A review of methods for input/output selection <s> Introduction <s> Process synthesis is the step in design where the chemical engineer selects the component parts and how to interconnect them to create his flowsheet. This paper reviews the rapidly growing process synthesis literature of over 190 articles, almost all of which have been produced in the last decade. ::: ::: The paper first introduces the nature of the synthesis problem and outlines the variety of approaches which have appeared to solve aspects of it. The problems include developing a representation, a means to evaluate alternatives, and a strategy to search the almost infinitely large space of possible alternatives. As the article demonstrates, effective solutions are very dependent on the nature of the synthesis problem being addressed. ::: ::: The article covers in detail the following five synthesis topics: chemical reaction paths, separation systems, heat exchanger networks, complete flowsheets, and control systems. Readily apparent are the development of industrially significant insights to aid in the design of heat exchanger networks. Reasonable progress exists in the synthesis of separation systems based on nearly ideal distillation technology and in the development of computer aids by chemists for reaction path synthesis leading to desired complex organic molecules. More work is needed for the remaining areas to become industrially significant. <s> BIB001 </s> A review of methods for input/output selection <s> Introduction <s> This article presents a survey of a set of interaction measures for multiple-input-multiple-output (MIMO) linear systems, and discusses their use to determine the best pairing of manipulated and controlled variables. Criteria to decide whether a multiloop control strategy can be applied successfully to a given process are also described. The classical approaches, such as Bristol's relative gain array and Niederlinski's theorem are reviewed in the first sections. Next, less common methods based on the Jacobi eigenvalue criterion, the direct Nyquist array, and singular value analysis are introduced. Finally, examples are used to illustrate the usefulness of each approach and criterion. <s> BIB002 </s> A review of methods for input/output selection <s> Introduction <s> The paper focuses on the selection of measured and manipulated variables and decentralized control configurations as a sub-problem of control system design. It outlines the key ideas of various methods encountered in literature and recommends topics for future research. <s> BIB003
Control system design could be split into the following six steps. First, the control goals are formulated. This involves choosing and characterizing the exogenous variables w and choosing and imposing requirements on the controlled variables z, see Fig. 1 . The control goals should be quanti"ed in the time and/or frequency domain. The choice of z may be a!ected by the outcome of the other steps of control system design, like the choice of the plant model G in the second step of control system design. The techniques used in other steps also determine the model type, e.g., linear or nonlinear, time-invariant or time-varying, physical principles or black box. In the third step, the control structure is selected. Fourth, the controller K is designed. The choice of the design method (PID, LQG, adaptive control, H optimization, etc.) depends on aspects like the control goal, model accuracy, and restrictions on the implementation. Fifth, the closed-loop system is evaluated via simulations or pilot plant experiments. In the last step, the controller and hardware like sensors, actuators, and control processors are implemented in the real plant. Iterative re"nements of these steps are often necessary, e.g., meeting the control goal might call for a more accurate model or a modi"cation of controller parameters. The third step of control system design, i.e., control structure selection, is usually split into two separate problems which are then solved successively: input/output (IO) selection, which is the focus of this paper, and control con"guration (CC) selection. Approaches to solve IO and CC selection jointly are seldomly encountered in the literature. Here, the IO selection problem is posed as follows: Select suitable variables u to be manipulated by the controller (plant inputs) and suitable variables y to be supplied to the controller (plant outputs). Both the inputs and the outputs of G are divided into two classes, but in this paper the terms`inputsa and`outputsa are reserved for u and y. Each combination of inputs and outputs is called an IO set. CC selection is only relevant for decentralized control, i.e., for controllers with one or more entries that are structurally zero. Establishing which outputs in y are used to determine each input in u is often called partitioning or pairing in case of a diagonal controller. Surveys of CC selection methods can be found in Cao (1995, Chapter 1) , BIB002 , BIB003 , and  . IO selection involves selecting an appropriate number, place, and type of actuators and sensors. In general, IO selection is performed prior to the physical realization of the plant, based on a plant model and a proposed set of candidate actuators and sensors. Sometimes it may be desirable to perform IO selection for a plant that is already equipped with actuators and sensors. Reasons for not using all the available actuators and sensors could be the reduction of the control system complexity and the costs of operation and maintenance. Also, devices may be present that cannot be used at the same time, e.g., two valves that in#uence exactly the same #ow. This can occur because di!erent plant con"gurations, e.g., at startup and at full load, require di!erent instrumentation. It is also possible to study the bene"ts of sensors and actuators besides or instead of those available. This situation occurs when new sensor or actuator technology becomes available, when an existing plant needs a re"t, or when a plant has to meet tighter speci"cations. IO selection involves more than actuator and sensor selection. Apart from physically sensed variables, y may include variables derived from the sensed variables (e.g., a di!erentiated version of a sensed position) and commanded setpoint or tracking variables. In analogy, apart from physically actuated variables, u may include reference variables for other control system parts. Despite a slight abuse in terminology, the outputs y will sometimes be called measured variables, whereas the inputs u will often be called manipulated variables. IO selection may also be used to decide on particular controller restrictions which will be called`controller schemesa. These re#ect the decomposition of the controller into di!erent units, like feedback, feedforward, and cascade loops. In case of the general control system set-up, distinct controller schemes result in distinct plants G and distinct IO sets. Distinct candidate controller schemes can also be incorporated simultaneously into G. The majority of the currently known IO selection methods cannot be used for systems giving rise to a decentralized K in Fig. 1 , due to the restriction to centralized controllers. An IO selection method that also handles decentralized controllers K in Fig. 1 could be used to solve IO and CC selection jointly, but such methods are rare in the literature. Sensible IO selection is important. First, the IO set may limit the performance, which may not be overcome by advanced controller design. For instance, the IO set may give zeros in the right half-plane, imposing an upper bound on the bandwidth. Second, the IO set determines aspects like reliability and the expenses of hardware, implementation, operation, and maintenance. In this respect, a small IO set (i.e., an IO set with a small number of inputs and outputs) is often preferred to a large IO set. Especially in the context of fault-tolerance, redundancy of actuators and/or sensors may also be desired. This should then be incorporated in the selection. Normally, the selection can be used to "nd IO sets that show no redundancy at all, providing information about the performance losses due to instrumentation faults. The number of candidate IO sets grows exponentially with the number of candidate inputs and outputs. Suppose there are N S candidate inputs and N W candidate outputs. Assume that these can all be used together if desired, i.e., assume that there is a well-de"ned full IO set including all N S inputs and all N W outputs. If certain devices are not compatible, the problem can sometimes be embedded in a larger problem where the devices are allowed to be used together. During IO selection, a subset of n S inputs and n W outputs, i.e., an n S ;n W IO set, is generated from the full IO set (n X will be used to denote the number of controlled variables z). The total number of distinct IO sets is given by (2, S !1)(2, W !1)#1, with #1a due to the empty IO set with n S "0 and/or n W "0 (open-loop system). The exponential growth of the problem motivates the need for systematic IO selection methods to quickly and easily assess a large number of candidate IO sets. Though IO selection could be performed by controller design and closed-loop evaluation for each candidate IO set, this is not feasible for anything but a small number of candidates. This paper provides a comprehensive review of the currently known IO selection methods. As far as we know, the only reviews in the 1990s that are related to this topic and that are also rather extensive were given by  and Skogestad and Postlethwaite (1996, Chapter 10) . A decade earlier, the articles by  and BIB001 should be mentioned. The main contributions are the following. First, a list of properties is proposed that a good IO selection method should possess (Section 2). This list is used to assess known methods and it could be used as a guideline to develop new ones. Second, a comprehensive review of IO selection methods is given that is believed to be rather complete (Section 3). To aid the control engineer who faces an IO selection problem in choosing the right method, these methods are grouped according to the control system property that they address. Third, an overview of applications of systematic IO selection methods is given, revealing that such methods are important for a wide variety of problems (Section 4). These applications are grouped according to the class of systems that is considered, so one can pick the method that best matches one's problem. Fourth, a qualitative assessment and comparison of the reviewed methods is given (Section 5). This sketches the state of a!airs and gives rise to some future research topics.