Computationally Efficient Adaption of the Window Size of Discrete Position Differentiators

Digital motion control requires precise and low-noise velocity information. Since this velocity information must be calculated from position encoders in each control cycle, time efficiency of these algorithms is a very important design goal. Additionally, it is required that these algorithms operate over wide ranges of both velocity and acceleration. Model-based feedback observers fulfill these requirements for many applications but in some cases they, for various reasons, cannot be formulated. Various applications have been presented in which adaptive filters are applied to overcome the compromises of fixed-length filters. However, it remains desirable to improve the performance of these methods especially in regions of very low velocity and to lower the computation time. This paper presents a new algorithm for the adaption of the window size of differentiator algorithms and a novel criterion for the velocity estimation. This criterion is used to take the dependence between the system´s acceleration and the velocity estimation error into account. The properties are studied in simulations and compared to other differentiation techniques. Additionally, results from experiments with a 6-degree-of-freedom servohydraulic Stewart-Gough platform equipped with the new velocity estimation scheme are presented and compared to the performance of concurrent algorithms.