An analysis of quantization errors in digital control systems and its application to a hard disk drive

The analog-to-digital (A/D) converters and the digital-analog (D/A) converters are required for construction of a digital control system, which convert analog signals to digital signals and digital signals to analog signals, respectively. However, it should be noticed that all the converters actually have finite wordlength implementation. Considering these quantization errors, we must decide the number of bits of the A/D converters and the D/A converters by trial and error. In this paper, we derive a theorem which shows the relation between the system parameters and the quantization errors caused by A/D and D/A converters in a general digital control system with two degrees of freedom. Therefore, the trial-and-error process can be excluded completely when the number of bits of A/D converters and D/A converters are decided. Moreover, we apply the obtained theorem to a simulation of a hard disk drive control system. The suitability of the obtained theorem for practice use is verified by the simulation