Parametrization of algebraic numerical differentiators to achieve desired filter characteristics

Two methods for the systematic parametrization of real-time derivative estimators based on recent algebraic techniques are introduced. These numerical differentiators are considered as finite impulse response filters the amplitude spectrum of which is chosen such as to compensate for relevant disturbances. The first proposed parametrization method allows for the elimination of harmonic disturbances. The second one relies on an approximation of the derivative estimators as low-pass filters of arbitrarily large order with an arbitrary cutoff frequency. The practical application of the first method is demonstrated in an experimental case study, where mechanical vibrations occur.