Response representations

There are two response representations which can be tested with a Box-Cox... 

FIGURE 3 Impulse-response representation of the response of the climate system to a... 

Table 2. Potentials, derivatives and differentials in the softness (response) representation...

The use of a finite impulse response representation was proposed in [17] and used in [18] in an optimization framework for dynamic operability assessment. In this formulation, the (i,j) element of the matrix Q is represented as... 

Before the data can be visualised, ie displayed in a two or three-dimensional representation, the ultrasonic responses from the interior of the test-piece must be reconstructed from the raw ultrasonic data. The reconstruction process projects ultrasonic indications into 3D space. As well as reconstructing the entire ultrasonic data set within an acquisition file, it is possible to define an arbitrary sub-volume of the test object over which reconstruction will take place. The image resolution may also be defined by the user. Clearly, larger volumes or greater resolution will increase the computation time for both the reconstruction and visualisation processes. 

Leforestier C and Museth K 1998 Response to Comment on On the direct complex scaling of matrix elements expressed in a discrete variable representation application to molecular resonances J. Chem. Phys. 109 1204... 

The remaining combinations vanish for symmetry reasons [the operator transforms according to B (A") hreducible representation]. The nonvanishing of the off-diagonal matrix element fl+ is responsible for the coupling of the adiabatic electronic states. 

Figure 7.9 shows a schematic representation of this effect, in which the ratio of the two isotopes changes with time. To obtain an accurate estimate of the ratio of ion abundances, it is better if the relative ion yields decrease linearly (Figure 7.9) which can be achieved by adjusting the filament temperature continuously to obtain the desired linear response. An almost constant response for the isotope ratio can be obtained by slow evaporation of the sample, viz., by keeping the filament temperature as low as is consistent with sufficient sensitivity of detection (Figure 7.9). 

We commented above that the elastic and viscous effects are out of phase with each other by some angle 5 in a viscoelastic material. Since both vary periodically with the same frequency, stress and strain oscillate with t, as shown in Fig. 3.14a. The phase angle 5 measures the lag between the two waves. Another representation of this situation is shown in Fig. 3.14b, where stress and strain are represented by arrows of different lengths separated by an angle 5. Projections of either one onto the other can be expressed in terms of the sine and cosine of the phase angle. The bold arrows in Fig. 3.14b are the components of 7 parallel and perpendicular to a. Thus we can say that 7 cos 5 is the strain component in phase with the stress and 7 sin 6 is the component out of phase with the stress. We have previously observed that the elastic response is in phase with the stress and the viscous response is out of phase. Hence the ratio of... 

Optimization should be viewed as a tool to aid in decision making. Its purpose is to aid in the selection of better values for the decisions that can be made by a person in solving a problem. To formulate an optimization problem, one must resolve three issues. First, one must have a representation of the artifact that can be used to determine how the artifac t performs in response to the decisions one makes. This representation may be a mathematical model or the artifact itself. Second, one must have a way to evaluate the performance—an objective function—which is used to compare alternative solutions. Third, one must have a method to search for the improvement. This section concentrates on the third issue, the methods one might use. The first two items are difficult ones, but discussing them at length is outside the scope of this sec tion. 

This representation is easily understandable by those knowledgeable about the process technology and is a convenient mechanism for conveying the process requirements to the control engineers responsible for implementing the batch logic. 

It is sincerely hoped that the information presented in this document will lead to an even more impressive record for the entire industry however, the American Institute of Chemical Engineers, its consultants, CCPS Subcommittee members, their employers, their employers officers and directors, and Arthur D. Little, Inc., disclaim making or giving any warranties or representations, express or implied, including with respect to fitness, intended purpose, use or merchantability and/or correctness or accuracy of the content of the information presented in this document. As between (1) American Institute of Chemical Engineers, its consultants, CCPS Subcommittee members, their employers, their employers officers and directors, and Arthur D. Little, Inc., and (2) the user of this document, the user accepts any legal liability or responsibility whatsoever for the consequence of its use or misuse. 

In this case, the shear stress is linear in the shear strain. While more physically reasonable, this is not likely to provide a satisfactory representation for the large deformation shear response of many materials either, since most materials may be expected to stiffen with deformation. Note that the hypoelastic equation of grade zero (5.117) is not invariant to the choice of indifferent stress rate, the predicted response for simple shear depending on the choice which is made. 

In fact, as Atluri [17] has pointed out, the hypoelastic equation of grade zero has inadequate latitude to represent realistic nonlinear response of various materials in large deformations, and it is necessary to use a hypoelastic equation of at least grade one to do so. If the grade is one, then, continuing to use Jaumann s stress rate and nondimensionalizing the stress as before, the isotropic representation (A.92) may be used in (5.112) with d = A and s = B to obtain... 

Fig. 5.2 Graphical representation of stable and unstable time responses.

SIMULINK The Control System Toolbox does not possess a ramp eommand, but the ramp response of a first-order system (Example 3.6, Figure 3.15) ean be obtained using SIMULINK, whieh is an easy to use Graphieal User Interfaee (GUI). SIMULINK allows a bloek diagram representation of a eontrol system to be eonstrueted and real-time simulations performed. 

This tutorial looks at how MATLAB commands are used to convert transfer functions into state-space vector matrix representation, and back again. The discrete-time response of a multivariable system is undertaken. Also the controllability and observability of multivariable systems is considered, together with pole placement design techniques for both controllers and observers. The problems in Chapter 8 are used as design examples. 

The response of this model to creep, relaxation and recovery situations is the sum of the effects described for the previous two models and is illustrated in Fig. 2.39. It can be seen that although the exponential responses predicted in these models are not a true representation of the complex viscoelastic response of polymeric materials, the overall picture is, for many purposes, an acceptable approximation to the actual behaviour. As more and more elements are added to the model then the simulation becomes better but the mathematics become complex. 

The electrical Itw-pressure impactor (ELPl) has been developed, using the Berner-type multijet low-pressure impactor stages. The cut sizes of the seven channel system range from 0.030 to 1.0 pm. Real-time measurements can be achieved due to the instrument s fast time response. The schematic representation of the impactor construction is shown in Fig 13.44. 

The one-dimensional representation described above is too simple to describe the behavior of a detonation in response to boundary conditions. Denisov et al. 

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