A novel numerical integrator for velocity and position estimation

Abstract

Velocity and position are the most important signals used in industrial controllers such as proportional-integral-derivative controllers. While in some real-time applications like structural control, acceleration measurements are easily accessible via accelerometers. The velocity and position have to be estimated from the measured acceleration. In this paper, offset cancellation and high-pass filtering techniques are combined effectively to solve common problems in numerical integration of acceleration signals in real-time applications. The integration accuracy is improved compared with other numerical integrators. Experimental results on a linear servo actuator and a shake table illustrate the effectiveness of the proposed method.

Sliding mode control of wind-induced vibrations using fuzzy sliding surface and gain adaptation

“…The ground acceleration is then subtracted from the top floor acceleration to get the relative acceleration. The relative velocity and position data are then estimated using the numerical integrator proposed in Thenozhi, Yu, and Garrido (2013). The proposed SMC with fuzzy sliding surface and gain adaptation is compared with the classic proportionalintegral-derivative (PID) controller and standard SMC.…”

Bond Graph Simulation of Error Propagation in Position Estimation of a Hydraulic Cylinder Using Low Cost Accelerometers

“…x(t) = x(0) + t 0 v(0)dt = x(0) + v(0)t + t 0 a(t)dt (2) where v(t) is the velocity, a(t) is the acceleration and x(t) displacement at time t, so, assuming that both initial displacement and velocity are known, the position and velocity of an object would be obtained at any time from the measurement of the acceleration. This strategy of indirect measurement of displacement has been exploited in several fields of engineering.…”

“…The estimation of velocity and position is also necessary for the proportional-integral-derivative (PID) control of mechanical devices [2]. The existence of noise in both low and high frequencies would cause a drift in the velocity and position reconstruction process.…”

“…An usual strategy for noise suppression is the use of some filters incorporated in the transfer function for the reconstruction of displacement from the acceleration in the frequency domain [21][22][23][24]. Thenozhi [2] proposed a method for the cancellation of decentering (Bias) by adjusting the baseline of the acceleration data. Boore [7] proposed a method of suppression of Analog to Digital Conversion (ADC) error by dithering technique (adding a small random noise signal).…”

“…where: is the cross correlation coeficient, CCC [x] defined for the displacement measurement x ( ) is the covariance between ( ) and ( ) is the standard deviation of Thus, a gain (K), obtained from a proper calibration, is applied to the resulting lecture in order to obtain the acceleration. Finally, the velocity and displacements are obtained from single and double integration, as described in Equations 1and (2). The simulation using the bond graph technique is carried out using the simulation software 20-sim © version 4.2.7 developed by the company Controllab Products B.V. (Enschede, the Netherlands).…”