Real-Time Error-Feedback Output Regulation of Nonhyperbolically Nonminimum Phase System

A real time implementation of an error feedback output regulation problem for the gyroscopical platform is presented here. It is based on a numerical method for the solution of the so-called regulator equation. The regulator equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Error-feedback output regulation problem aims to find a dynamic feedback compensator using only tracking error measurements to ensure tracking given reference and/or rejecting unknown disturbance. Solving the regulator equation is becoming difficult especially for the non-minimum phase systems where reducing variables against algebraic part leads to possible unsolvable differential part. The proposed numerical method is based on the successive approximation of the differential part of the regulator equation by the finite-element method while trying to minimize functional expressing the error of its algebraical part. This solution is then used to design real-time controller which is successfully experimentally tested.