automatica
N. N. Nikolov, Control of Single Input Single Output Objects with Large Delay via a Discrete State Controllers

Key Words: Discrete state controller; objects with a delay; state observer; Smith predictor systemр Pade series.

Abstract. The control is a purposeful impact on the object of control, as a result of which it is brought to a desired state, which is determined by the requirements of the technological process. The main requirement is that this process is sustainable, but this is not enough. There are also certain requirements regarding the quality of the processes that take place in the system – quick action when working out disturbing effects or when changing the mode of operation, permissible deviations from the established mode, amplitude limitations of the controlling effects, etc. Often the requirements for the managed process are mutually contradictory and it is necessary to seek a reasonable compromise between them. It is accepted, when the feedback in a control system is carried out by means of the state vector, the controller in this system is called a State Controller (SC). If the state x(k) can be measured directly at every moment k=0, 1, 2, … we speak of control in the presence of complete information. When the state cannot be measured directly, but is estimated by other quantities that are related to it and available for measurement, it is said to be control with incomplete information. The delay in the object of control, whatever its nature, its presence creates difficulties in the implementation of the control system, worsening the quality indicators of the ongoing processes. When using a discrete state controller to control objects with a delay, in order to be able to synthesize the state observer it is necessary to represent the delay unit with a fractional-rational function using a Pade series. This enables the object of control to be represented as a higher-order object without delay, but leads to a significant extension of the transition process in the system.