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A5-2 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo...

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COMPARATIVE ANALYSIS OF D AND ID FRACTIONAL REGULATORS FOR THE ROBUST CONTROL OF STATIC PLANTS IN THERMAL ENERGETICS Bela Benova 1 1 Technical University, Sofia, Bulgaria, [email protected] , [email protected] Abstract – In this paper are given the basic properties and features of the CRONE control in conditions of uncertainty for the plant’s model. One of the most popular methods for the synthesis of non-integer-order control systems the approximation by a fractio-rational recursion – is used for the conception of fractional differentiator and integro-differentiator. The dynamic and robust characteristics of two control systems including, respectively, the D and ID regulators and the same static plant, are compared. Conclusions are made on the advantages and inconveniences in using these fundamental types of fractional-order controllers. Keywords – Fractional differentiation, fractional integration, CRONE control, fractio-rational recursion, robust analysis. 1. INTRODUCTION The particular class of the fractional-order robust control systems CRONE ( Commande Robuste d’Ordre Non-Entier in french) [2,3] finds its application when uncertainty is present in the plant’s model. CRONE systems realize an efficacious counteraction to perturbations, maintaining the robust features to satisfy the requirements of the synthesis criterion. Using the approximation by the fractio- rational recursion are synthesized two fundamental fractional-order controllers – a differentiator and an integro-differentiator. The comparative analysis of the time, frequency and robust characteristics, observed in simulation for a preliminary set static plant, decides about which structure performs better control. 2. BASIC NOTIONS IN THE ROBUST ANALYSIS The robust analysis [2,3], uses the following expressions for the additive (1) and multiplicative (2) perturbations, the system’s sensitivity (3) and complementary sensitivity (4). ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ω ω ω ω ω ω ω ξ a a a a j j j G j G j G j A A A = = * (1) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ω ω ω ω ω ω ω ω ω ω ξ m m m a m j j j G j G j G j G j j G j A A A A = = = * * * (2) ( ) ( ) ( ) ( ) ω η ω ω ω j j G j R j e = + = 1 1 1 (3) ( ) ( ) ( ) ( ) ( ) ( ) ω ω ω ω ω ω η j e j G j R j G j R j = + = 1 1 (4) For the preliminary defined multitude [ ] [] * G , G Π , if (5) is satisfied, the system is characterised by the robust stability, the robust performance is obtained for (6) and if both expressions are validated together (7), the system possesses both robust characteristics. ( ) ω η ω < , 1 m A (5) 1 y e o m < + A η (6) ( ) ω η ω η ω < + < , 1 ; , 1 o m m y e A A (7) 3. SYNTHESIS OF NON-INTEGER-ORDER CONTROL SYSTEMS: METHOD OF THE POLYNOMIAL FRACTIO-RATIONAL RECURSION The large number of methods for the synthesis of robust systems can be classified as follows: QFT (Quantitative Feedback Theory), RMM (Robust Model Matching), FDM (Frequency Domain Methods) and a combination of the last two - RMM – FDM. Knowing that the physical realization of a non- integer controller is impossible, different approximations of its mathematical description were
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