non-linear modelling based on the conservation equations of mass, momentum, and energy, a scheduling LQR (Linear Quadratic Regulator) controller is designed for several actuator locations in a compressor from the first stage to the plenum. In this controller design, the LQR weighting matrices are selected so that the associated cost function includes only air bleeding mass flow leading to the minimisation of the air bleed. The LQR cost function represents a measure of the consumption of air bleeding and can be calculated analytically using the solution of an Algebraic Riccati Equation. From analysis of the cost at different compressor stages, the location of an air bleeding actuator is selected at the stage with the minimum cost. Finally, using an ACSL simulation program, the scheduling controller has been integrated with a non-linear. stage-by-stage model and the time response of the air bleeding mass flow at different locations has been obtained to confirm the results from the analytical approach. Results are presented to show actively stabilised compressor flow beyond the surge point where the air bleed is minimised. These results also indicate the preferred location of the actuator at the compressor downstream stages for both low and high compressor speeds.