CONTROLLABILITY ESTIMATION FOR HEATING SYSTEMS WITH INFRARED TUBE HEATERS The method for controllability estimation for heating systems with infrared tube heaters is considered in the article Keywords : infrared tube heater , reliability , сontrollability , method for estimation

The researches, described in the article is referred to the field of power engineering. The actual direction of heating development is smart decentralization of the systems. It results on the account of use traditional and comparatively new sources of heat supply of lowcapacity as well. The subjects of the study are heat and mass transfer processes in the infrared tube heaters in industrial apartment that are equipped with these heaters. The object of investigation is the heating systems with infrared tube heaters. They simultaneously are the sources of heat supply and heaters. At decentralization of heating systems of industrial and agricultural enterprises these systems provide considerable capital investment economy and also current expenses on fuel. The reliability of these systems one of the most important requirements to them both as on the design point as in the process of exploitation. Reliability is important property of heating systems and can be determined as an object property to perform the prescribed functions in the prescribed volume at certain conditions of operation     1 . It is the complex property that can consists of single properties. The single properties of reliability include stabilability, controllability, survivability and safety. These properties were investigated in works     2,3,4 and reflected the important side of functioning objects. Necessity for including these properties in the notion «reliability» is caused by specific features of heating systems. Research methodology of heating systems with infrared tube heaters implies the study of such a single property as controllability. Controllability can be determined as an object property to maintain normal operating conditions by control. The estimation of controllability of the heating systems with infrared tube heaters was carried out on the basis of existing mathematical models. For sufficiently full reflection of real processes of development and operation of the modeled objects the mathematical models constructed must take into account main properties of these objects that are significant from the viewpoint of the problems solved. At present moment there are no definite statements about method of estimation of controllability of the heating systems with infrared tube heaters. There are useful mathematical methods for solving the reliability problems in the investigation of the reliability of power systems in the modern theory of reliability. Some of these methods do not allow to reliability estimation and increase it saving capital costs for equipment and exploitation costs on fuel and energy resources for heating systems with infrared tube heaters. There is a need to introduce the controllability indices. Thus, the direction of the work is actual in scientific as well as in technic.


Introduction
The researches, described in the article is referred to the field of power engineering.
The actual direction of heating development is smart decentralization of the systems.
It results on the account of use traditional and comparatively new sources of heat supply of lowcapacity as well.
The subjects of the study are heat and mass transfer processes in the infrared tube heaters in industrial apartment that are equipped with these heaters.The object of investigation is the heating systems with infrared tube heaters.They simultane-with infrared tube heaters.They simultane-with infrared tube heaters.They simultane-infrared tube heaters.They simultane-infrared tube heaters.They simultane-tube heaters.They simultane-tube heaters.They simultane-heaters.They simultane-heaters.They simultaneously are the sources of heat supply and heaters.At decentralization of heating systems of industrial and agricultural enterprises these systems provide considerable capital investment economy and also current expenses on fuel.The reliability of these systems one of the most important requirements to them both as on the design point as in the process of exploitation.
Reliability is important property of heating sys-is important property of heating sys-important property of heating systems and can be determined as an object property to perform the prescribed functions in the prescribed volume at certain conditions of operation     1 .It is the complex property that can consists of single properties.The single properties of reliability include stabilability, controllability, survivability and safety.These properties were investigated in works and reflected the important side of functioning objects.Necessity for including these properties in the notion «reliability» is caused by specific features of heating systems.
Research methodology of heating systems with infrared tube heaters implies the study of such a single property as controllability.Controllability can be determined as an object property to maintain normal operating conditions by control.
The estimation of controllability of the heat-the heat-heat-heating systems with infrared tube heaters was carried out on the basis of existing mathematical models.For sufficiently full reflection of real processes of development and operation of the modeled objects the mathematical models constructed must take into account main properties of these objects that are significant from the viewpoint of the problems solved.
At present moment there are no definite statements about method of estimation of controllability of the heating systems with infrared tube heaters.There are useful mathematical methods for solving the reliability problems in the investigation of the reliability of power systems in the modern theory of reliability.Some of these methods do not allow to reliability estimation and increase it saving capital costs for equipment and exploitation costs on fuel and energy resources for heating systems with in-with in-with in-in-infrared tube heaters.There is a need to introduce the controllability indices.Thus, the direction of the work is actual in scientific as well as in technic.

Problem formulation
A general problem of the heating systems with infrared tube heaters consists in determining the given values of controllability indices during the considered time period by using the available means and possibilities.

Description of literature sources
Mathematical model heat transfer and air flows is proposed     5,6 .Algorithm for numerical solving of hydraulic circuit is formulated.
Special infrared tube heaters are considered that satisfy radiant and convective heat capacity with heating force air    

.
The new method for controllability estimation of these systems was worked out.
We consider the let Ω of elementary events ω i Ω = ω  i , where i-order number of the event.
The definition of the complex controllability in-definition of the complex controllability indices was proposed as and the additional condition where: ′ 1 y (x) -the derivative of pressure along tube heater; φ -the known function.
For every elementary event with external temperature ext i t it is numerical integrated the differential system (1) with condition (2) and any value n y (0) .Then with the help of random search it is calculated n y (0) that satisfy condition (3).Knowledge of the numerical values of ( ) j y x gives possibility to calculate capaсity of heating and ventilation and to calculate the complex controllability indices.

Conclusions
The method for controllability estimation for heat-controllability estimation for heat-estimation for heat-estimation for heat-for heating systems with infrared tube heaters was worked out.The definition of the complex controllability indices was proposed.The method is based on the mathematical model of hydraulic and thermal regimes for heating systems with infrared tube heaters.