Multivariable DMC

Undoubtedly the most popular multivariable controller is the multivariable extension of dynamic matrix control. We developed DMC for a SISO loop in Chap. 8. The procedure was a fairly direct least-squares computational one that solved for the future values of the manipulated variable such that some performance index was rninirnized. 

The procedure can be extended to the multivariable case with htde conceptual efibrt You simply expand the 4 matrix discussed in Chap. 8 to include aU the individual A matrices relating all of the outputs to all of the inputs. The performance index is expanded to include the errors in all the controlled variables plus weighting the moves in all the manipulated variables. The bookkeeping and the nrimber-crunching become more extensive but the concept is the 

CALL LEQ2C(H,NN,IA,H1N,M,IB,IJ0B,WA,WK,IER) CALL LOADTF(GL,W,N,KL,TAUL,DL) 

Using the multivariable DMC produces some improvement for setpoint disturbances. However, as Fig. 17.3 shows, there are only slight differences between DMC and the diagonal structure (with BLT tuning) for load disturbances. Thus the real economic incentive for the more complex multivariable configuration has yet to be demonstrated by impartial evaluators. 

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Figure 17.3 gives some comparisons of the performance of the multivariable DMC stmctuie with the diagonal stmcture. Three linear transfer-function models are presented, varying from the 2 x 2 Wood and Berry column to the 4 x 4 sidestream column/stripper complex configuration. The DMC tuning constants used for these three examples are NP = 40 and NC = 15. See Chap. 8, Sec. 8.9. 

In practice, however, this extension is not as straightforward as in DMC. In multivariable DMC, there is a definite design procedure to follow. In multi-variable IMC, there are steps in the design procedure that are not quantitative but involve some art. The problem is in the selection of the invertible part of the process transfer function matrix. Since there are many possible choices, the design procedure becomes cloudy. 

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