A Simple Fixed Point Iteration-Based Digital Noise Filter for Control Applications

In various control applications as robotics, chemistry, life sciences, etc., the controllers need feedback terms that contain various integer or fractional order time-derivatives of the variables that describe the physical state of the controlled system as well as certain properties of the “nominal trajectory” that has to be precisely tracked. Normally these derivatives cannot be directly measured by dedicated sensors, so they numerically must be estimated by other, normally noise-burdened sensor signals. The higher the relative order of the control task is the higher the control method's sensitivity to the sensor noises is. To improve the situation the sensor signals and especially the time-derivatives calculated by the use of the sensor signals have to be “filtered” to reduce the undesirable consequence of the measurement noises. Filtering normally happens by somehow “averaging” a few past signals therefore it inevitably introduces “delay” -like effect that can degrade the controller's operation. Physically the act of filtering can be interpreted as the insertion of a dynamically coupled physical subsystem into the controlled engine + controller system. Electronic and electrical engineers developed various filters made of constant and passive elements as resistors, inductors, capacitors that can be described by differential equations. For these linear, time-invariant systems the use of the frequency domain became prevailing. In the case of digital controllers more primitive, fictitious models can be applied without physical realization. These subsystems can be even strongly nonlinear. In this paper a primitive noise-filtering technique for digital controllers is suggested. It has two simple, tunable parameters. Its operation is illustrated in the Fixed Point Iteration-based adaptive control of a propeller-driven pendulum.