In this paper the identification of generalized linear dynamical differential systems by the method of modulating elements is presented. The dynamical system is described in the Bittner operational calculus by an abstract linear differential equation with constant coefficients. The presented general method can be used in the identification of stationary continuous dynamical systems with compensating parameters and for certain nonstationary compensating or distributed parameter systems.

Contemporary empirical research on combustion engines are processed based on the theory of experiment. Available software applications analyzing the experimental data commonly utilize multiple regression models, which enables studying of the effects and interactions between input values of the model and a single output variable. Using multi-equation models gives free hand at analyzing measurement results because it enables analysis of the effects and interaction of many output variables. It also allows analysis of the measurement results during dynamic processes. In this paper the author presents advantages of using a multidimensional regression model on the example of research conducted on engine test stand.

The paper presents the possibilities of using B-splines to determine a mathematical model in the form of linear differential equations describing the change of the motion parameters of floating objects depending on the values of the control signals. The elaborated identification system is a collection of algorithms including: approximation of input and output signals, optimal selection of differential equation coefficients and model verification. The basic spline functions were used to approximate the values of the input and output signals. The developed method was illustrated by an example of identification of underwater submarine motion equations describing the change in draft depth and trim angle depending on the difference between buoyancy force and ship’s weight.