Correcting variables

The bias is then subtracted from the appropriate measurement, the reconciliation repeated, and the statistic compared with that of the base case. If the comparison is favorable, then the correct variable has been identified to contain a bias. If not, the procedure is repeated for a new suspected measurement, until the correct one is identified. 

Thus the corrected variables indeed satisfy (3.79) at convergence. 

PARAMETER ESTIMATES 2 NZ) CORRECTED VARIABLES FURTHER RESULTS PRINTED IN THE MODULE REM USER-SUPPLIED SUBROUTINES ... 

LPRINT LPRINT TAB(15)j"mmmt CORRECTED VARIABLES 1 " LPRINT iLPRINT FOR M=1 TO NM FOR IT=1 TO IM ZE=0... 

The correcting variable Au is computed from the state variables using the optimal feedback law... 

Is the controller structure correct Have the correct variables been chosen for MVs, CVs, and DVs ... 

To adopt the same spatial operators for aU variable families, the contra-curl will be systematically used, inducing the presence of a minus sign in front of the magnetic potential vector A. In fact, as for the pressure P in hydrodynamics, the correct variable is always the opposite of the usual one, because historically this vector has been defined without sign rationalization. 

Transthoracic Very rapidly initiated Pacing wires are frequently not placed correctly Variable effectiveness for pacing (often because the patient is in extremis) High complication rate... 

The above example of a simple technical controller leads us to a general consideration of the control circuit. If a system is to fulfill its function, a certain type of behavior must be expected of it namely the desired behavior denoted by the input X. The system can be influenced by the correcting variable Y. It is to be assumed that, acting on a system, whose exact behavior in time is unknown, will trigger unforeseeable changes in the system s behavior. The actual behavior X does not equal the desired behavior, but deviates from the latter by an amount A (r) which, in the course of time, will undergo certain changes ... 

If it is desired that the actual behavior deviate from the desired behavior only by an amount permissible for the function of the system in question, a correction of the deviation by means of a reverse measure will be necessary. This is based on the premise that, first, the actual behavior X is being monitored by a corresponding monitoring device and is constantly checked inside the controller against the desired behavior, and, second, each deviation detected will trigger a modification of the correcting variable Y. By this feedback a control circuit is established. 

However, the above formulation does not yet take into consideration that delays in time must likewise be taken into account in the monitoring of the specified behavior in the conversion of the information into variations of the correcting variable within the controller and in the reaction of the control system to these variations. If the delay times ra, and Ta are allocated to the control system, the monitoring device, and the control device, respectively, the following result will supplant the above equations ... 

Selecting a standard illuminant, a standard observer, and the proper expression of results is essential to obtaining color data that correspond to color perception. However, because instruments are simple to operate, many operators are untrained in instrument and color theory. They make bad parameter choices or instrument adjustments and measure specimen colors incorrectly (30). If the operator can define the color task, he or she will probably choose the correct variables and solve his or her color mea-... 

Finally, we follow the solution map to solve the problem. The equation below the arrow shows the relationship between K and °C, but it is not solved for tire correct variable. Before using the equation, we must solve it for °C. 

Then solve the equation for C and substitute the correct variables into the equation. Finally, calculate the answer to the right number of significant figures. 

Solve Boyle s law for V2 and substitufe the correct variables to calculate its value. 

Determine the goal and mode of operation of the process unit Determine the process boundaries and the external distiubances Determine the goal of the model and the associated level of detail Establish the controlled variables (conditions, mass and qualities) Select, if required, the correcting variables for the throughput and recycle loops... 

During the development of the enviromnental model, it is advisable to ideahze the interfacing between the process and the control system as much as possible. Assume that the communication takes place via variables with a maximum possible level of abstraction. It is not necessary to take measurement and control specifications already into account. For example, for correcting variables one can take material flows or energy flows and for controlled variables one could take pressures and mass fractions. It is advisable, however, to use measurable variables, which can also be measured in reahty, for example the mass instead of the level in a vessel. 

If one chooses a less abstract correcting variable (for example the valve position, valve opening or the pnemnatic pressure), the pressure drop across the valve has to be taken into account in the internal model. The pressure drop is determined by the mass accumulation in the process unit and the external pressure. This leads usually to a much more complicated model. A controlled variable (the accumulation) is internally coupled with the correcting flow, also additional disturbances (from adjacerrt process units) should be taken into account. Such a detailed model is only useful if pressure control or pressure propagation through the equipment has to be modeled. These are relatively fast phenomena. 

By inclnding control loops between the correcting variables and controlled variables, the degrees of freedom are used. The degrees of freedom are not eliminated, they are shifted to the setpoints of the control loops. 

A central issue is when is the model complete When correcting variables have not been taken into account, the system is usually undetermined. If important state variables have been forgotten, they will also not appear in the behavioral model and in any control scheme. For example, if, for simplicity reasons, in the case of distillation the column pressure has not been taken into account as state variable, the pressure will not appear in the behavioral model and pressure control will not be part of the system. 

In the developed model, it is already determined how many degrees of freedom for control are available the number of correcting variables minus the variable used for control of the throughput. System behavior is determined only if these variables are given. The disturbance variables do not play a role, since they are already determined externally. 

The number of equations should be minimally equal to the number of correcting variables. Every additional variable that is introduced in the internal model, also introduces an additional equation. If the process model contains single input-single output controllers, every correcting variable determines one controlled variable. The new variable (is the new degree of freedom) in the control algorithm is the setpoint of the controller. 

Once a model has been defined, we would like to get more insight into the behavior of the process variable we are interested in when the correcting variable or the disturbance variable changes. This information could be obtained in different ways. 

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