Complex Issues in Regulator Designing

Abstract

The problem of control object with the use of feedback loop is extremely relevant, because only this method provides for the accurate control. It happened that the theory of automatic control paid much attention to the methods of regulators design based on mathematical transformations, using a mathematical model of the object. It describes the transformation of an input signal into an output signal inside the object. The methods were imperfect, so one of the following simplification methods was the most frequently used: the mathematical model of the object was simplified, or the calculations were carried out with approximation, for example, the oscillations in the system were studied by the amplitude and phase of the first harmonic only. Therefore, the result of using such regulators in practice did not exactly correspond to the theory provisions. To get mathematical and experimental basis of system developer tool, a solution of the elementary sub-problems was required. Among them there are tasks of the control of an object of the first and second order. Today the situation has changed. There is a means of sufficiently accurate mathematical modeling of the behavior of the system consisting of the loop with an object and a regulator. There are software and mathematical means for regulator calculating by the method of numerical optimization. Now there is sufficient software for calculating the regulators of the object, having a rather complex mathematical model. However, this did not change the situation. A lot of articles are still published, in which it is suggested performing additional fine tuning to achieve the required parameters after calculating the regulator and its technical implementation. Quite a big number of articles is still being published; they consider the methods of the empirical tuning of regulators based on the parameters of the transient process with a given fixed gain coefficient. This situation demonstrates insufficient using of the important theoretical result that the first- and second-order models are not fully adequate to any real object. The article explores this problem using the methods of numerical mathematical modeling and numerical optimization.