Filter constant

For those purposes, the authors used constant-time version of the sensitivity-enhanced HMBC sequence,79 combined with a two-step low-pass J filter. Constant-time experiments have no coupling structures in the carbon dimension making it easy to identify the centre of signals in... 

The filter-feeders are assumed to filter constant proportions of phytoplankton, bacteria, faeces and POM from the water column, so that losses to filter-feeders are calculated for each component as ... 

Here, y k) represents the estimate of the true signal. Further, / is the filter constant, or, in other words, the filtering bandwidth. By a judicious choice of / , one can remove high-frequency noise components from the signal and retain the relevant signal characteristics. Figure 6.10 shows the frequency response of a first-order filter and how the bandwidth changes as a function of / . 

Figure 6.10. The frequency response of a low-pass filter with different filter constants. (3 = 0.1 (solid), [3 = 0.5 (dash), [3 = 0.9 (dashdot)...

Figure 6.11. The actual test signal, the test signal with noise and its de-noised estimates using three different filter constants.

Low-pass filter constant Vector of regression coefficients Magnitude of step change... 

Fully understanding this accident requires understanding why the error in the roll rate filter constant was introduced in the load tape, why it was not found during the load tape production process and internal review processes, why it was not found during the extensive independent verification and validation effort applied to this software, and why it was not detected during operations at the launch site—in other words, why the safety control structure was ineffective in each of these instances. 

Figure B.4 shows the automated controller flaws leading to the accident. Hie Inertial Measurement System (IMS) process model was incorrect specifically, there was an incorrect roll rate filter constant in the IMS software file (figure B.4) that led to a dysfunctional interaction with the flight control software. ...

The accident report does not explore whether the PCS software could have included sanity checks on the roll rate or vehicle behavior to detect that incorrect roll rates were being provided by the IMS. Even if the PCS did detect it was getting anomalous roll rates, there may not have been any recovery or fail-safe behavior that could have been designed into the system. Without more information about the Centaur control requirements and design, it is not possible to speculate about whether the Inertial Navigation Unit software (the IMS and PCS) might have been designed to be fault tolerant with respect to filter constant errors. 

Ground crew models of the rate check software Apparently, the ground crew was unaware that the checking software used default values for the filter constants. 

Control Algorithm Flaws After the ground launch personnel cutbacks, SSLS management did not create a master surveillance plan to define the tasks of the remaining personnel (the formal insight plan was still in draft). In particular, there were no formal processes established to check the validity of the II filter constants or to monitor attitude rates once the flight tape was loaded into the INU at Cape Canaveral Air Station (CCAS) prior to launch. SSLS launch personnel were provided with no documented requirement or procedures to review the data and no references with which to compare the observed data in order to detect anomalies. 

The CD engineer s immediate supervisor, the lead for the CD section, did not review the signoff report or catch the error. Once the incorrect filter constant went undetected in the signoff report, there were no other formal checks in the process to ensure the II filter rate values used in flight matched the designed filter. 

Process Flaw The internal LMA quality assurance processes did not detect the error in the role rate filter constant software file. 

Dysfunctional Interactions Each component of the FV V process performed its function correctly, but the overall design of the process was flawed. In fact, it was designed in such a way that it was not capable of detecting the error in the role rate filter constant. 

The filter constant Kp depends on fiber diameter, volume fraction of fibers in the filter, and a fiber effectiveness factor (Chen, 1955). 

Here the index j refers to the / th record, t is the associated time, t is the filter constant and the notation = indicates that the yth value of conductivity C is recursively replaced by the right hand side of Eq. (3-16), starting with j=2. For homogeneous conditions, there is no change in C. 

Tungsten lamp at 588 nm. T-Jump 20 —>24 C. Signal jump 2450 mV log nat scale of 25 V unity. Zero-suppression At = 0.32ms. Dual trace record. Filter constant 0.2ms with fast trace (tail of zero-suppression transient at l.h.s. incompletely blanked out) 5ms with consecutive slow trace. Cooling corrected for a ... 

Not all filtering is implemented in the DCS. Most transmitters include filters. Provided the filter constant is not changed then model identification will include the effect of the transmitter filter in the overall dynamics. However, if the filter in the transmitter is changed by a well-intentioned instrument technician unaware of its implications, this can cause degradation in controller performance. 

The PID form implemented usually includes a derivative mode filter such as a first-order filter to eliminate noise, which would be written in the time domain as Eqs. (90), where ep(t) is the filtered error and 0.05 < a < 0.2 is the dimensionless filter constant [7]. 

Figure 12.24 shows the dynamic response of P, PI, and PID controller types to a step-change in the input of the first-order plus dead time (FOPDT) process of Figure 12.22 with parameters Kp = 10 min m , r = 20 min, 0 = 2 min. For the FOPDT example the tuning for the P controller is Kc = 0.595 min m, for the PI controller it is Kc = 10 min m , r/ = 19.7 min, and for the PID controller it is Kp — 0.691 min m , t/ = 25.6 min, tp — 0.725 min. The derivative mode filter was used for the PID controller with a filter constant of a = 0.1. The control loop was simulated numerically for Figure 12.24. It can be seen that the P controller produces a long-term offset, which the PI controller eliminates, but with some overshoot of the set point. The addition of the derivative action for the PID controller eliminates the overshoot and produces the best controller performance.

Another useful digital filter is the double exponential or second-order filter, which offers some advantages for dealing with signal drift the second-order filter is equivalent to two first-order filters in series where the second filter input is the output signal yp k) from the exponential filter in Eq. 17-9. The second filter (with output yp k) and filter constant 7) can be expressed as... 

If so, check the filter constant is sensible Check alarm limits hihi/hi/lo/lolo Check sampling frequency... 

The deconvolntion filter is a simple exponential filter of the form e where y is the deconvolntion filter constant and X is the array (i.e., data file) whose X-axis range is normalized between 0 and 1. This function is multiplied by the Fourier transformed trace, and the data is then reverse Fourier transformed to give the result. 

---