Identification and Control via Data of Finite Wordlengths

Abstract

For digital control of mechanical systems, pulse encoders, linear scales, or photonic devices with A/D converters are commonly used to measure displacements. Also, D/A converters are employed to generate control forces computed by control algorithms. That is, the measured and control signals are digital, while inputs and outputs of controlled systems are analog variables. Since digital variables are of finite wordlengths, they contain quantization errors. In precision control, such errors may deteriorate control accuracies significantly. To overcome this problem, the present paper proposes to estimate the quantization errors from the quantized input and output signals in real time, and improve the output measurements by adding the estimated quantization errors. For this purpose, we first consider identification of systems based on data of finite wordlengths, where we estimate system parameters and quantization errors simultaneously by the least square method. By simulation, it is illustrated that accuracy better than the resolution of quantization can be achieved.