Overall system response

Higher-Order Lags If a process is described by a series of n first-order lags, the overall system response becomes proportionally slower with each lag added. The special case of a series of n first-order lags with equal time constants has a transfer function given by ... 

Instrument measurement response can often be important in the overall system response. The thermal response of a simple thermometer bulb, immersed in fluid, as shown in Fig. 2.6, is the result of a simple heat balance in which... 

Dynamic interaction between primary disease neurobiology and adaptations — measuring overall system response ... 

What elfect(s) do uncertainties in the component models give to overall system response uncertainty ... 

The time resolution of the electronics in a single photon counting system can be better than 50 ps. A problem arises because of the inherent dispersion in electron transit times in the photomultiplier used to detect fluorescence, which are typically 0.1—0.5 ns. Although this does not preclude measurements of sub-nanosecond lifetimes, the lifetimes must be deconvoluted from the decay profile by mathematical methods [50, 51]. The effects of the laser pulsewidth and the instrument resolution combine to give an overall system response, L(f). This can be determined experimentally by observing the profile of scattered light from the excitation source. If the true fluorescence profile is given by F(f) then the... 

Overall system response in time domain can then be evaluated from the system response in Laplace domain for first and zero order kinetics ... 

The Relap 5/mod 3 input deck developed by Ansaldo w-as sufficient to predict the overall system response, to reproduce reasonably the timing of the transients and the interactions between the safety systems. 

Figure 1.64. Normalized fast component of the photocurrent in oriented Omham trans- C )x excited with 25 ps lasser pulses (532 nm) at room temperature. The energy of the incident light pulses with polarization perpendicular to the stretch direction is 0.95 / J at a sample area of 200 /xm 300 /xm. The integral under the peak corresponds to 1.5 x 10 electronic charges (17o = 100 V). The solid line represents the best fit to the curve obtained by convoluting the photoconductivity response with the overall system response (assumed to be Gaussian). (Reprinted with permission from ref. 149)...

To describe the decay of the real-time spectra, one might think of using the simple energy-level model described in Sect. 2.2.2. However, the experimental data (ignoring the fast oscillation) do not at all fit to a convolution of the overall system response with a single exponential decay. Therefore, the extended energy-level model developed in Sect. 2.2.2 was applied. The real-time spectra were fitted with the convolution function ... 

To take account of the temporal width of the laser pulses the transient spectra are compared with the convolution function, where t) is the overall system response of our measuring system, which is represented by the cross correlation of the laser pulses. 

Fig. 4.9. Real-time spectra of Nas D excited at three different excitation energies Epump excited with laser pulses of 30 fs (taken from [397]). The shaded curve is the overall system response i t). The lines are least-squares fits calculated within the extended energy level model...

In the extended model the transient intensity of the detected ions is proportional to the convolution of the population density n[t) of excited clusters (Types I and II) with the overall system response i[t) to the laser pulses ... 

The temporal evolution of the ion yield provides information on the vibrational dynamics in the neutral ground state. Figure 5.12 shows the time-resolved yield of AgJ g 9 compared to that of Aga. The curves for Ags and Ag9 exhibit a pronounced peak at = 0 fs and a gradual descent to a constant value for longer delay times At. The decay time of this decent is 667 fs for Ag9 and 283 fs for Ags. The data were obtained by deconvoluting the realtime spectra with the overall system response of the measuring system. The FWHM of the system response was estimated by a least-squares fit procedure to be close to 200 fs (see Fig. 5.13). The real-time response of the heptamer is rather weak the decay time constant is close to 500 fs. As shown in Sect. 5.1,... 

Feedforward control can be used to combat the control problems associated with processes containing significant dead time. This is achieved by measuring process disturbances and compensating for them before they affect the controlled variables. Ideal feedforward control is realized if pre-emptive control action is taken to cancel out the effect of measured disturbances completely before they enter the process. Sometimes the ideal feedforward controller is not realizable, because disturbances affect the system more quickly than the manipulated variable. However, feedforward control can still be useful in these scenarios when teamed with feedback control, because the feedforward control reduces the duty on the master controller and improves the overall system response. Clearly, no action can be taken if the disturbances are not sensed or measured. 

Even if a is very large, if s t) is a slowly varying function, the system responds slowly. To follow this slow response numerically is problematic since the stability of the method depends only on a and has nothing to do with s(t). A very small time step might be required, even though the overall system response is a slowly varying function. This is one example of a phenomenon called stiffness. 

---