Feedforward signal prediction for accurate motion systems using digital filters

A positioning system that needs to accurately track a reference can benefit greatly from using feedforward. When using a force actuator, the feedforward needs to generate a force proportional to the reference acceleration, which can be measured by means of an accelerometer or can be created by double differentiation of the reference position. The positioning system’s response to the feedforward usually shows some delay, caused by calculation time of the digital control computer, the digital-to-analog converter that drives the actuator’s amplifier, and digital differentiation of the reference position. At higher frequencies, even a small delay causes a large tracking error. Prediction of the feedforward signal by one or two samples can reduce this error. This paper describes three methods to predict a feedforward signal over a time span of a few samples. Polynomial extrapolation of past data does not require knowledge of the signal’s properties. Sinusoidal extrapolation produces an exact prediction at a set of chosen design frequencies. Both filter types can be implemented as FIR filters. A particular form of frequency sampling filters, having digital zeros which are not each other’s conjugates, can also be used for prediction purposes. The complex filter output allows reconstruction of input signal properties and its prediction. The filters are compared with regard to their suitability for predicting feedforward signals