A review of methods for input/output selection <s> The minimum singular value <s> Abstract With increased process integration it has become very important to evaluate and compare the dynamic operability characteristics (dynamic resilence) of alternate designs. Based on recent results in multivariable frequency response theory a new framework is developed for this purpose. It is shown that dynamic resilence is determined by characteristics inherent in the system and that it is independent of the imposed controller structure and type. This gives the new method considerable intuitive appeal and allows it to avoid the lengthy optimization procedures which are typical for the previously published techniques. <s> BIB001 </s> A review of methods for input/output selection <s> The minimum singular value <s> Methode de conception logique, systematique, qui produit un systeme SISO a boucles multiples. Application a une colonne a distiller d'un melange ternaire <s> BIB002
A "rst IO controllability measure that is often used for IO selection is the frequency-dependent minimum singular value of the plant: (P(j ))50 (usually,`( j )a will be omitted). In Tzouanas, Luyben, Georgakis, and Ungar (1990), (P) is suggested for on-line selection of the input set, to adapt to changing operating conditions. The general rule is that IO sets should be selected which yield a large (P). Three reasons for this are given below. The xrst one is related to independent control of all the outputs y (Skogestad & Postlethwaite, 1996, Section 6.3) . Apart from the prerequisite n S 5n W , the IO set should guarantee (P)'0 (except at possible zeros on the imaginary axis), which implies the rank of P to be equal to n W . If (P)+0, independent control is probably di$cult to achieve. The second reason is related to input constraints. BIB001 argues that for a plant to have good tracking (r) and disturbance rejection (d) in case of input magnitude limitations, (P) should be large. BIB002 call (P) the`Morari Resilience Indexa (MRI). Dynamic resilience is synonymous to IO controllability. BIB002 suggest to select the input set with the largest MRI over the frequency range of interest, which is adopted by  and  . This quanti"es the rulè choose inputs which have a large e!ect on the outputa, see BIB001 and Seborg, Edgar, and Mellichamp (1989, Chapter 28) . The third reason is from and Skogestad and Postlethwaite (1996, Section 10.3) . Assume that the plant in Fig. 4 has additional manipulated inputs u that are not used for controlling y and additional outputs y that are not fed back, but that are important for performance. The reference r (assumed constant) and the input u are generated by a controller at a higher level. For a given disturbance d, assume that there exist u and u that optimize the performance. The inputs will not be equal to the optimal values in practice, due to imperfect control, model uncertainties, disturbances, and sensor noise. An approach to output selection is thus to select outputs y that keep u and u close to the optimal values. and Skogestad and Postlethwaite (1996, Section 10.3) show that this corresponds with large (P), at least for low frequencies where feedback is e!ective.