Disturbance sensitivity analysis

For example, let us consider a simple distillation column in which we have specifications on both the distillate and bottoms products (v-ahK and x b lk We go through the design procedure to establish the number of trays and the reflux ratio required to make the separation for a given feed composition. This gives us a base case from which to start. Then we establish what disturbances will affect the system and over what ranges they will vary. The most common disturbance, and the one that most affects the column, is a change in feed composition. Next we propose a partial control structure. By partial we mean we must decide what variables will be held constant. We do not have to decide what manipulated variable is paired with what controlled variable. We must fix as many variables as there are degrees of freedom in the system of equations. 

Next we use a steady-state simulator to calculate the values of all the dependent variables for each feed composition while holding HK and xB LK constant. Finally we look at the steady-state changes in the manipulated variables. If these changes are reasonably small, the proposed control structure may provide good control. We can draw this conclusion from the following argument. 

The output signal from a PI controller is the sum of two terms the error term and the integral of the error term. At the new steady state, the error must be zero. Therefore the integral of the error is directly related to the change in the controller output, which is the change in the manipulated variable. 

This steady-state analysis tells us only where we are going. It does not tell us the path we travel to get there. Hence it provides a necessary but not sufficient condition test for a proposed control structure. The structure may have dynamic problems that make it a poor performer, even though the steady-state analysis looks good. 

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Sensitivity analysis can show which plantwide manipulated inputs (setpoints of BFS control) are necessary. Variability of the streams connecting BFS indicates which disturbances must be rejected. In this way, the designer can identify control objectives of the basic flowsheet structures, and set them as explicit targets for design. 

The control of the distillation columns has been discussed in the Example 13.2. It should be remarked that the range of feed disturbances affecting the separation section was obtained as a result of the sensitivity analysis performed at the previous design level. This way, disturbance rejection can be set as a distinct design specification. 

When a large change is made in Zqb,b (to 0.90), the new steady-state values of the manipulated variables were only slightly different from the base-case values. The makeup flow rates of fresh feed change Fqa increases 10 percent and Fqb decreases 10 percent. Production rates of D2 and B3 stay the same, as do other flow rates and compositions throughout the process. Thus, the steady-state sensitivity analysis suggests that this structure should handle disturbances easily. Dynamic simulations confirm that this control structure works quite well. 

A small change in the composition of the fresh feed of component A from lQA,A = 1 to Zqa.a = 0-99 and Zqa.b = 0.0 1 produces 15 to 20 percent changes in the recycle flow rates Vi and D3. Therefore, the steady-state sensitivity analysis predicts that this control structure will not be able to handle large disturbances. 

D smart s interface shows some integrated error analysis functions. An error analysis can be carried out by comparing more accurate system approximations with less accurate reference approximations. Within this regard it shall be differentiated between error analysis, sensitivity analysis (comparing disturbance of input and output) and uncertainty analysis (when different system properties appear to not be preferable... 

Another ambient method, called AP-DIOS-MS, was also used for the identification of amphetamines and fentanyls in forensic samples. The principle is similar to that of DIOS, but occurs at atmospheric pressure. The use of tandem mass spectrometry (MS/MS) allowed unambiguous identification of the amphetamines and fentanyls (Pihlainen et al. 2005). AP-DIOS-MS/MS was also successfully applied to the identification of authentic compounds from drug seizures. Common diluents and tablet materials did not disturb the analysis and compounds were unequivocally identified. The limits of detection (LODs) for amphetamines and fentanyls with AP-DIOS-MS/ MS were 1-3 pmol, indicating excellent sensitivity of the method (Pihlainen et al. 2005). Protein digest analysis (250 finol of bovine serum albumin) by AP-DIOS-MS was also performed... 

The alternative designs generated for the two test cases (heat exchanger and binary distillation) on basis of this TCA principle prove to be remarkably well aligned with the results of a black-box, input-output controllability analysis using the steady-state disturbance sensitivity approach. 

Closed-loop sensitivity analysis is again used to choose the proper tray temperature as the control point. Runs are made holding the two product purities constant for the two above-mentioned load disturbances. Similar to Figure 9.25, Figure 9.34 shows the deviation of each tray temperature under the ideal control situation when holding two product purities. 

Finally, a temperature controller can be added to provide a method of controlling the conposition of the liquid side draw. This controller can have its temperature sensor on the bottom tray of the main tray section and use the bottoms flow rate as a manipulated variable. Temperature sensitivity analysis can be performed using the steady-state model to ascertain the proper location for the tenperature sensor. Using the bottoms flow rate allows a method for excess heavies to be removed from the system in the event of a disturbance while retaining the target composition of the liquid side draw. The resulting control scheme for the liquid side draw benzene column is shown in Figure 8.11. 

Ozone has been shown to initiate many physiological and biochemical changes in sensitive plant species. Decreases in photosynthesis and increases and decreases in respiration have occurred in response to ozonation. The bioenergetic status of mitochondria and chloroplasts is disturbed by ozone. Decreases in oxidative- and photo- phosphorylation have been reported as have increases in adenosine triphosphate and total adenylate content of plant tissue. The variable physiological responses appear to be related to the stage of symptom development at the time of analysis and to the mode of ozone exposure, viz. in vivo and in vitro. 

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