Application of robust state estimation and asymmetric order-doubling for endpoint feedback of nonminimum phase systems

A new robust control design method developed by the authors is experimentally implemented on a 3D coordinate measuring machine (CMM). The method developed involved designing a controller for the nominal system that gives high performance. An asymmetric order doubling controller is designed for this purpose to control the nonminimum phase system behavior of the CMM. However, the uncertainties and nonlinearities present in the system degrade the state estimation considerably. A new robust state estimator designed with uncertainties and nonlinearities described in the form of integral quadratic constraints is implemented on the CMM. The solution of the robust filtering problem is expressed in the form of linear matrix inequalities. The method when compared with the standard filtering is shown to have high performance for both nominal and perturbed systems