Modal Synthesis of Adaptive Regulators of an Interval System with Interval Parameters Based on Critical Root Diagrams

A nonstationary control system with an interval characteristic polynomial, the coefficients of which are set by their intervals, is considered. For such a system, the problem of modal synthesis of an adaptive regulator providing the maximum degree of dominance is solved. To solve it, a decomposition approach based on the separation of the regulator parameters into dominant and free ones is proposed. To place the free poles at the maximum distance from the dominant one, conditions based on vertex critical root diagrams are formulated. With the found free parameters of the regulator, it is proposed to organize the self-tuning of the dependent parameters in accordance with the values of the interval parameters. The application of the technique is considered on a numerical example.