Statistical Design of Control Systems Containing Digital Devices

Abstract

The sampling and quantization of signals are essential to the digital devices such as digitalcomputers and A-D converters. This paper develops statistical optimum design methods of thecontrol systems containing these digital devices under random disturbances.
In the first part, neglecting the quantization effects the pulse transfer function of a sampled-datacontrol system which minimizes the mean square error is presented as a function of the powerspectrum of reference input signal, under several constraints which come from physicalrealizability of the system, time constants and dead time of controlled process, etc. Althoughquantizing operation is nonlinear, it can be linealized as a superposition of white noise on thesignals in statistical treatments, and the corrections due to quantizing effect to the optimum designare discussed theoretically.
The optimum pulse transfer functions has been calculated for several kinds of random inputsand these results are examined using a high speed simulator of the sampled-data system.