Control synthesis by full state vector in systems with fractional-order derivatives using Caputo-Fabrizio operator

In the paper, the control system synthesis by means of the full state vector is considered when using fractional derivatives in the description of this system. To conduct research in the synthesized system with fractional derivatives in the Caputo--Fabrizio representation, a fundamental matrix of the system is formed, which also allows us to analyze the influence of initial conditions on the processes within the system. In particular, the finding of the fundamental matrix of the system in the case of multiple roots of a characteristic polynomial, which are obtained by transforming the synthesized system to the binomial form, is demonstrated. The influence of the fractional derivative index and the location of the roots of the characteristic polynomial transformed to the binomial form on the system operation is analyzed.

Modeling and Robust Optimization of the Technological Mode of Electrotechnological Complexes with the Renewable Energy Systems of Heat

The article works out the structure of the relationship between the managerial levels of the food enterprise, which is developed taking in-to account the use of robust control systems in the abnormal mode and systems of repair of heat power. To optimize renewable energy systems to the existing range of technological equipment of the bakery, a cogeneration unit is installed, due to its ability to generate and consume both heat and electricity. Also it is shown that the emergence of an abnormal situation at the electrotechnological complex of food production leads to a significant change in the transfer coefficients of the object over the direct and cross-channel channels, which will lead to loss of stability of the closed control system. Synthesized structure robust control system which has roughness properties and minimal sensitivity to parametric and structural uncertainties facility in case of emergency situations and elected its optimization criterion. The basic properties of the electrotechnological complexes of food industries are analyzed and on the example of the baking furnace the robust control system synthesis and renewable energy systems are shown. A comparison of the characteristics of the control system with local and robust controllers has shown that a robust controller system has better robust properties in case of emergency situations.

Method for the fuzzy control system synthesis for the analytical approximation characteristics of the typical nonlinear elements characteristics

The solution of the problem concerning the control system synthesis with a fuzzy controller on the basis of typical nonlinear analytical approximation characteristics with continuous differentiable functions like sigmoid type has been considered. A method of synthesis which is based on the fact that the rulebase and membership function are formed by the way of comparing the control or corrective impacts of the fuzzy controller (prototype) or a controller with approximating control (CAC) has been suggested for problem solving. For the CAC construction the closest coincidence of graphically installed controllers’ impacts are taken. This makes it possible to exclude subjective errors connecting with a possible non-representative ruleset for the rulebase forming. The result of the work is to obtain a new class of controllers based on the approximating continuous functions, which are simpler for constructing multi-mode control systems. The practical significance lies in the fact, that the tuning of the fuzzy controller based on the analytical continuous approximation of the typical nonlinear elements’ characteristics comes down to two basic parameters: the coefficient that determines the curvature (slope) of the characteristic in the transit mode and the parameter that determines the control impact value in the static mode. The advantage of this smooth characteristic in relation to the piecewise linear approximation is that there is no need to determine the moments (points) of switching nonlinear characteristics during the system operation.