Second-integral control

If the measured variable decreases from its initial value of 50 gpm to a new value of 45 gpm, as seen in Figure 21, a positive error of 5% is produced and applied to the input of the integral controller. The controller has a constant of 0.1 seconds 1, so the controller output rate of change is 0.5% per second. 

The eantilever oseillation amplitude is kept constant within a few Angstroms by a digital proportional/integral feedback controller. A second feedback controller was used to keep the distance between tip and sample surfaee constant via keeping the frequeney shift of the cantilever oscillation at a preset value. 

Example 11.4 demonstrates very clearly how the simple first-order dynamic behavior of a tank can change to that of a second-order when a proportional-integral controller is added to the process. Also, it indicates that the control parameters Kc and r can have a very profound effect on the dynamic behavior of the system, which can range from an underdamped to an overdamped response. 

The reader can verify easily that for the regulator problem the integral control action produces a second-order closed-loop response and leads again to zero offset. 

To decide whether Xt drifts to lower or to higher wavelengths, one must either modulate the laser frequency or use a digital servo control, which shifts the laser frequency in small steps. A comparator compares whether the intensity has increased or decreased by the last step and activates accordingly a switch determining the direction of the next step. Since the drift of the reference FPI is slow, the second servo control can also be slow, and the fluorescence intensity can be integrated. This allows the laser to be stabilized for a whole day, even onto faint molecular lines where the detected fluorescence intensity is less than 100 photons per second [5.70]. 

The first and second parts of this book are therefore about the basic technologies -high-integrity control systems and pressure vessels - that all (or almost all) hazardous industrial plants rely on. 

Having established the ease with which a single-capacity process may be controlled, the complications involved in adding a second capacity may be evaluated. Since each capacity contributes a phase lag approaching 90 , the total phase lag in the loop can only approach 180 . As a result, the loop can oscillate only at zero period. This is exactly like a first-order lag with an integrating controller. 

The obvious solution is to add a second integral mode. But double integral by itself is unstable, in that it produces 180 phase lag at all periods. But if the first integral, i.e., the volume error, is acted upon by a proportional-plus-reset controller, the system can be stable. Such an arrangement is functionally described in Fig. 6.13. 

The exclusion of xmimportant component functions has several advantages. Firstly, since the error of the Monte Carlo integration controls the accuracy of the RS-HDMR expansion, it is possible that the inclusion of uimecessary terms can increase the integration error, reducing the accuracy of the HDMR metamodel. Secondly, if the metamodel were to be used for subsequent analysis, the lower number of terms aids its computational efficiency. The exclusion of component functions also provides an immediate level of complexity reduction, before parameter importance ranking has been performed. 

A second approach to coulometry is to use a constant current in place of a constant potential (Figure 11.23). Controlled-current coulometry, also known as amperostatic coulometry or coulometric titrimetry, has two advantages over controlled-potential coulometry. First, using a constant current makes for a more rapid analysis since the current does not decrease over time. Thus, a typical analysis time for controlled-current coulometry is less than 10 min, as opposed to approximately 30-60 min for controlled-potential coulometry. Second, with a constant current the total charge is simply the product of current and time (equation 11.24). A method for integrating the current-time curve, therefore, is not necessary. 

The main power source is a 2,200 kW rated motor, which drives two high-speed pinions through integral gears. The first stage of the compressor operates at 17,900 rpm, while the second and third stages operate at 21,800 rpm. The unit is controlled by a local control system, but operators can also monitor the operating parameters from the plant control room. 

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