A review of methods for input/output selection <s> Accessibility <s> Abstract This paper addresses the problem of evaluation of alternative control configurations on the basis of structural characteristics of the process. Relative order is proposed as the main analysis tool for this purpose. Using tools from graph theory, it is shown that generic calculation of relative orders requires only structural information about the process. Relative order is interpreted as a structural measure of the initial sluggishness of the response, as well as a structural analog of dead time, which expresses fundamental structural limitations in the control quality. A matrix of relative orders of input/output pairs is introduced, which leads to a characterization of structural coupling among input and output process variables. On the basis of the above properties, general structural evaluation guidelines are proposed for alternative sets of manipulated inputs and alternative input/output pairs. The application of the theory is illustrated in the case of an evaporation unit, a chemical reactor and a network of heat exchangers. <s> BIB001 </s> A review of methods for input/output selection <s> Accessibility <s> Abstract Quantitative measures are determined for the evaluation of the structural properties of nonlinear processes. These include simple structural measures for the evaluation of the “best” achievable control quality in a given process, regardless of the type of the controller being used. The notions of relative orders (time delays) with respect to manipulated inputs and disturbances and characteristic matrix are used to determine the best achievable closed-loop response for each controlled output and to derive the conditions under which the best closed-loop response in all outputs together with complete input-output decoupling is feasible. <s> BIB002
The ideas by BIB001 could be useful for input selection for nonlinear plants. They de"ne the relative degree r GH of a controlled variable z G with respect to a manipulated variable u H (y"z is assumed). In that way, r GH is a measure of the e!ect of each one input on each one output, such that it can also be used for CC selection. The generic computation of r GH only requires structural information on the system. The relative degree is proposed as a measure of the dynamic interaction between manipulated and controlled variables or as a measure of the sluggishness of the response of the controlled variables to steps in the manipulated variables. Intuitively, the relative degree is related to thè physical closenessa of manipulated and controlled variables, or to the`direct e!ecta of manipulated variables on controlled variables. These heuristics are often used for IO selection. In a cause-and-e!ect graph, r GH #1 is the minimum number of edges connecting u H to z G , provided r GH is "nite; an in"nite r GH indicates nonaccessibility of u H to z G . In Fig. 3 , r "1 for the two edges u Px and x Pz , while r "R. The relative degree is thus related to the number of states in the shortest cause-ande!ect path. This is consistent with the interpretation of the relative degree as the number of integrations the input has to go through before it a!ects the output. The relative degree could form the basis for a quantitative accessibility measure for input selection: the lower r GH , the better the accessibility of u H to z G . Thus, compute for a given input set, then candidate input sets with small r XS are preferred. BIB001 propose the relative degree also as a tool for CC selection, since it measures dynamic interaction between (groups of) inputs and outputs. BIB002 proposes output selection based on the relative degree of a measured variable with respect to an exogenous variable.