Algebraic identification and control of an uncertain DC motor using the delta operator approach

An algebraic parameter identification method for, high rate, sampled linear systems is proposed for the output feedback control of a completely unknown DC motor. The parameter estimation method is based on the algebraic methodology (introduced by Fliess and Sira-Ramírez in [1]) for continuous time systems. In this article, we adapt the algebraic parameter identification methodology so that it takes into account sampling effects. We apply the algebraic identification method within the delta operator framework developed by Middleton and Goodwin in [2]. Delta operators constitute an effective alternative, over the Z-transform, for working with fast sampled systems. One of its advantages ensures a smooth transition between a continuous and a high sampled discrete sampled system. We use a delta operator-based algebraic identification scheme for the construction of the involved linear regressor in combination with a special invariant filtering to improve the identifier against additive noise effects. Our invariant filtering coincides with the least squares solution of the linear regressor equation. A delta-operator based output feedback controller of the Generalized Proportional Integral (GPI) type is also proposed for the solution of the output trajectory tracking problem, for the DC-motor, as a certainty equivalence controller. The fast identification of all system parameters is used in the certainty equivalent feedback control law design. Some experimental results are presented which validate the effectiveness of the proposed approach.