Non-parametric Noise Filtering in PID Control Loops using Singular Spectrum Analysis

Abstract

PID controllers are still widely used in industrial processes, and their efficient operation requires the design of a filter. This filter makes the derivative action feasible and attenuates the measurement noise, reducing the variability of the control action. However, it influences the closed-loop performance and robustness. In this context, we analyze the effects of introducing a non-parametric noise filter based on the Singular Spectrum Analysis (SSA) technique. The SSA decomposes a signal into a set of additive components, including the measurement noise, in an adaptive manner. The filter was tested in First-Order Time Delay (FOTD) models, typical in industrial processes, for PI and PID controllers, designed by a optimized method, in scenarios with and without measurement noise. The Integral Absolute Error (IAE) metric measured the performance and the Total Variance (TV) the signal variability. The lag-dominated dynamics showed high sensitivity to changes in the filter attenuation degree in comparison with other processes. In contrast, for balanced and delay-dominated dynamics, the filter could improve both TV and performance. The PID achieved better performance than the PI for all processes and scenarios considered, but for higher TV.