A review of methods for input/output selection <s> Ezciency of estimation <s> Methods are presented for the design of a static estimator which infers unmeasurable product qualities from secondary measurements. The secondary measurements are selected so as to minimize the number of such measurements required to obtain an accurate estimate which is insensitive to modeling errors. Unlike previous work, the number of secondary measurements can be fewer than the number of unmeasured disturbances. If the statistics of the disturbances and/or measurement noise are available, this information can be incorporated into the design procedure to obtain an optimal static estimator. ::: ::: The design procedure is illustrated by application to a simulated industrial debutanizer. Data for the simulation were supplied by the Marathon Oil Company. Deviations in bottoms product quality are compared for the current control policy (maintenance of a stage temperature at its set point) and the inferential control system with the column subjected to representative feed composition disturbances. Results show that inferential control based on four, five, or six tray temperature measurements improves the steady state control performance by as much as 400%. <s> BIB001 </s> A review of methods for input/output selection <s> Ezciency of estimation <s> Abstract The optimal location of temperature measurements along the length of a non-adiabatic tubular reactor in which a first-order exothermic reaction is occu <s> BIB002 </s> A review of methods for input/output selection <s> Ezciency of estimation <s> The method of false nearest neighbors (FNN) is presented here as a tool for analyzing the "dimensionality" of a nonlinear input/output system directly from data. A unique feature of this method is that no specific model structure is assumed, the dimensional determination is made directly from topological considerations. An extension to the FNN algorithm is given to consider the problem of inferential measurement selection for a nonlinear system. Methods of control relevant modeling for distillation are considered, and some ideas on how to accurately model high purity distillation columns are presented. <s> BIB003
Morari and Stephanopoulos (1980b) select (secondary) measurements aimed at minimizing the errors in the estimates of relevant variables, like the controlled variables z. This aim is transformed into the minimization of cost functions J W . The error sources are model uncertainties, process disturbances, and sensor noise. These are treated from a stochastic point of view by introducing colored process noise w V and white sensor noise w W . Four output selection criteria are proposed. These are all based on a static estimator, derived for the steady-state model. The "rst aims at minimizing the static estimation error, the second aims at minimizing the e!ect of model uncertainties on the estimates, and the third and fourth aim at minimizing the estimation errors if the static estimator is used for the dynamic system. The "rst criterion is essentially a multivariable extension of thè projection error criteriona derived by BIB001 who estimate single variables. According to this criterion, the results tend to improve if measurements are added. The second criterion is essentially the same as the`condition number criteriona of  , involving the open-loop steady-state TFM from the disturbances w V to the measurements y. According to this criterion, the results tend to degrade if n W increases, which is quite surprising. Hence, a trade-o! must be made when the projection error criterion and condition number criterion are used concurrently for output selection. The counter-intuitive result for the condition number criterion can (partially) be attributed to an uncertainty model that is physically inconsistent for the candidate output sets, see also Lee (1991, Section 3.5) . The output selection method proposed by BIB002 aims at minimizing state-estimation errors using a dynamic estimator (Kalman "lter) instead of a static one. Model uncertainties, process disturbances, and sensor noise are again approached from a stochastic point of view by adding white noise to (2) and (3). The cost function J W to be minimized as a function of the output set involves the trace of the estimation error covariance matrix (t): with '0 and '0 weighting parameters. The matrix (t) is obtained by solving a di!erential Riccati equation. For a "xed number of sensors, an iterative algorithm identi"es the optimal ones among all candidates. BIB003 make an attempt towards output selection for a nonlinear autonomous plant x "f (x), y"g (x) . The basic idea is not minimization of estimation errors, but minimization of`modeling errorsa. The aim is to designate the smallest number of (secondary) measurements y that enables an accurate recreation of the nonlinear system dynamics. This only involves sampled system data y(k). After output selection, the outputs that are needed to accurately describe the system are known, but a model still has to be derived. As in  , the derived output sets may be well suited for modeling, but not for control where the outputs may have di!erent tasks. This is also recognized by  , who consider actuator selection for control and for identi"cation, using di!erent criteria depending on the task. In  , the criterion for selecting sensors for modal identi"cation of #exible structures is maximization of the determinant of the observability Gramian, which is also among the criteria proposed by MuK ller and Weber (1972) for selecting control sensors.