Mitigating noise-induced tracking loss in PI controlled systems with saturating actuators

This technical note addresses a problem of mitigating noise induced tracking loss in a closed-loop system with linear plant, PI controller, saturating actuator, and anti-windup. For such systems, it was recently discovered that with the presence of zero mean measurement noise the mean of the output process at steady-state exhibits a level of tracking error. This phenomenon was termed as 'Noise-Induced Tracking Error (NITE).' Low pass filtering the measurement noise may be a solution to mitigate NITE, however, adding a filter affects the stability and also the transient tracking performance. This paper proposes to use an observer as a filter to decouple filter dynamics and the system stability, avoid performance loss in transient tracking, and most importantly, eliminate the noise induced tracking error. To accomplish these, a standard is necessary for observer gain selection, which is provided based on Quasilinear Control Theory. Finally, proof of the separation principle for PI-controlled feedback system is derived and the region of stability that considers the actuator saturation nonlinearity is presented.