Active Structural Control with Stable Fuzzy PID Techniques by Wen Yu & Suresh Thenozhi

Author:Wen Yu & Suresh Thenozhi
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.7)

The velocity and position are obtained by dividing by and , respectively. These are then converted back to the time domain by using the inverse Fourier Transform. However, this method does not have a good low-frequency characteristics, for example, the leakage problem.

3.2 Novel Numerical Integrator

Time integration of the acceleration is a straightforward solution for estimating the velocity and position. However, there are four problems affecting the performance of numerical integrators:

(1) Bias: The behavior of a numerical integrator is similar to a low-pass filter. It amplifies the low-frequency components, reduces the magnitude of high-frequency signals, and causes a phase error. Therefore, any bias in the acceleration measurement results in integration drift. Ambient temperature change is another major offset source. A low resolution analog-to-digital converter (ADC) also adds an offset when the acceleration is slow compared with the quantization level of the analog-to-digital conversion [17].

(2) Noise: There are different sources of noise in the accelerometer, which is generally modeled as white noise. Integrating these noisy signals result a large error in the velocity and position estimations. The root mean square (RMS) of the position estimation error of the acceleration signal with a bias can be approximated as [7]

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