Sensorless jerk monitoring using an adaptive antisymmetric high-order FIR filter

In the computerized numerical controllers (CNC) machine-tool processes many finishing and wear problems are related to jerk (derivative of acceleration). Since jerk sensors are expensive and scarce, a sensorless approach is presented as novelty. By taking the incoming signal from a digital incremental encoder included in the standard servo-loop of a CNC machine, the jerk is calculated with a new digital signal processing technique. The contribution of this work focuses on a simple high-order FIR filter with an adaptive algorithm that makes it possible to extract the jerk from the digital position measurement in a sensorless fashion. The algorithm reaches a good approximation to the expected jerk shape by overcoming the intrinsic quantization noise in the digital measurement and the changing dynamical conditions of a real machining process. The algorithm is tested on simulations and over one real CNC machine achieving great similarity between analytical and monitored jerk. It preserves most of the important jerk characteristics like peaks and coarse shape, getting a maximum of 2% of average jerk error on simulations, and 5% of average jerk error on real experiments. This computational efficient algorithm reaches a processing rate up to 760,000 samples per second in an FPGA implementation, which makes it suitable for high speed applications.