Background. Traditional criteria for assessing system properties allow us only to analyze qualitatively the controllability and observability of dynamic systems, which limits the possibility of predicting the success of the synthesis of control systems. Research shows that the established methodology to obtain and apply quantitative assessment of controllability and observability cannot be considered complete, and thus, the task of their improvement continues to be relevant. One of the least developed issues of the theory is the development and application of quantitative criteria to assess the system properties of objects for predicting and improving the robust properties of synthesized control systems.
Materials and methods. The paper uses methods of vector-matrix and structural representation of dynamic objects and systems in state coordinates and in input-output relations. Methods of calculating controllability and observability Grammians are applied, as well as their singular decompositions for the initial and canonical forms of object representation. Parametric synthesis of state controllers and input-output polynomial controllers is performed using modal and modal-polynomial control methods. Evaluation of the effectiveness of the obtained results is carried out using digital modeling methods.
Results. A method has been developed and matrix criteria have been obtained for quantitative assessment of the degree of controllability and observability of an object. They are based on comparison of the degree of closeness of its real structure to reference models in the form of canonical forms of controllability and observability, pre-coordinated by input and output with the real structure of the object. The proposed criteria to assess system properties are not only more convenient and informative for assessing and comparing system properties of control objects, but also useful when developing methods to improve them.
Conclusions. In comparison with the traditional method of assessing the system properties of control objects based on the use of singular decompositions of controllability and observability grammians, the developed method and the criteria for assessing the degree of controllability and observability of minimum-phase SISO objects formed on its basis allow us to predict more accurately the robust properties of synthesized modal control systems with inertialess and dynamic controllers, to perform their structural optimization, and also to assess quantitatively the effectiveness of various methods to improve the indicated system properties.