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Introduction. The research of linear dynamic systems of regulation of the process of biological purification of contaminated water with fractional regulators was conducted in order to determine the boundaries of D-domains of their global stability and to determine the space of the parameters of the adjustment of the fractional controller for fixed orders of the diereintegrators in its composition.Materials and methods. Studies were conducted on the stability of the automatic control of the water treatment process. Using the Dsplit method, we obtain analytical formulas that determine the limits of the region of stable stabilization of the "object" + "fractionalregulator" system.Result and discussion. Automatic control systems of fractional order are more precisely described by dynamic equations, in which the order of derivatives can be any number, valid and not only integer. Proportional-integral-differential (PID-) regulators that are widely used in practice of automation also fall under a fractional generalization, if in their structure, instead of ordinary integer derivatives and integrals, fractional analogues are used. The

Key words: ABSTRACT Fractional calculus Differentintegrator Optimal control Numerical modeling Bio-purification of watersThe problem of modeling the control of the process of biological treatment of polluted water using fractional regulators is considered and solved in the paper. Mathematical modeling of the biological purification process as a control object is considered, a linear dynamic control model is obtained. The criterion of the quality of automatic control of a fractional regulator by the functioning of a biological water purification system has been introduced. Optimum tunings of fractional regulators are obtained, the dynamics of transient processes of control action and the state of the purification system is investigated. Numerical simulation of fractional and classical control is carried out, a higher efficiency of fractional regulators is shown.

Introduction. The research of the scenario approach in the automation of the control of the processes of baking bakery products [3, 4] has been carried out in order to increase the efficiency of production and improve the quality of products. Research methods. Are analysis of the characteristics and criteria of the chosen problem, compilation of qualitative assessments and previous scenarios of process management, estimation of the realistic solutions (expert, cross-influence, Saati method [1]), rules and sequence of their application in the writing of generalized scenarios. Result and discussion. The article deals with the main components of the stages and operations of bread production and various possible schemes for their regulation. The disadvantage of the typical scheme of automatic humidity control on dough machines of continuous action is its orientation to the stable quality of flour. To regulate the duration of fermentation, the mass of the semifinished product in the fermentation vessel fixes the weighing mechanism, and the consumption takes into account the flow meter, these data are processed according to the corresponding formula. At the stage of mechanical treatment of the dough, it is necessary to control the mass of the dough and its degree of readiness for baking. The controlled parameters are the temperature and humidity of the air in the cabinet, as well as the durability of the stand. It is proposed to develop an automated multipurpose control system based on a scenario approach and intelligent technologies [5, 8, 10] in order to increase productivity, reduce specific losses and cost of resources while improving product quality. The essence of the situational approach to the management of technological processes of baking bread is outlined. The abstract (A-) and structural (C-) scenarios of bread production are offered, which can be used in the quotient-purpose analysis of bread production. Cscenario details the A-script based on the evolution of the object when performing operations and transferring objects from one operation to another [6, 7]. Each class C-scenario runs autonomously and interacts with other classes and the environment to make new objects in the input queues and to remove from the output queues "worked out". Conclusions. The analysis of the state of the problem of control of technological processes of bread production and the examples of control scenarios are given.