Design of controllers for MG3 compressor models with general characteristics using graph backstepping

We discuss the design of controllers for compressors with general character istics, including the right-skewed ones. The controllers can be represented graphically by plotting their throttle surfaces. The graphical representat ion of controllers enhances understanding of controller action and allows t o compare various controllers. We discuss the issue of the right skewness o f a compressor characteristic. We show how to design controllers using a gr aph backstepping procedure involving the construction of the throttle surfa ce. We show that for a quite general compressor characteristic, every poten tial axisymmetric equilibrium on the decreasing part of the compressor char acteristic, the peak of the characterisitic, and every rotating stall equil ibrium close to the peak can be globally or semi-globally stabilized by an appropriate choice of the throttle surface and the controller gains. We obt ain lower bounds on the gains of the controller in terms of the divided dif ferences related to compressor characteristic. These bounds can be expresse d using some bounds on the first and second derivatives of the characterist ic in the region of operation. In this way we establish a direct relationsh ip between the shape of the compressor characteristic and the required cont roller gains. We discuss controllers that stabilize a range of the desired equilibria and guarantee a soft bifurcation of the equilibria as a set-poin t parameter varies. We give an example of controller design for a right-ske w compressor. We provide simple general guidelines for choosing the throttl e surface. (C) 1999 Elsevier Science Ltd. All rights reserved.