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

We discuss the design of controllers for compressors with general characteristics, including the right-skewed ones. The controllers can be represented graphically by plotting their throttle surfaces. The graphical representation of controllers enhances understanding of controller action and allows to compare various controllers. We discuss the issue of the right skewness of a compressor characteristic. We show how to design controllers using a graph backstepping procedure involving the construction of the throttle surface. We show that for a quite general compressor characteristic, every potential axisymmetric equilibrium on the decreasing part of the compressor characteristic, the peak of the characterisitic, and every rotating stall equilibrium close to the peak can be globally or semi-globally stabilized by an appropriate choice of the throttle surface and the controller gains. We obtain lower bounds on the gains of the controller in terms of the divided differences related to compressor characteristic. These bounds can be expressed using some bounds on the first and second derivatives of the characteristic in the region of operation. In this way we establish a direct relationship between the shape of the compressor characteristic and the required controller gains. We discuss controllers that stabilize a range of the desired equilibria and guarantee a soft bifurcation of the equilibria as a set-point parameter varies. We give an example of controller design for a right-skew compressor. We provide simple general guidelines for choosing the throttle surface.