Apparent dead time

The controller is placed on manual control (i.e. effectively removing it from the control loop) and the response of the measured variable to a small step change in the manipulated variable is recorded as shown in Fig. 7.58a(21). This response is called the process reaction curve. A tangent is drawn to this curve at the point of inflexion (Fig. 7.586). The intercept of this tangent on the abscissa is termed the apparent dead time (rad) of the system. The gradient of the tangent is given by ... 

The most common continuous emulsion polymerization systems require isothermal reaction conditions and provide for conversion control through manipulation of initiator feed rates. Typically, as shown in Figure 1, flow rates of monomer, water, and emulsifier solutions into the first reactor of the series are controlled at levels prescribed by the particular recipe being made and reaction temperature is controlled by changing the temperature of the coolant in the reactor jacket. Manipulation of the initiator feed rate to the reactor is then used to control reaction rate and, subsequently, exit conversion. An aspect of this control strategy which has not been considered in the literature is the complication presented by the apparent dead-time which exists between the point of addition of initiator and the point where conversion is measured. In many systems this dead-time is of the order of several hours, presenting a problem which conventional control systems are incapable of solving. This apparent dead-time often encountered in initiation of polymerization. 

These lags are cumulative as the liquid passes each tray on its way down the column. Thus, a 30-tray column could be approximated by 30 first-order exponential lags in series having approximately the same time constant. The effect of increasing the number of lags in series is to increase the apparent dead time and increase the response curve slope. Thus, the liquid traffic within the distillation process is often approximated by a second-order lag plus dead time (right side of Figure 2.82). 

The maximum reaction rate is the slope at the point of inflection, 8, and the apparent dead time is the abscissa intercept of the maximum reaction rate line, TD. 

Two data points were taken from each response curve in Figure 10.2 when the process variable had reached 10% and 20% of the steady-state response. The results are listed in Table 10.1. These data can be used to calculate the maximum process response rate and apparent dead time for each case. 

The apparent dead time, ADT, is determined by extrapolating the maximum process response rate, MPRR, back to the starting value of the process variable. The maximum process variable response from 51% to 52% took 2.6 min. A straight line extrapolation back another 2.6 min would get back to the starting point of the process variable of 50%. So, 5.5 - 2.6 =... 

The recommended proportional gain is 0.9 times the step size in controller output divided by the maximum response rate of process variable and the apparent dead time (Table 10.2). The CO step size was 10% as listed in the title of Table 10.1. So, the recommended controller gain would be... 

Corripio reviewed the two-point Smith method for characterizing the open-loop process variable response to a step change in controller output by an apparent dead time, ADT, and an apparent first-order time constant, TFO. The two data points on the process variable response curve are taken at... 

The step change is given at t=10 min, it can be seen that the apparent dead time in the response is also approximately 16 minutes. 

Also important is the effect of detector dead time. When ions are detected using a pulse counting (PC) detector, the resultant electronic pulses are approximately 10 ns long. During and after each pulse there is a period of time during which the detector is effectively dead (i.e. it cannot detect any ions). The dead time is made up of the time for each pulse and recovery time for the detector and associated electronics. Typical dead times vary between 20 and 100 ns. If dead time is not taken into account there will be an apparent reduction in the number of pulses at high count rates, which would cause an inaccuracy in the measurement of isotope ratios when abundances differ markedly. However, a correction can be applied as follows ... 

If operated on clean, dry plant air, pneumatic controllers offer good performance and are extremely reliable. In many cases, however, plant air is neither clean nor dry. A poor-quality air supply will cause unreliable performance of pneumatic controllers, pneumatic field measurement devices, and final control elements. The main shortcoming of the pneumatic controller is its lack of flexibility when compared to modem electronic controller designs. Increased range of adjustability, choice of alternative control algorithms, the communication link to the control system, and other features and services provided by the electronic controller make it a superior choice in most of todays applications. Controller performance is also affected by the time delay induced by pneumatic tubing mns. For example, a 100-m run of 6.35-mm ( -in) tubing will typically cause 5 s of apparent process dead time, which will limit the control performance of fast processes such as flows and pressures. 

Pick the best path and check it out, but always keep in mind the other alternatives in case the first one does not work out. In writing down the alternatives, you may get other ideas. Don t waste a lot of time at an apparent dead end before going back to check out other possibilities. 

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