Drift-free integrators

Abstract

Bias errors introduced by systems designed to measure low-frequency transients negate zero-mean assumptions on the measurement noise. On-line signal processing methods that require accurate low-frequency information can be adversely affected by bias errors. On-line integration of dynamic signals is a classical example of a process that is unstable in the presence of bias errors. Accurately integrated quantities (like velocity and displacement), from easily measured quantities (like acceleration), can inform control systems and reduce on-line computational burdens. This article introduces a feedback stabilization method for a hybrid digital-analog integrator. The analytical performance of this integrator is compared to a filtered analog integrator in the time and frequency domains. For wide-band random signals, the analog circuit performs well with respect to linearity and hysteresis, but does less well for long-period signals. A stabilized hybrid analog-digital integrator has exceptional accuracy when integrating long-period signals, but produces phase and bias errors when integrating wide-band signals. The integrators examined in this study are unconditionally stable and robust to bias on the input, internal bias currents in the operational amplifiers, and finite slew rates of the components.

Simultaneous parameter and state estimation of shear buildings

“…Eq. (32) indicates that signals χ, Φ c and Φ k are filtered by H 3 , H 2 and H 1 , respectively. These filters are designed to encompass the frequency band covered by the seismically excited structures in order to keep all relevant information, and to attenuate high-frequency measurement noise.…”

“…Finally, references [29][30][31] propose Sequential Monte Carlo (SMC) methods that are robust against measurement noise, have gained popularity due to their superiority over the EKF, can simultaneously estimate the state and parameters of buildings, and require a discrete-time model of this system; with the SMC methods, the state and parameter identification consist in the computation of a non-Gaussian probability density function pðx k ; θjD k Þ, where x k is the state, θ contains the parameters of the structure, and D k is a set that contains the measurements available up to time instant k. It is worth mentioning that most of the references consider the presence of measurement noise, but none of them take into account offsets in the acceleration measurements. It is well known that accelerometers usually have a constant voltage disturbance at their output [32]. Therefore, the velocity and displacement of the structure cannot be obtained by simple numerical integration of the acceleration measurements since the integration of biased signals produces a drifting output.…”

Damage Diagnosis under Environmental and Operational Variations Using Improved Restoring Force Method

“…The reason for this step is that, for large-scale structures in real applications, displacement is very difficult to measure for fixed reference. A great number of digital processing techniques (Bardella et al, 2003;Gavin et al, 1998;Smyth et al, 2007) have been proposed to reconstruct velocity and displacement from measured acceleration. Among them, the Finite element method based Finite Impulse Response (FFIR) filter, presented by Hong et al (2010) was chosen to perform velocity and displacement integration for the following research.…”

Identification of shear buildings using an instrumental variable method and linear integral filters

“…This happens because it is not possible to measure the absolute displacements and velocities in a structure since it is difficult to establish a static reference. On the other hand, acceleration measurements exhibits offsets [1]; as a consequence, the velocity and displacement of the structure cannot be obtained by simple numerical integration of the acceleration measurements since the integration of biased signals produces a drifting output.…”