A study on Non-parametric Filtering in Linear and Nonlinear Control Loops using the Singular Spectrum Analysis

Abstract

This study proposes the application of non-parametric filters based on the Singular Spectrum Analysis (SSA) method in linear and nonlinear control problems. The SSA is a general method for time series analysis that decomposes a signal into a set of additive components, including the measurement noise, in an adaptive way. It is highly adaptive to the behavior of signals and does not require any statistical assumptions. These flexible characteristics motivate the usage of SSA for control applications that demand filters with changing order or parameters, according to unknown disturbances of modeling errors, and applications that require the generation of smooth trajectories and commands. To show the feasibility of linear control, the SSA was used to attenuate the measurement noise in PID control loops, and in the nonlinear case, the SSA was used in an online trajectory generation approach. Experimental results showed that the SSA reduces the system’s sensitivity to noise, allowing the use of the derivative action while maintaining satisfactory performance. As a trajectory filter, the SSA successfully generated bounded derivatives from discontinuous input signals with similar response curves as those obtained by a parametric trajectory filter.