Selection of Controlled Variables

Problem Definition Selection of Controlled Variables 13.2.1 Engineering Judgment / 13.2.2 Singular Value Decomposition Selection of Manipulated Variables Elimination of Poor Pairings BET Tuning... 

Selection of controlled variables. Ca should be selected because it affects the product quahty directly (Guideline 3). T should be selected because it must be regulated properly to avoid safety problems (Guideline 2) and because it interacts with Q (Guideline 4). Finally, h must be selected as a controlled output because it is non-self-regulating (Guideline 1). 

Selection of Controlled Variables. The guidelines in Section 20.2 are not helpful because no output variable has a direct effect on the product quality, all are self-regulating, and none are directly associated with equipment or operating constraints. Nonetheless, and are obvious choices for the controlled variables because the objective of this subsystem is to control the temperature and flow rale of the utility stream fed to the reactor jacket. 

Quite independently from the state of the system, we may characterize the process whereby the system changes from an initial to a final state by means of a cost function. This function, C say, is in some sense to be a measure of the cost of processing the system. (We might alternatively consider its compliment, the profit function.) In many cases, the selection of control variables to achieve the desired change of state is not unique, and it then becomes feasible to seek some optimum or least cost function. A general form for the cost function can be written... 

SELECTION OF CONTROLLED VARIABLES FOR SELF-OPTIMIZING CONTROL... 

However, for nonlinear problems (e.g. g is a nonlinear function), the optimal solution may be unconstrained in the remaining variables, and such problems are the focus of this paper. The reason is that it is for the remaining unconstrained degrees of freedom (which we henceforth call u) that the selection of controlled variables is an issue. For simplicitly, let us write the remaining unconstrained problem in reduced space in the form... 

Step 7 Further analysis and selection of controlled variables... 

The selection of controlled variables for different systems may be unified by making use of the idea of self-optimizing control. The idea is to first define quantitavely the operational objectives through a scalar cost function J to be minimized. The system then needs to be optimized with respect to its degrees of freedom Uo- From this we identify the active constraints which are implemented as such. The remaining unconstrained degrees of freedom u are used to controlled selected controlled variables c at constant setpoints. In the paper it is discussed how these variables should be selected. We have in this paper not discussed the implementation error n = c Cg which may be critical in some applications (Skogestad 2000). 

Some local controls are assumed to be in place, such as anti-surge control for the compressors. In addition, some valves are fiilly open or fixed, as shown in Fig. 35.1. The selection of controlled variables is strongly related to the goals that are set for operation of the fluid catalytic cracker. There are numerous constraints that all have to be met. Moreover, two main objectives should be met maximization of the total feed rate and dismtbance rejection. 

B. 2. Employ multivariable control for highly interactive processes. So far we have assumed that a multiloop control approach will be sufficient and that multi-variable control will not be necessary. One way to help ensure that this assumption will eventually be validated is to design the individual control loops so they interact as little as possible by careful selection of controlled variables and their pairing with manipulated variables. For example, adjusting the value of wi and the ratio of wilwi (in order to control W4 and x j), respectively), instead of directly controlling the two flow rates individually, is one way of physically decoupling the two control loops (see Chapter 18). 

The selection of controlled and manipulated variables is of crucial importance in designing a control system. In particular, a judicious choice may significantly reduce control loop interactions. For the blending process in Fig. 8-40(d ), a straightforward control strategy would be to control x by adjusting w, and w by adjusting Wg. But... 

This selection of control structure is independent of variable pairing and controller tuning. The MRI is a measure of the inherent ability of the process (with the specified choice of manipulated variables) to handle disturbances, changes in operating conditions, etc. 

The chemical plant will be first decomposed to its subsystems of unit operations with functional uniformity and common objectives in terms of economics, operation and control. Within each subsystem resulting from the decomposition of the overall plant, we employ the same general approach described in the previous section to (a) classify the plant constraints at the current optimum, into active and inactive ones (b) select the controlled variables for the decentralized subsystem controllers (c) select the manipulated variables for each subsystem (d) establish the initial search direction (ISD) to achieve feasibility and (e) to define the resulting new search directions (NSD) that will ultimately lead to the new optimum operation. 

The optimal robust controller designed with one of the new synthesis techniques is generally not of a form that can be readily implemented. The main benefit of the new synthesis procedure is that it allows the designer to establish performance bounds that can be reached under ideal conditions. In practice, a decentralized (multiloop) control structure is preferred for ease of start-up, bumpless automatic to manual transfer, and fault tolerance in the event of actuator or sensor failures. Indeed, a practical design does not start with controller synthesis but with the selection of the variables that are to be manipulated and measured. It is well known that this choice can have more profound effects on the achievable control performance than the design of the controller itself. This was demonstrated in a distillation example [17, 18] in which a switch from reflux to distillate flow as the manipulated variable removes all robustness problems and makes the controller design trivial. 

Quantitative description of catalytic properties requires that the system under consideration be unambiguously described with respect to system boundaries (mass of catalyst mc, area of catalytic surface Ac, or volume of porous catalytic particle Vc) and conditions such as composition, pressure, temperature, prevailing at the boundary (control variables). A set of data characterizing a catalyst must permit the prediction of material balance of the system containing the catalyst at steady state under at least one set of control variables. It is sometimes possible to represent a number of experimental observations by rate equation or a set of rate equations which may or may not be based on a mechanistic model. The model has to fulfil the above criteria within a certain range of validity which should be indicated. The catalytic system should be characterized with respect to the rate of chemical change (activity) and with respect to product composition selectivity). 

For the procedure of successive substitution to be guaranteed to converge, the value of the largest absolute eigenvalue of the Jacobian matrix of F(x) evaluated at each iteration point must be less than (or equal to) one. If more than one solution exists for Eqs. (L.17), the starting vector and the selection of the variable to solve for in an equation controls the solution located. Also, different arrangements of the equations and different selection of the variable to solve for may yield different convergence results. 

Manipulated variables (inputs). These are available degrees of freedom left after considering the basic control. The selection of manipulated variables could also be the object of a local controllability analysis. A typical example is the use of SVD for the selection of the sensitive stage for inferential quality control in a distillation column. 

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