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Show For example, for three factors the design would be a cube (8 corners) with 6 axial points (through each face) and several centerpoint replicates. In general, central composite designs require 2/+2/ points plus some center point replicates. To screen large numbers of factors (f>5) w e use screening designs which require 2 M >/+l, where l'k is the degree of fractionation. For example the Vi fraction for f=5 requires 25"1=16 points plus centerpoint replicates. Montgomery gives a good overview of the various experimental designs and techniques. x2 -0-* Xi Figure 2, Central Composite Design Linear Transforms One transforms the actual values of the factors (e.g., lb/h N H 3 flow, psig air pressure) to non-dimensional unit ranges. Subtracting the mean and dividing the result by half the range will normalize factors to ±1. Such linear transforms do not affect the conclusions but greatly simplify the analysis of the data, rendering each coefficient independent. One may easily invert the transforms when required. The response surface then functions as a predictive algorithm. Feedforward NOx Control The algorithm in the purely feedforward operation gives good control. Figure 3 depicts the control logic. In this particular case the process is a steam boiler for paper-making. 8 As Figure 4 shows for this case (r=99.4%), M R S M is highly accurate despite using only a few parameters. This is typical. Generally, the correlation PROCESS VALUES Firing % % % Rate 02 LFG FGR Estimated N Ox NOx SP MRSM "NOx" Controller 1 FGR Controller VFD Fan Controller zsx 20 25 30 35 40 45 50 55 60 65 70 Actual NOx (ppm) Figure 4, Predicted Vs. Actual Emissions from M R S M algorithm Figure 3, Feedforward N O x Control coefficient will be greater than 90%. The boiler fuel is a combination of natural gas and landfill gas (LFG). The following variables input to the M R S M algorithm: firing rate, excess oxygen concentration, fuel landfill gas fraction, and the amount of flue gas recirculated (measured as windbox oxygen concentration). 4 |