Study of Noise-Induced Tracking Error Phenomenon in Systems with Anti-windups

Abstract

PI controller has been widely used in various industrial fields and played important role of eliminating the tracking error. In PI controlled system with saturation actuator, method called “Anti-windup” has been used for avoiding undesirable phenomenon such as performance degradation, instability, and windup [2-3]. In PI controlled systems with anti-windup, tracking loss due to measurement noise has been recently discovered, where measurement noise persistently triggers anti-windup mechanism in a certain operation range that result in non-zero steady state tracking error, which was called “Noise Induced Tracking Error (NITE)” [10]. Such a system was analyzed under both zero-mean Gaussian noise and quantification of the tracking loss is given in terms of system parameters and noise standard deviation. In this work, we show that NITE could occur in all PI controlled systems if both anti-windup and measurement noise exist, regardless of anti-windups. We also extend the existing results to a case with uniformly distributed noise. Using stochastic averaging approach, we quantify the noise induced tracking error with respect to system parameters and noise characteristics, and shows that the phenomenon of tracking loss occurs with uniformly distributed noise as well. Conditions under which the tracking loss occurs are derived. The result is compared with that under zero mean Gaussian noise with the same level of standard deviation. We suggest two solutions to prevent NITE. One method is using a virtual saturation. We explain how effective the virtual saturation to mitigate NITE. An analysis of internal stability based on linear matrix inequalities is conducted on the system with a virtual saturation. The other method is changing static P gain to dynamic P gain. Dynamic P gain plays the role of eliminating an effect of noise in the systems. The result shows that NITE does not occur due to the two solutions. We also show the differences between two solutions. ⓒ 2015 DGIST