Filters accelerometers

Assume that the accelerometer has the ideal response shown in Figure 4-223, with a measurement range of 2 g (32.2 ft/s ). We want to measure 1 g, but the ambient vibration level is +3 g. In this case, the accelerometer s indications are shaved and the mean value obtained is not 1 g but 0.5 g. The maximum acceleration due to vibrations which are not filtered mechanically, plus the... 

Most silicon accelerometers are based on a micromachined variable capacitance element (g-cell) that is converted to a voltage using a C-V converter and then amplified, filtered, and buffered to provide an analog output as shown in Fig. 7.1.4. To date, open-loop implementations for capacitive read-out circuits are more widely employed than closed-loop systems, primarily as a result of the stability of such systems [16]. Interface electronics for micromachined sensors depend not only upon the transduction technique (input specification) and the product requirements (output specification) but also on the packaging approach, as parasit-ics are introduced when a multiple-die packaging technique is used. 

When subjected to such high-g, high-frequency shocks the output of the accelerometer would be driven to full scale (or saturated) if the 400 Hz bandpass filter was not present. In theory the 400 Hz bandpass filter would suppress these signals so that they would contribute little to the output signal. But, as will be discussed, such ideal accelerometers are not easily produced. 

In the analysis for this study a fifteen-dimensional state-vector was considered besides the nine states necessary to describe a complete three-dimensional inertial positioning system three additional gyro drifts and three accelerometer biases were introduced. For the filter based on zero-velocities as measurements a numerical observability analysis was performed, using the 5in(/ /ar-Vh/ue-Decomposifionapproach, see, e.g., Kothe (1987), Bolcsvolgyi-Ban and Schroder (1990). It turned out that each state (with the exception of the well-known singularity of the longitude) is observable. 

First some results about the determination of the initial values using the Kalman-Filter approach are presented. Besides the nine states necessary to describe the error behaviour of a complete three-dimensional solution, three gyro drift and three accelerometer bias parameters are introduced, modelling the main sensor error in... 

A different way to manipulate the heterogeneous data of the electronic camera and of the accelerometer in a joint model is possible, if we consider the horizontal movements of the abutment as a dynamic process. Then we can estimate the state of the system for each moment within the measuring time from all measurements in advance by using a Kalman Filter (Schrick 1977). In addition to the measurements for a Kalman Filter we need a priori knowledge of the dynamic system, start values and characteristic quantities of the system error and measuring error. I will give only a short summary of the nesessary algorithm here, whereby the dynamic system is not forced. 

We get the filter equations to estimate the movements, the velocities, and the accelerations of the abutment during the brake tests, from measurements of the electronic camera and the accelerometer, in a joint model... 

Alarms are provided as part of the "human engineered" control complex (see CESSAR-DC, Chapter 18) and are included in the plant computer annunciator systems. After passing through the alarm unit, the amplified accelerometer signals are multiplexed, filtered, digitized, and transmitted to a computer for further analyses. The computer maintains data storage, performs comparisons, develops trends, and performs analyses to enhance the signal characteristics. 

Among several applications in space and machine tools, a nice application has been developed using this concept the active damping of a ski [19]. The first flexural vibration mode of the ski occurring at 14 Hz is actively damped (the initial quality factor of 100 is decreased down to 10) through a piezo actuator and an accelerometer (Fig. 6.26a). A special filter is necessary to avoid instabilities coming from the high order vibration modes. The piezo actuator is mounted in front of the shoe and the accelerometer is mounted at the top of the ski. This implementation is an important step to the adaptronic application, in which it is foreseen to adapt the quality factor of the ski as a function of the snow hardness. 

The block diagram depicted on Fig. 6.29 has been realised with analogue boards the first step corresponds to the tests of the filtering cells in an open loop. As a first step, one checks that the pilot and the measurement accelerometer give a correct response under an excitation of the shaker. As a second step, one checks that the filtering cell Fi p) is correct. As a third step, one also checks that the filtering cell Hi p) allows isolation of the acceleration loop from a position order. 

Apart from an adjustable rauge, current accelerometers also provide for configurable offsets, allowing calibration of the sensor at run-lime whereby the (X 1 ) offset values are kept in the sensor. An integrated low-pass filter can furthermore be controlled via the bandwidth parameter, going from 1 kHz down to 8 Hz for the BMA150. 

Here b means the IMU body frame e denotes the ECEF frame i indicates the inertial frame Cl is the Direction Cosine Matrix (DCM) from body frame to ECEF frame, ft is the skew-symmetric matrix for angular rate measurements is the vector of acceleration measurements from the accelerometers. F is the system matrix applied in the ECEF frame is the distance from the earth geometric center to the earth surface g is the local gravity is the position of the IMU in ECEF. The noise vector w contains, in the indicated order, gyroscope bias, acceleration bias, acceleration noise, angular rate noise, receiver clock error and receiver clock rate noise. These noise terms are described by the error covariance matrix Q in the Kalman filter routine ... 

The dynamic tests were carried out in Jrme 2007, using a 16-channel data acquisition system and WR 731A piezoelectric accelerometers (10 V/g sensitivity and 0.5 g peak acceleration). Each accelerometer was coimected with a short cable (1 m) to a WR P31 power unit/amplifier, providing the constant current needed to power the accelerometer s internal amplifier, signal amplification, and selective filtering. 

Few weeks after the execution of the second AVT, a simple dynamic monitoring system was installed in the tower. The system is composed by a 4-channel data acquisition system (24-bit resolution, 102 dB dynamic range, and anti-aliasing filters) with three piezoelectric accelerometers (WR model 731A, 10 V/g sensitivity, and 0.50 g peak). The response of the tower is measured in three points, belonging to the cross section at the crowning level of the tower. Furthermore, a temperature sensor is installed on the S-W front, measuring the outdoor temperature. 

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