Adaptive optimizer based on the sequential simplex method applied to the control of a thermo-mechanical pulping screening room

Abstract

An adaptive optimizer is designed for control of multi-variable processes where the operating characteristics of the plant are time varying. Based on the original sequential method for static applications, the modified direct search method is made adaptive by allowing only limited expansion and contraction and by re-measuring all points of a simplex when improvement of the simplex position is not possible by reflection of the vertices, and when expansion or contraction occurs. In one method, suitable for performance functions that have a known optimum value, i.e., sums of squares of errors from target values, expansion and contraction is determined by a threshold value of the performance function. In a second method, expansion and contraction is determined by ranking the newest measurement against the historical measurement values in the simplex, similar to the Nelder-Mead method. The optimizer was tested on simulated two by two multi-input multi-output first order plus delay processes. It worked best in the absence of dynamics, but could give acceptable performance where the delay and time constants were less than five measurement sample times. The adaptive optimizer is applied also to a simulated model of a thermo-mechanical pulping screening room to control the accepts fibre distribution, using the main line and reject screen volumetric rejects ratios. Two types of screens are modeled: screens with smooth holed apertures in the screening baskets, and screens with slotted apertures. The adaptive optimizer is capable of controlling the accepts fibre distribution over limited ranges of disturbances in mean fibre length. The control range o f the slotted screen is narrower than that of the holed screen because of its flatter fractionation profile. Transport and capacity lags do not have a great impact because most of the fibre flow follows the main accepts line.