Lag in the system

Liquid flows through a system of two tanks arranged in series, as shown below. The level control of tank 2 is based on the regulation of the inlet flow to the tank 1. This tank represents a considerable lag in the system. The aim of the controller is to maintain a constant level in tank 2, despite disturbances which occur in the flow F3. 

Lag in the system 509 Langmuir-Hinshelwood kinetics 321 Laplace transformation 80, 536 Latent heat of vapourisation 517 Least squares 112 Level control 509... 

Basically, the equipment is a standard Wicke-Kallenbach cell, except that provision is made for introducing a pulse of the trace component on one face of the porous sample, i.e. z=0. However the design does have to take into consideration the need to calibrate the detection unit for lags in the system.This does not seem to have been carried out in other work reported which used this technique. Failure to make this correction can lead to significant errors in the values of the diffusion coefficient which are extracted from the experimental data e.g. see Fig.l. 

Unless the dynamics of the system are well known, and the lags in the system are acceptable, sampling from the top of the next column should be avoided. The sample flashpot technique (Fig. 18.106) can be used to exclude the heavies from the sample before it enters the sample conditioning system. 

Here, A is a constant which characterizes a lag in the system, and p is a small positive parameter. 

Oscillatory instability is the most important form and occurs because of feed-back effects due to time lags in the system. If the inlet flow is oscillated at a given frequency, all components of pressure drop may be additive, but as the frequency increases, lag occurs In the various components. Oscillatory instabilities can be present even in the absence of excursive instability and can occur between parallel tubes forming part of a flow circuit. System instabiiity of the completed circuit can aiso occur. 

On an energy-content basis, the system is balanced at all times i.e., there is sufficient energy in the gas (or solids) present in the system at any time to complete the work on all the solids (or gas) present at the same time. This is significant in that there is no lag in response to control changes or in starting up and shutting down the system no partially processed residual solids or gas need be retained between runs. 

On the Bode plot, the comer frequencies are, in increasing order, l/xp, Zq, and p0. The frequency asymptotes meeting at co = l/xp and p0 are those of a first-order lag. The frequency asymptotes meeting at co = z0 are those of a first-order lead. The largest phase lag of the system is -90° at very high frequencies. The system is always stable as displayed by the root locus plot. 

A disadvantage of 1ST measurements is that the experiments take time (days to weeks). Also, several experiments at different temperatures are necessary to get information with respect to the kinetics of the exothermic decomposition. Finally, it may take several hours to reach equilibrium after inserting a sample due to the time-lag of the system. Thus the recorded heat effect may be inaccurate. This is a particular disadvantage in the case of rapid reactions. 

Our examples above demonstrated this quantitatively. For this reason, it is vital to design a reactor control system with very fast measurement dynamics and very fast heat-removal dynamics. If the thermal lags in the temperature sensor and in the cooling jacket are not small, it may not be possible to stabilize the reactor with feedback control. 

It should be noted that regulatory conformational changes need not be rapid. In fact, in some cases these transitions are extremely slow (see Table V), and an observable time lag in the enzyme response may occur. The molecular basis for regulation is not fundamentally different for slow and rapid conformational transitions, but slowly responding systems are often termed hysteretic.S7... 

A scan speed compensation calibration compensates for lag time in the system when the instrument is scanned rapidly. If only a scan speed compensation is performed (without a scanning calibration having been performed), the scan speed compensation is treated as a scanning calibration and the instrument is calibrated correctly only for scanning acquisitions over the same mass range and at the same scan speed as those used for the calibration. The scan speed recommended for the scan speed compensation is 1000 amu/s. 

If a system is disturbed by periodical variation of an external parameter such as temperature (92), pressure, concentration of a reactant (41,48,65), or the absolute configuration of a probe molecule (54,59), then all the species in the system that are affected by this parameter will also change periodically at the same frequency as the stimulation, or harmonics thereof (91). Figure 24 shows schematically the relationship between stimulation and response. A phase lag <)) between stimulation and response occurs if the time constant of the process giving rise to some signal is of the order of the time constant Inim of the excitation. The shape of the response may be different from the one of the stimulation if the system response is non-linear. At the beginning of the modulation, the system relaxes to a new quasi-stationary state, about which it oscillates at frequency cu, as depicted in Fig. 24. In this quasi-stationary state, the absorbance variations A(v, t) are followed by measuring spectra... 

For purposes of discussion, ignition delay is frequently divided into physical delay and chemical delay (11,41,44)> although it is recognized that the two cannot be separated. Physical delay includes time lags in the injection system and the time required for heat and mass transfer processes to form a combustible mixture of fuel vapor and air. 

The expectation value of the property A at the space-time point (r, t) depends in general on the perturbing force F at all earlier times t — t and at all other points r in the system. This dependence springs from the fact that it takes the system a certain time to respond to the perturbation that is, there can be a time lag between the imposition of the perturbation and the response of the system. The spatial dependence arises from the fact that if a force is applied at one point of the system it will induce certain properties at this point which will perturb other parts of the system. For example, when a molecule is excited by a weak field its dipole moment may change, thereby changing the electrical polarization at other points in the system. Another simple example of these nonlocal changes is that of a neutron which when introduced into a system produces a density fluctuation. This density fluctuation propagates to other points in the medium in the form of sound waves. 

Temperature control is normally carried out using thermocouples in a stainless steel pocket. The type of thermocouple used is either a platinum resistance detector (RTD) or a thermocouple using two dissimilar metals that produce a voltage (EMF). The indicators for these thermocouples must match the probe type and grade. The positioning of the probes is very important as well as any lag (delay) in the system. The output from the probe is connected to the indicator and/or controllers. Most indicators have at least a set point with an on/off output. The more advanced units will allow anticipated switching, more than one set point, temperature ramping between temperatures, time, and hold facilities. Thermocouple break and over-temperature alarm outputs are also commonly provided features. 

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