Frequency-Based Design of Internal Model Controller Using the Method of Inequalities

Alabi, S.B.
Department of Chemical and Petroleum Engineering
University of Uyo, Uyo, Akwa Ibom State, Nigeria.
E-mail: sundayalabi@uniuyo.edu.ng, uniquebola@yahoo.com
ABSTRACT: In the traditional frequency domain design of an internal model controller, the
design problem is cast in terms of 2 H and  H norms of sensitivity functions in order to
obtain the parameters of a robust controller for an uncertain system. This requires the use of
weights, which are often obtained in a cumbersome trial-and-error manner. In this paper, a
computer-aided robust internal model control design method which eliminates trial-anderror
selection of weights was formulated within the context of the method of inequalities
(MoI). Lead, lag and lead-lag networks were used as weights and the model uncertainty was
described both in exact and norm-bounded forms. The robust stability and performance
criteria of the feedback system were defined as a set of algebraic inequalities. Moving
boundaries process (MBP), a search algorithm, was used to automatically and
simultaneously obtain the parameters of the controller and the weights which satisfy the
performance criteria. An uncertain system from the literature was chosen to illustrate the
new technique. The MoI-based method gave rise to internal model controller filter
parameters which in most cases are in close agreement with the filter parameters obtained
using the traditional trial-and-error method. Furthermore, the uncertainty weights obtained
via the MoI-based method are of lower order in comparison with those obtained via the
tedious trial-and-error method. It is concluded that the MoI-based method can effectively
replace the trial-and-error method for the frequency-based design of internal model
controller.