Filtering time constants

Sample times for the microprocessor-based SLCs vaiy from O.I to 0.4 seconds. Low-pass analog electronic filters are installed on the process inputs to stop abasing errors caused by fast changes in the process signal. Input filter time constants are typically in the range From O.I to I s. Microprocessor-based SLCs may be made part of a DCS by using the communication port (RS-488 is common) on the controller or may be operated in a standalone mode independent of the DCS. 

T = Filter time constant provided by the surge, min Q = Maximum throughput, fP/min... 

Sweep time Field offset Modulation amplitude Filter time constant... 

In general, the longer the sweep time the better the sensitivity since the filter time constant parameter can be set longer with consequent improvement in signal-to-noise ratio. In practice, however, sweep times are usually set in accordance with the expected lifetime of the radical species, the stability of the instrument, and the patience of the operator. Decay of the radical or drift of the spectrometer during a scan is clearly undesirable. The sweep time is most commonly set in the range 4-10 min. 

If the filter time constant is r, a datum independent of the preceding one will be got after a time r. The S/N ratio for a time of measurement r is ... 

Note that if the filter time constant x is made very large, the present value of the input (m ) has little effect on the output. But as t is made very small, the output changes directly with the input. 

Filter time constant Integral time (PID controller)... 

Table 8-2 summarizes these rules for minimum-lAE load response for the most common controllers. The process gain and time constant im are obtained from the product of Gt, and Gp in Fig. 8-23. Derivative action is not effective for dead-time-dominant processes. Any secondary lag, sampling interval, or filter time constant should be added to dead time 0. 

The degree of smoothing is determined by the filter coefficient a, with a = 1 being no smoothing and a = 0 being infinite smoothing (no effect of new measurements). The filter coefficient a is related to the filter time constant xF and the sampling interval At by... 

It is usually more convenient to use the filter time (i.e., the time constant of the hrst-order hlter), Xf, to specify the amount of filtering applied to a sensor reading. In this manner, the time constant of the filter can be directly compared to the time constants of the actuator, process, and sensor to determine whether it affects the closed-loop dynamics. The filter factor, /, and the cycle time for applying the filter, Atf, can be used to calculate the filter time constant by the following equation ... 

For most DCSs, sensor readings are updated five or six times per second (i.e., Atf is 0.16 to 0.2 s). For a filter time constant of 3 s, the hlter factor is equal to 0.06 therefore, relatively extensive sensor hltering can result for most sensors using high-frequency updahng by a DCS. 

Filtering. For control variables, when filtering is needed, use a first-order filter to reduce the effects of high-frequency noise. Do not excessively filter measurements unless absolutely necessary. The filter time constant, x, should be much less than feedback dynamics. 

Figure 15.7.1 A low-current transducer for insertion between the working electrode and the current follower (CF) of a potentiostat. Depending on which feedback resistor is chosen in the first stage, the ampUfication factor in this system is 10, 10, or 10. The capacitors in the feedback loops provide some filtering (time constant, 100 fjLs). An inductor-capacitor network was inserted in each power supply connection to minimize noise coupling. [Reprinted with permission from H.-J. Huang, P. He, and L. R. Faulkner, Anal. Chem., 58, 2889 (1986). Copyright 1986, American Chemical Society.]...

After the signal emerges from the lock-in amplifier it still contains a considerable amount of noise. Most of the noise contributions to the signal can be eliminated by passing the signal through a low-pass filter. The filter time constant is a measure of the cutoff frequency of the filter. If accurate linewidth and g-factor... 

Table 4-3. Influence of the filter time constant t on the height and FWHM of a Gaussian peak [14, 15]. >...

In order to more precisely ascertain the degree of difficulty of the multivariable interactions, a 2 X 2 IMC controller [17] is considered next. The controller in this case is the inverse of the full 2x2 model matrix augmented with a diagonal filter block with first-order elements. The filter time constants are chosen to be the same as those used in the equivalent PI designs. The... 

---