A review of methods for input/output selection <s> Controllability and observability in a binary sense <s> The classification of control objectives and external disturbances in a chemical plant determines the extent of the optimizing and regulatory control structures (see Part I). In this article we discuss the structural design of alternative regulatory control schemes to satisfy the posed objective. Within the framework of hierarchical control, criteria are developed for the further decomposition of the process subsystems, reducing the combinatorial problem while not eliminating feasible control structures. We use structural models to describe the interactions among the units of a plant and the physicochemical phenomena occurring in the various units. The relevance of controllability and observability in the synthesis of control structures is discussed, and modified versions are used to develop all the alternative feasible regulatory structures in an algorithmic fashion. Various examples illustrate the developed concepts and strategies, including the application of the overall synthesis method to an integrated chemical plant. <s> BIB001 </s> A review of methods for input/output selection <s> Controllability and observability in a binary sense <s> A voltage variable tuning capacitor structure is disclosed. A pair of metal-insulator-semiconductor (MIS) capacitors are fabricated in a body of semiconductor material in back-to-back configuration. The back-to-back configuration reduces the effect of intermodulation distortion. The device has a relatively high quality factor, Q, because of a relatively low transverse resistance which is provided by a doped region between the pair of capacitors. The device may be used for the electronic tuning of integrated RF receivers for television, VHF, UHF, AM or FM tuners. <s> BIB002 </s> A review of methods for input/output selection <s> Controllability and observability in a binary sense <s> Abstract We study the controllability of unstable processes, with emphasis on selection of measurements and manipulated variables, and the pairing, problem for dessatralized control. The well known pairing criteria based on the Niederlinski Index and the steady state Relative Gain Array (RGA) have been generalized to open loop unstable plants. Right Half Plane (RHP) zeros in individual transfer func-tion dements may make it practically impossible to stabilize the individual loops, and in such cases these pairing criteria are not very helpful. We have found RGA ≈ I in the bandwidth region to indicate good pairings also when paired elements have significant RHP zeros, but have found the Direct Nyquist Array (DNA) to perform poorly as an indicator of good pairings. In some cases it is preferable to avoid pairings giving narrow Gershgorin bands. <s> BIB003 </s> A review of methods for input/output selection <s> Controllability and observability in a binary sense <s> Structural approaches to synthesizing the control system are gaining popularity. At the early stages of the process design, information on process control systems is available only in the structural form involving qualitative information on relationships between the process variables, so that a structural approach is the most appropriate option for control system design at this stage. A thermally integrated distillation sequence was studied for the design of control structures during the early process design stage. A new structural approach is used to synthesize automatically the best control structure. <s> BIB004
A straightforward IO selection method would be to reject candidate IO sets for which (A, B) is uncontrollable or (C, A) is unobservable. Various simple tests are available (Zhou, Doyle, & Glover, 1996, Section 3.2) . Nevertheless, such IO selection methods have not been encountered in the literature, probably due to the lack of rigor. BIB003 use stabilizability (i.e., controllability of the unstable modes) and detectability (i.e., observability of the unstable modes) for the selection of inputs and outputs, respectively. BIB001 propose structural state controllability and observability as IO selection criteria. The plant is represented in a structural model which requires only information related to whether a variable is involved in a particular system equation or not. A structural version of (2)}(3) would have only two types of matrix entries: entries which are "xed at zero and entries which can take any numerical value, including zero. A numerical model also depends on the values of the parameters which may be uncertain (typically at the early stages of process design) or which may vary with the considered linearization point. Structural controllability and observability thus provide generic information about the system, but they are only necessary for controllability and observability in the numerical sense. Necessary and su$cient conditions for structural state controllability and observability consist of (1) accessibility conditions (the states should be accessible from the inputs and the outputs should be accessible from the states) and (2) rank conditions on the structural pairs (A, B) and (C, A), see BIB001 . So, structural controllability and observability imply (but are not implied by) accessibility. Structural models are also used to describe nonlinear plants  BIB001 . By`linearizinga a nonlinear model, a structural linear model can be obtained. Structural controllability and observability thus provide prospects for IO selection for nonlinear systems. In Lin, Tade, and Newell (1991) and BIB004 , the key idea for IO selection is structural output controllability. This means that each output in y can be in#uenced by at least one input in u independently (so, at least n S 5n W ). Structural output controllability and cause-and-e!ect are thus strongly linked. The main motivation to introduce structural output controllability is that, in practice, it may not be necessary to (structurally) control and observe all states. For meaningful IO selection, controlled variables z should be properly represented by any of the candidate output sets y. More on structural controllability and observability can be found in  and BIB002 .