Application of the Directed Cone Method for the Identification of Mathematical Models of Electromechanical Systems

Electromechanical systems are inherently hybrid in nature, combining electrical and mechanical processes, and their increasing complexity requires the development of universal and computationally efficient mathematical models. In this study, we propose a macromodeling approach that represents the electromechanical system as a “black box,” in which internal physical processes are disregarded and the system behavior is defined solely by the relationship between input and output signals. The identification of such macromodels is reduced to solving a nonlinear optimization problem. To address this challenge, the directed cone method is applied, which searches for the global minimum of the objective function through stochastic movement across the hyperplane defined by the optimization problem. Several algorithmic improvements of the directed cone method are investigated, including step-size adaptation, simultaneous adaptation of step size and hypercone opening angle, and a tunneling procedure. Their effectiveness is evaluated using the construction of a macromodel of a single-phase asynchronous motor as a case study. Performance was assessed according to computational complexity (measured as the number of objective function evaluations until convergence), relative modeling accuracy, and the dynamics of progression toward the global minimum. The experimental results show that the tunneling-based algorithm provides the highest modeling accuracy with the lowest computational cost, whereas the step-size-only adaptation was found to be the least effective. The proposed approach demonstrates the feasibility of constructing accurate macromodels of electromechanical systems that can be integrated into computer-aided modeling environments such as MATLAB/Simulink R2023b. Future work will focus on extending the approach to a broader class of electromechanical systems and developing hybrid algorithms to enhance robustness with respect to model nonlinearity.