Designs Neuro-Fuzzy Models in Control Problems of a Steam Heater

The article deals with the design of neuro-fuzzy models in the tasks of creating a system of automatic control by technological processes of steam-generating heat engines. A methodology has been developed for creating a temperature control system for a superheated operating under a priori uncertainties. Such control systems relate to adaptive systems capable of controlling the object with significant, previously unknown, changes in the parameters of the object. The use of an artificial neuron is proposed as adaptive regulation. A fuzzy model of the proportional-integral-differential-regulator adapter has been developed, an automatic control system based on the Mamdani algorithm. The proposed method for constructing an adaptive controller makes it possible to exclude the active identification stage from the automatic tuning process and the associated deterioration in the operation of the regulatory object. The feasibility and effectiveness of the method is proven experimentally. Computer testing of the obtained model in uncertain conditions was carried out, when the values of the transfer function of a complex control object changed. Regulation is carried out on the basis of the proposed hybrid high-speed algorithm of fuzzy-logical derivation of the main parameters: vapor pressure and temperature. The algorithm for setting the weight coefficients of the neuron is presented. The use of an adaptive fuzzy-logical controller allows us to provide a fairly good quality of controlling the temperature of superheated steam. To create process control algorithms, a hybrid application of a neural network and fuzzy logic is proposed, which allows taking into account the uncertainty of changes in the parameters of the object and the environment. The results can be used in the development of adaptive control systems and other heat power devices.


Introduction
The quality of the developed systems of automatic control of technological processes is largely determined by the usefulness of the mathematical models used in the control of technological objects. The steam generating heat engines under consideration are the technological basis of many industrial facilities. This role requires close attention from both technologists and industrial automation specialists, because modern technological progress requires ensuring the optimal operation of equipment, reducing energy consumption, increasing reliability, efficiency, environmental friendliness with an increase in efficiency.

Materials and Methods
A steam boiler as an object of regulation is a complex dynamic system with a large number of input and output interrelated quantities, therefore, examining it, in most cases they are decomposed into separate sections of regulation. At the same time, the influence of other circuits on the studied one is automatically excluded, which complicates the task of practical application of the newly developed control algorithms. Proceeding from this, it is proposed to use a complex mathematical model of object dynamics to study the synthesized algorithms and control systems, which allows one to take into account the mutual influence of control loops through the object and bring the behavior of the tested system closer to industrial realities. From a technological point of view, the task of controlling a superheater is to provide a given temperature in the steam path of the boiler. The temperature regime is ensured by increasing or decreasing the amount of water injected into the desuperheater. In the existing power system, a typical automatic control scheme is mainly used, which is called the cascade temperature control system for superheated steam, the control circuit of which includes a PI controller and a correction device [8,13]. The practice of operating such a system shows that with significant changes in the task, i.e. the desired values of the parameters of the temperature regime, there is a need to reconfigure the values of the coefficients of its control loop. In fact, this is an important objective sign that the functioning of the control system proceeds under conditions of a priori uncertainty. Indeed, the analysis of the operational characteristics of the superheater shows that the control object has a variable value of transport delay, its dynamic properties substantially depend on the oxygen content in the exhaust gases, steam consumption, heating surface contamination, as well as on operational factors -load, type and type of fuel burned, conditions of heating surfaces, excess air, etc. [1]. In addition [11], obtaining a mathematical model of a superheater is usually associated with the use of experimental methods, in particular, the method of acceleration curves, and, as a result, the mathematical description a priori becomes inaccurate. Thus, the development of a temperature control system for a superheater operating under conditions of a priori uncertainty is expediently carried out using adaptive control methods.

Solution Method
In the work, to adapt the parameters of the regulator, a mathematical apparatus is proposed. When constructing the circuit of the main control loop, we will consider a superheater together with a thermocouple as a control object (Fig. 1 (1) where s is a complex variable; y(s) and v(s) -mages of scalar functions of the output and input of the object; K -is the injection coefficient; h -is the transport delay; a 1 , a 2  The level of a priori parametric uncertainty in the object (1), following, we will set the relations:  The transfer function of the actuator (moving the control body of the control object -the valve), given its low inertia with respect to the object, we will describe in the form where Т ИМ = const-actuator time constant. In order to give the linear part of the control system the desired properties, we similarly introduce a stabilizing device into the main circuit with the following description: where K 1 and T 1 , T 2 , T 3 -gear ratio and time constants of the stabilizing device. The structure of the adaptive controller is set in the form where K 2 and T 0 -gear ratio and time constant of the linear part of the adaptive controller; To control complex, poorly formalized technological processes of the power system, fuzzy logic controllers based on linguistic information are widely used.This approach is applied to regulating the parameters of the boiler in conditions of uncertainty. In these objects, the collection of necessary statistical information is difficult due to the lack or absence of measuring instruments of some higher orders. Therefore, the application of methods of probability theory does not give the required results, it is in connection with this that the use of the theory of fuzzy sets is proposed.
The fuzzy logic controller algorithm uses the following four variables that describe the process being controlled:P E -the pressure deviation in the steam boiler, defined as the difference between the current value and the pre-selected value corresponding to the norm; S E -rate of change P E ; C PE -change in pressure deviation, defined as the difference between the current pressure P E and the pressure value obtained in the previous measurement; C EEdeviation rate change C PE .
Regulation is carried out according to two algorithms: the degree of steam heating is adjusted one at a time, i.e. the pressure is regulated (H C-heating change), differently changes the position of the throttle (T C -throttle position). Each algorithm takes into account all the above variables. The linguistic rules that describe the control algorithm are determined in advance by an experienced person -the operator.
Variable H C -was represented by a discrete set of values from 32 points, and T C -ten points. Variables C PE , P E , C E E , S E represented 13 points evenly distributed between the maximum positive and negative values.
To describe the values of variables by a human operator, the following linguistic values were used (abbreviated names correspond to the first letters of words in English):PB-big positive, PM-positive average, PS -small positive, NO -zero, NS-small negative, NM-average negative, NB-big negative.
For these fuzzy parameters, we construct an membership function of exponential type. Variable P E and S E negative values close to zero are additionally highlighted (below normal -NO) and positive, close to zero values (above normal-PO). Along with the indicated subsets, a fuzzy value was used to estimate the values of variables ANY, described by such a membership function, which is equal to unity for any element. Complex values based on the specified values were obtained through the operation AND, OR, NOT. Management rules were formulated as conditional sentences, for example, "if P E =NB, then H C =P B ". The above conditional clause defines the relationship between two fuzzy variables P E and H C, which is described by the Cartesian product of two fuzzy subsets NB and PB. It is convenient to represent the Cartesian product as a matrix of n columns and m rows, where m and n are the number of elements of universes for subsets NB and PB. Assume that the relation R between the variables is known PE and HC, then for some value you can determine the output value using the composition rule y=x o R. For conditional expressions "if А, then (if В then С)" the Cartesian product is determined А х В х С, which is used to determine the output C 'at the inputs A' and B ': In the described algorithm, two or more rules were combined with the help of a bundle ELSE, which was interpreted as the operation max.
For example, "if P E =NB and C PE = NOT (NB or NM) and S E = ANY, then H C =PM, otherwise if P E =NB and C PE =NC and S E =ANY and C EE =ANY, then H C =PM, otherwise, if ...".
Both algorithms, the pressure control algorithm and the speed control algorithm (throttle), are given in [2] in the Similarly, a speed control algorithm is compiled.

The Formulation of the Synthesis Problem
With a known level of a priori uncertainty of the form (2) given relative to the object coefficients (1) for the control system (1), (3) - (7), it is required to determine the explicit form of the self-tuning algorithm of the nonlinear part of controller (7) -a neuron, an adaptive controller ( 6)

Algorithm for Setting the Weight Coefficients of the Neuron
We perform the identical transformation of the linear part of the control system (1), (3)(4)(5)(6)(7). Since for the equivalently transformed linear part of the main loop of the control system (1), (3) -(7) (see the selected fragment of the structural diagram in Fig. 2), we can write the equation

s T s y s g s T s a s a s a s T s T s T s
it is obvious that the systems of equations (1), (3) - (7) and (6), (7), (10) will be equivalent. If we assume that in system (6), (7), (10), target conditions (8), (9) are attainable, then in the steady-state mode of the stabilization process, the system is described by the equations (13) where the index * is the designation of the steady-state values of the corresponding variables. Equations (11) - (13) can be combined and represented identically in the form of the expression which is often called the implicit reference model equation. In particular, from (14)  In our case, the reference output signal will be (15), and the reference input signal -е * =0.
We can formulate a measure of error based on a comparison of signals (15) and (18) To correct the weight coefficient w, you can use the rule of steepest descent, which in our case takes the form , ) ( where, γ >0 determines the size of the correction step. Note that ).
We introduce the notation ) ( then algorithm (20) takes the form Given (24), the algorithm for setting the weight coefficient of the neuron (25) and the weight coefficient 0 Finally, subject to (15) ), The use of an adaptive fuzzy-logical controller allows you to provide a fairly good quality control of the temperature of superheated steam. The error back propagation algorithm for setting the weight coefficient of one neuron or the set of weight coefficients of an artificial neural network can be used as an algorithm for adapting a control system in conditions of significant a priori uncertainty or partial change in the parameters of the control object.
The key advantage of the model is the possibility of its implementation on industrial software and hardware complexes (PTC) with physical inputs and outputs. The model performs computational operations to calculate the values of technological parameters. Further, these values are transferred to the SCADA-system, which provides the output of information on the screen of the stand operator. In turn, the programmable logic controller (PLC) in accordance with the laid down algorithms generates control actions on the object, and also transfers data to the upper level.

The Results of the Study
The synthesis of usable control systems is complicated by the change in the dynamic characteristics of individual elements of boiler units depending on the load and other factors, as well as the significant transport delay characteristic of the control circuits of heat and power processes. Thus, to ensure the required quality of control, the controller parameters must be changed in significant ranges. To analyze the dynamic properties of the above channels, the acceleration curves of the contours are approximated by inertial links of the first order with delay. As a result of the approximation, the obtained transfer Smoke exhaust performance -vacuum in the boiler furnace.
Air consumption -rarefaction boiler boiler ( ) The physical implementation of the model is assigned to the industrial programmable logic controller of the modular type Phoenix Contact ILC. This allows you to bind the required number of logical inputs / outputs of the model to the physical unified controller interfaces, and, therefore, to external hardware in which control algorithms were implemented. The controller software implemented standard laws for controlling control loops. As a result of the work, the following transients were obtained, which are reflected in Figure. 3. Figure. 3. Transient along the disturbance channel -output in the temperature control system of superheated steam Thus, control systems must determine the final settings of the regulators when commissioning an object, after its modification or a significant change in characteristics. In fact, automated adaptive control systems are used all the time, just the functions of the adaptation modules are performed by an experienced operator. Therefore, the development of systems that can independently or under the supervision of an operator adapt to changes in the control object is an urgent scientific and practical task. Maintaining high quality control of the circuits and components of the equipment helps to save resources and energy, increase the life of the equipment, will positively affect the overall work of controlled processes and engineering systems. And the solution to this problem is facilitated by bench research of the dynamics of the controlled facility as part of real industrial PTKs.

Conclusion
The place of a complex mathematical model of the control object in the design of high-performance automated process control systems of the energy industry is described. Using the dynamics model of a drum boiler as an example, the advantages of using a neuro-fuzzy model for testing, debugging, and optimizing control algorithms are shown. The results of the study of the model show the possibility of creating a custom non-linear dynamic simulation model of a drum steam boiler, which with the appropriate software and hardware PTK can be used in industrial control systems for the purpose of controlling the technological parameters of a drum boiler.