Robust endpoint feedback control of nonminimum phase systems with actuator saturation

A pole placement method was developed by modifying the symmetric root locus method of a class of linear quadratic regulators (LQR). It was successfully applied to the case of a coordinate measuring machine. The performance and robustness properties of this method were also examined by the same authors. The need for a slight modification of this method to include theoretical guarantees on the robust stability and performance was emphasized. In this paper, we present a method, originally developed by Megretski, as an suitable modification to include uncertainty description and saturation type nonlinearities. We also derive the discrete time results that makes the method suitable to implement in practical applications. The presence of nonlinearities like saturation or rate limiters in addition to parametric uncertainty complicates both the analysis and design procedure. This method is implemented on a 3D-coordinate measuring machine which exhibits nonminimum phase behavior. Significant improvements and good robust performance is exhibited over the traditional LQG method