An asymmetric order doubling approach to the control of nonminimum phase systems

A new method for the control of nonminimum phase systems using “asymmetric order-doubling” is presented. The number of poles and zeros is doubled by placing additional poles and zeros in such a way that the root locus plot is shaped in a desired manner and that all the branches of the root locus can be separated into LHP and RHP. We pick the stable LHP portion of the root locus to design a state feedback controller using the positive semidefinite solution of a certain algebraic Riccati equation. This generalizes the LQR method and is more suitable for nonminimum phase systems where the symmetric choice of poles and zeros doesn´t necessarily satisfy all the design criteria, for example, when they are close to the imaginary axis. This also broadens the loop transfer recovery method by providing a systematic way of continuously shifting the location of poles to a much larger set. This algorithm is implemented on a coordinate measuring machine which exhibits a nonminimum phase behaviour. A significant improvement over the traditional LQR method is obtained in terms of speed of response and settling time when the asymmetric, order-doubling method is used