Un regulador PID de asignación de polos y varianza reducida.

Résumé

In this paper a method for tuning digital PID type controllers according to a pole placement rule is described and generalized to allow the output system variance to be reduced at the same time. The method is based on a suitable controller overparametrization so that, while preserving the original closed loop pole positions gives some extra degrees of freedom which can be used to fix some other characteristic of the system. Using the fact that the extra controller parameters modify the noise-spectrum of the output, an optimization techniques is employed in order to choose them to get minimum output variance. The final result is a new controller which retains the original structure of a PID regulator addign an extra term, with both pole placement and minimum variance properties. Examples are presented showing the use of the new algorithm and its advantages in rejecting output noise with little computational effort. Particularly a comparison with the Minimum Variance Control shows that the variance of the system output is similar in both cases, but additionally the proposed method gives also the possiblility of pole assignment.