Robust optimization of highly reliable automatic control systems

DOI: 10.31673/2412-9070.2024.045864

Abstract

The article proposes a method for achieving a compromise between the robustness and quality of control systems for nominal and parametrically disturbed object models in deterministic and stochastic cases. The multi-model Н₂/Н_∞ robust optimization approach is used to solve the problem. Ensuring nominal quality and robust stability can be achieved using a complex optimization criterion that includes (with appropriate weighting factors) H₂-norms calculated for both deterministic and stochastic cases, as well as the abovementioned H_∞-norm, and all these norms are calculated as for nominal and parametrically disturbed models of the control object. This allows you to adjust the contributions of the deterministic and stochastic parts to the minimized quality indicator, while by combining the H₂- and H_∞-norms into one optimization criterion, you can achieve a compromise between the requirements for suppressing external (coordinate) and internal (parametric) disturbances.
A new result of this work is the development of the named approach for a discrete model. The results of the work are directly demonstrated on the examples of robust parametric optimization of the discrete СS of the longitudinal and lateral movements of a small UAV.
The root-mean-square deviations of the state variables of the nominal and disturbed models of the system, stability reserves in terms of phase and amplitude, values of norms have small differences, which are quite acceptable from the point of view of the functioning of the system as a whole. Small values of root mean square deviations of state variables in the stochastic case indicate that the system has a significant reserve of quality that can be sacrificed if it is necessary to increase the robustness of the system. A small deviation of the logarithmic characteristics of the nominal and disturbed models indicates the high robustness of the system.

Keywords: robustness; multi-model approach; comprehensive quality indicator; quality-robustness; parametric optimization; system reliability.