A low-noise estimator of angular speed and acceleration from shaft encoder measurements

This paper deals with the differentiation of discrete-time, quantized signal provided by an encoder. In particular, speed and acceleration estimation with large bandwidth is required for feedback control in automation and robotics applications. The main problem in the differentiation of the encoder measurements is to combine the large bandwidth and the strong filtering of the quantization noise. The proposed speed-acceleration estimator relies on typical filtered differentiator nonlinearly combined with a state-variable filter. The former produces a strongly filtered estimation, while the latter is characterized by a large bandwidth, in order to track fast signal transients. In this way, the resulting estimator has a variable bandwidth depending on the harmonic content of the encoder signals. Two versions of the estimator are presented and compared. The first one gives only a speed estimation, while the second provides also an acceleration signal. Simulative and experimental tests verify the performance of the proposed solutions. A 5k c/r encoder and a high resolution sine/cosine encoder are considered. Keywords— Real differentiators, nonlinear observers, encoder measurements, velocity estimation, acceleration estimation