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.