On Certain Noise Filtering Techniques in Fixed Point Iteration-based Adaptive Control

Abstract

In control applications the use of noise-burdened sensor signals cannot be evaded. Also, certain signals can be lost. This problem traditionally is tackled by the use of Kalman filters that provide some “optimal solution” to these problems based on reasonable assumptions that are not always well underpinned in the practice. These are assumptions are made with regard to the system model and the statistical distribution of the noise signals. The Fixed Point Iteration-based adaptive controller is applicable for various strongly nonlinear models. Because feeding back the order of time-derivative of the system’s variable that immediately can be varied by the control signal, its noise sensitivity can be considerable. In this paper the operation of an unscented Kalman filter-based technique is compared with that of a simple moving window with affine signal approximation, and the use of a third order low pass filter in the control of a modified van der Pol oscillator. In this model a quadratic drag term is added to the original model to describe the motion of the system in turbulent fluid environment. According to the numerical simulations it can be stated that the simpler methods can replace the more complicated Kalman filter.