Computed variable

A host of gadgets and software are available to perform a variety of computations and logical operations with control signals. For example, adders, multipliers, dividers, low selectors, high selectors, high limiters, low limiters, and square-root extractors can all be implemented in both analog and computer systems. They are widely used in ratio control, in computed variable control, in feedforward control, and in override control. These will be discussed in the next chapter. 

Thirty years ago these computed variables were calculated using pneumatic devices. Today they are much more easily done in the digital control computer. Much more complex types of computed variables can now be calculated. Several variables of a process can be measured and all the other variables can be calculated from a rigorous model of the process. For example, the nearness to flooding in distillation columns can be calculated from heat input, feed flow rate, and... 

Computed variable control, (a) Maas flow rate (b) heat input (c) composition (piessure-compcnBated temperature). 

The initial profile is computed by the Saeman model (Eq. (1)). The inlet flow rate and/or the operating parameters can be modified during the resolution of the dynamic equation. Spurting et al. [7] give a similar equation, but the computed variable is not the local height of the bed, but the maximum half angle subtended by the bed at the cylinder axis. 

Florida Crushed Stone in Brookville, Florida, was feeding TDF into the preheater, but had to discontinue use because of plugging of the preheater (most likely due to oil condensate from the incomplete combustion of the tire chips). The company is in the process of installing a whole tire feeder with weight-belt, computer, variable rate belt, and triple gate chute to feed tires into the kiln.10... 

The time variable t, the initial time to, the values of the input u(t) for / e [to. t[, and the initial state xo = x(to) are assumed to be known without noticeable experimental errors. On the other hand, the parameters are to be considered constants, whose value are unknown (or, at least, not exactly known) a priori. The parameters can be changed in a suitable range in order to analyze the model sensitivity, i.e., its capability to describe different scenarios, or can be adjusted, in order to improve the correspondence between the experimental data and the computed variables in chemical kinetics, this is usually the case of rate constants and of activation energies. 

One of these methods is NAMFIS (NMR Analysis of Molecular Flexibility in Solution) [62], which considers all candidate conformations that are theoretically accessible to the molecule and optimizes their mole fractions until their computed variables match the experimental NMR data (usually NOEs and J couplings, in the future potentially also residual dipolar couplings). NAMFIS has been used to analyze the solution structures of several tubulin-binding drugs, such as PTX [63], epothilones [26], discodermolide [60] or laulimalide [64],... 

Click OK. The correspondence between the computer variables and the reactor variables is ... 

Common chemometric tools may be applied to deal with similarity matrices. Particularly, partial least squares (PLS) [73,74] stands as an ideal technique for obtaining a generalized regression for modeling the association between the matrices X (descriptors) and Y (responses). In computational chemistry, its main use is to model the relationship between computed variables, which together characterize the structural variation of a set of N compounds and any property of interest measured on those N substances [75-77]. This variation of the molecular skeleton is condensed into the matrix X, whereas the analyzed properties are recorded into Y. In PLS, the matrix X is commonly built up from nonindependent data, as it usually has more columns than rows hence it is not called the independent matrix, but predictor or descriptor matrix. A good review, as well as its practical application in QSAR, is found in Ref. 78 and a detailed tutorial in Ref. 79. 

A feedforward controller can be used to transport information already available somewhere to other place in the flowsheet. Figure 3.21 displays a typical implementation. Flere the controller sets a downstream sampled variable at a given value based on an upstream computed variable. 

Computed variable control, (a) Mass flow rate, (b) Heat input, (c) Composition (pressure-compensated temperature). 

Modem fast-acting micro-computers are capable of storing and manipulating a reasonably detailed mathematical model of the motor. It is therefore possible to compute the model in parallel with the actual motor and compare the computed variables with those measured at the output of the inverter. An algorithm can be developed that will adjust the rectifier and inverter set-points so that the actual motor responds more like the mathematical model. An advantage of such a scheme is the... 

Second, we raised the speder of indifferent situations. These occur when either the number or type of knowns does not allow computation of all unknowns. Most troublesome are those situations in which the problem is initially well-posed but during the computation, variables that were initially independent become coupled. When such coupling occurs, the behavior of trial-and-error search algorithms may be erratic or erroneous, so we should not accept results as reliable merely because they were generated on a computer using a sophisticated algorithm. 

Note, one may also use the Design-SpecA ary tool to achieve the same task as a Calculator block. Both can be effective, but the Calculator block is more direct and should be faster because the Design-Spec tool uses a guess-and-check method to compute variables that are otherwise trivial to compute directly. 

Aspen HYSYS screen captures (modified for space) for advanced features, (a) Setting up spreadsheet variabies (b) Computing variables for export in a spreadsheet (c) Adjusting the recycie biocks for simuitaneous mode (d) Absorber column profiles (e) Setting up case studies (f) interpreting the results of case studies. 

The means and covariance matrices of the computed variables characterize statistically the propagation of errors in the (linear) system. Generally, if some (vector) variable x is measured and some other y is a (deterministic) function of x, committing an error in x this error is propagated among the components of y. In the present case, with measured x = x the unmeasured y is determined only if x obeys the solvability condition we thus can examine the (observable) components of y only as functions of the adjusted (reconciled) values x. 

Where s,- is the estimated statistical uncertainty on the computed variable while is the associated experimental measurement (either ln(F "), AH ap or / /,). F is considered as a function of four parameters to optimize, namely the interaction energies of carbon and nitrogen atoms Sc, En and their molecular diameters (Jc, CTn which represent the parameters of the LJ potential (see equation (1)). This methodology leads to the results listed in Table 1. 

The remain parameters (ai, a2,. .., ans) are calculated as a functions of its influences in the output result. If one is computing variable 1 influence, the signs of the first column are entirely used, as well as for variables 2,3 and 4 the columns number 2,3 and 4 are fully adopted. Equation (3) and (4) elucidate it. 

Applications processed on this platform are cychcal during each cycle, the inputs are read, the calculations are made, taking into account these inputs and, of course, the internal states of the computer (variables), and determining the outputs. Finally, the outputs are applied. The inputs and outputs can be of several kinds ... 

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