Технические науки /12.Автоматизированные системы управления на производстве.

Ph.D. Lyashenko A.

National mineral resources university

DEVELOPING SYSTEMS WITH OPTIMAL ADAPTIVE TRANSFER FUNCTION

In many cases, the static and dynamic properties of the systems change over time, and the regulator with a constant setting can not provide the optimal condition. In these cases it is necessary to change the setpoint setpoint or parameters of any elements, change the wiring diagram elements or introduce new elements: such as logic gates, computers, and the elements of the automatic search, which leads to the creation of automated systems with properties of self-adjustment or adaptation. In this connection, in real time, the development of the theory of automatic control systems, and its practical application, is characterized by intensive development of adaptive management. These techniques are used for construction of control systems with significant uncertainties of the control object and the conditions of its functioning (environmental characteristics), available at the design stage or before the commencement of operation of the system. We consider such management tasks for which the dynamic properties of an object can vary widely unknown in advance way. Available primary (a priori) is not enough information to build control systems with optimal (or given) quality indicators. In adaptive control systems, the lack of a priori information compensated during its operation on the basis of the current data on the behavior of the object. These data are processed in real time (the flow rate control process) and used to improve the quality control system.

Application of the principles of adaptation allows you to:

- To ensure the system is operating in a significant change in the dynamic properties of the object;

- To make optimization of operating modes of the object by changing its parameters;

- To reduce the technological requirements for the construction of individual components and elements of the system;

- To unify separate controls or blocks of regulators, adapting them to work with different kinds of similar objects;

- Shorten design tests;

- To increase system reliability.

Widespread in practice the task is to stabilize the dynamic properties of industrial objects for which the transients are considered primary modes of operation. Under the influence of random factors and due to changes in the parameters of the system may be in breach of these regimes. Stabilization of transients can be done by comparing the timing of objects with some reference to the subsequent minimization of their differences. The objective being to achieve optimal accuracy and optimal performance under varying environmental conditions and characteristics of the object. Here, the best solution is obtained using adaptive systems.

Consider the process of adaptation in the presence of the reference model (Fig. 1) as an example of thermal processes.

Fig. 1. A block diagram of an adaptive system model

Thermal processes in objects with distributed parameters (PPR) can be described by the following transfer function [1]:

(1)

where: – the gain of the object;

– time constant; G – generalized coordinate; τ_η –

time lag, n – a weighting factor..

The transfer function of the synthesized distributed PID controller according to [2] is:

(2)

We introduce the notation and write the expression:

(3)

where: ; (4)

; (5)

. (6)

The model specifies the desired values of the transfer, the time constant and the time delay of the control object.

. (7)

With the identification of the object management unit define the parameters the results of numerical simulations. For this test signal generator generates and supplies the input to the system input action of the form:

(8)

where: ; ; .

According to the results of numerical simulations we define the parameters , which is input adaptation unit.

Adaptation unit calculates the controller parameters in accordance with a specially developed technique. This uses the expression (4) - (6).

Adaptation procedure can be represented as a block diagram in Fig. 2.

Fig. 2. A block diagram of an adaptive system model

Using this method, we calculated the settings adaptive distributed PID control system for thermal fields thermohousing protective circuit television camera. The simulation results of the closed system management demonstrated the high quality management of the facility in full accordance with the requirements of the control system.

Literature

1. Pershin I.M. The analysis and synthesis of systems with distributed parameters. - Pyatigorsk, RIA at CMS. 2007. - 244c.

2. Lyashenko A.L. Development of methods for the synthesis of optimal control of distributed systems / Components and Technology - 2013. - № 2 (139). - c. 122-124.