A Quantization Algorithm without Accumulative Error

In this paper, a quantization algorithm by which the accumulative error can be prevented is presented. In digital control systems, the quantization cannot be avoided because of the finite word length of digital computers. The error due to quantization of the computed values may be tolerable in case of directly using them. In case of using the accumulated values, the error between sum of the original values and that of the quantized values becomes larger as the number of the values to be summed increases. Such an increasing accumulative error is critical for the control of precise NC machines, robots and autonomous vehicles. To solve this problem, a quantization algorithm without the accumulative error is presented. Basically, the algorithm is based on the feedback loop by which the accumulationive of the quantization error can be prevented. The error boundness of the proposed algorithm is proven and a computer simulation is performed to show the validity of the algorithm.