Model of digital control system by complex multi-loop objects

A digital eco-monitoring platform is considered as a control system for a complex multi-circuit object with a Von Neumann-type regulator. Common analytical models of object under control and data processing by digital controller are obtained. It is shown, that transfer functions, obtained from analytical description of discrete data processing by digital controller may be combined with transfer functions, obtained from analytical description of object under control reaction on continual actions. Typical flow-chart and analytical mathematical model of system functioning, which takes into account time delays between transactions, caused by sequential interpretation of control algorithm operators and random character of data processed, is worked out. It is shown, that time lags between transactions adduce to an appearance in transfer function both numerator and denominator of closed through digital controller system, complex exponents, which describes such phenomena as data skew, and pure lag. The method of time intervals between transactions estimation in cyclic algorithms of arbitrary complexity, based on their representation as semi-Markov process, is proposed. Theoretical postulates are confirmed by simulation of two-loop digital control system functioning.