Investigation of robust optimum control systems with multifunctional technological objects
DOI:
https://doi.org/10.31548/energiya2018.05.068Abstract
A part of the technological objects of the food industry are characterized by the multiplicity of variables. This is requires synthesis of the control system with use of additional techniques of unleashing channels. Also, technological objects function in conditions of uncertainty caused by the inaccuracy of compiling a mathematical model, changing the conditions of the object and environment. Autonomous systems used to unleashing channels in a system with uncertainties impair quality and may lose stability that is unacceptable in the functioning of the system. On the other hand, robust systems are designed to control objects with uncertainty. The logical improvement of the control systems of multifunctional objects with uncertainty is a combination of robust and autonomous systems based on complexation methods.
The purpose of this work is to study the influence of cross-links in a robust control system with a multifunctional technological object, as well as the development of a control system based on the complexation of autonomous and robust synthesis methods. The control system built on the complexation of these methods will minimize cross-links in the robust control system for technological objects operating in conditions of significant uncertainty, thereby increasing the quality of the system and reducing energy costs.
In the work for the development of a compensator, an autonomous control method was used. Also, for synthesizing the control device, robust control methods are used, in particular the GCD search formula for the minimum H∞-norm, as well as the non-smooth optimization method for the H∞-optimization. For the proposed control system of multifunctional objects used general methods of system analysis and complexation, and for comparison of research results – the mathematical modeling, which offers Matlab-applications.
The robust optimum control system for the technological object of the sugar industry, containing a multidimensional regulator, is developed based on the loop shaping approach. In particular, the latter uses a singular Bode diagram to design a compromise between the quality and robustness of the multidimensional system. The control system, based on the model of the levels of the evaporation plant of the sugar plant, was investigated. The simulation revealed a partial solution of cross-links and robustness both in relation to structural and parametric uncertainties and in relation to external perturbations. The disadvantage of such a system is the high order of the regulator, which requires the further application of methods of order reduction. The structure of the robust optimum regulator with cross-link compensation is proposed, consisting of connected of a series compensator and local PID-regulators, in which the latter are formed in the form of a diagonal matrix transfer function. Parameters of the resulting device are calculated by optimizing the H∞-norm of the closed system by the method of non-smooth synthesis.
On the example of the levels of multi-units evaporation, the mathematical model of which is described by the system of differential equations of the fifth order, the simulation of the proposed system was carried out and were investigated cross-links in the nominal and uncertain systems. Comparison with autonomous and robust systems has confirmed the effectiveness of a robust optimal multidimensional system, in particular, the quality of the system increases and the range of uncertainty in which the system remains stable. The benefits of such a multidimensional regulator are low order and easy to calculate and implement.
The developed control system maintains stability throughout the range of uncertainty of the object, but in nominal mode, the quality of the system is somewhat worse than in traditional control systems. This is due to the rough settings of the system that characterize robust optimal systems. Elimination of the last disadvantage by expanding the structure with the methods of optimal, adaptive control based on the integration and is the prospect of further research.
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