Controlled variables selection

If perfect steady state control is employed (integral action is included in the controller) then for each controlled variable selected in the regulatory structure its deviation from the steady state (set point) value should be zero, i.e. yj=0. The ones not selected, however, should have acceptable variability, i.e. Yj < Yj < Y should hold, where the superscripts L and U denote lower and upper bound values, correspondingly. Taking the definition of the binary variables S into consideration these conditions can be expressed in the form of the following linear constraints... 

Table 35.2. Control variable selection for pressure and pressure difference control.

The concept of inferential control can be employed for other process operations, such as chemical reactors, where composition is normally the controlled variable. Selected temperature measurements can be used to estimate the outlet composition if it cannot be measured on-line. However, when inferential control... 

Both control schemes react in a similar manner to disturbances in process fluid feed rate, feed temperature, feed composition, fuel gas heating value, etc. In fact, if the secondary controller is not properly tuned, the cascade control strategy can actually worsen control performance. Therefore, the key to an effective cascade control strategy is the proper selection of the secondary controlled variable considering the source and impact of particular disturbances and the associated process dynamics. 

Feedback Control In a feedback control loop, the controlled variable is compared to the set point R, with the difference, deviation, or error e acted upon by the controller to move m in such a way as to minimize the error. This ac tion is specifically negative feedback, in that an increase in deviation moves m so as to decrease the deviation. (Positive feedback would cause the deviation to expand rather than diminish and therefore does not regulate.) The action of the controller is selectable to allow use on process gains of both signs. 

Selective and Override Control When there are more controlled variables than manipulated variables, a common solution to this problem is to use a selector to choose the appropriate process variable from among a number of available measurements. Selec tors can be based on either multiple measurement points, multiple final control elements, or multiple controllers, as discussed below. Selectors are used to improve the control system performance as well as to protect equipment from unsafe operating conditions. 

The type and extent of automatic processing to be carried out immediately after a chromatogram has been measured is controlled by a "processing" variable selected from a table displayed by the SETUP program. In our implementation, the choices are... 

Selection of the control variables which are the most sensitive and easily measurable. 

Identify the key process variables that need to be controlled to achieve the specified product quality. Include control loops using direct measurement of the controlled variable, where possible if not practicable, select a suitable dependent variable. 

For all commercial devices, the proportional gain is a positive quantity. Because we use negative feedback (see Fig. 5.2), the controller output moves in the reverse direction of the controlled variable.1 In the liquid level control example, if the inlet flow is disturbed such that h rises above hs, then e < 0, and that leads to p < ps, i.e., the controller output is decreased. In this case, we of course will have to select or purchase a valve such that a lowered signal means opening the valve (decreasing flow resistance). Mathematically, this valve has a negative steady state gain (-Kv)2... 

If there is more than one load variable, we theoretically could implement a feedforward controller on each one. However, that may not be good engineering. Unless there is a compelling reason, we should select the variable that either undergoes the most severe fluctuation or has the strongest impact on the controlled variable. 

The setpoint indicator, located in the center of the upper half of the controller, indicates the setpoint (desired value) selected for the controller. The scale may be marked 0% to 100% or correspond directly to the controlled variable (e.g., 0 - 1000 psig or -20°F to +180°F). 

To minimize /, you balance the error between the setpoint and the predicted response against the size of the control moves. Equation 16.2 contains design parameters that can be used to tune the controller, that is, you vary the parameters until the desired shape of the response that tracks the setpoint trajectory is achieved (Seborg et al., 1989). The move suppression factor A penalizes large control moves, but the weighting factors wt allow the predicted errors to be weighted differently at each time step, if desired. Typically you select a value of m (number of control moves) that is smaller than the prediction horizon / , so the control variables are held constant over the remainder of the prediction horizon. 

Override control (or "selective control as it is sometimes called) is a form of multivariable control in which a manipulated variable can be set at any point in time by one of a number of different controlled variables. 

Select controlled variables. Use primarily engineering judgment based on process understanding. 

Flowever, sometimes the selection of the appropriate controlled variable is... 

Once the controlled variables have been specified, the control structure depends only on the choice of manipulated variables. For a given process, selecting different manipulated variables will produce different control structure alternatives. These control structures are independent of the controller structure, i.e., pairing of variables in a diagonal multiloop SISO structure or one full-blown multivariable... 

R. Heikka, P. Minkkinen, and V-M Taavitsainen, Comparison of variable selection and regression methods in multivariate calibration of a process analyzer. Process Control and Quality, 6, 47-54 (1994). 

At this point an attempt has been made to identify all of the important v ari-ables. It has also been decided which variables will be fixed and which will be varied. For the nonfixed variables, the range and number of levels (complexity) have been determined. Classical experimental design tools will be used to specify the design for the controllable variables. The design is selected via a software package or statistical reference materials and it specifies (1) the number of runs, (2) the levels of the variable(s), and (3) tlie order of the runs. 

Our study group consisted of 167 individuals, of whom 99 were healthy women controls and 68 breast cancer cases. The experimental group was comprised of women who had been diagnosed with breast cancer at the Department of Medical Oncology, Mersin University, Turkey. Controls were selected by taking age and sex variable into consideration. Genomic DNA from breast cancer patients and control subjects was analyzed by PCR-RFLP. 

There is a tendency among control and statistics theorists to refer to trial and error as one-variable-at-a-time (OVAT). The results are often treated as if only one variable were controlled at a time. The usual trial, however, involves variation in more than one controlled variable and almost always includes uncontrolled variations. The trial-and-error method is fortunately seldom a random process. The starting cycle is usually based on manufacturers specifications or experience with a similar process and/or material. Trial variations on the starting cycle are then made, sequentially or in parallel, until an acceptable cycle is found or until funds and/or time run out. The best cycle found, in terms of one or a combination of product qualities, is then selected. Because no process can be repeated exactly in all cases, good cure cycles include some flexibility, called a process window, based on equipment limitations and/or experience. 

The problem of optimization will first be considered from the viewpoint that complete freedom of choice may be exercised in assuming values for the selected controllable variables. Then the more realistic case where only a limited choice exists will be treated. This will lead finally to a consideration of linear programming for solution of certain classes of restricted optimization problems. 

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