## 2 Materials and Methods  
The methodological basis for solving the formulated scientific and practical problem and achieving the main aim of the article is a set of interrelated theoretical and applied research methods that combine the general scientific principles of systematicity, modelling, formalisation, optimisation, and structural and functional analysis. In particular, a critical review and logical and analytical generalisation of modern scientific approaches and practical results in the field of the energy-efficient control of asynchronous electric machines is carried out. The basic research approaches are based on the theory of electromechanical systems, including electric drives, as well as on the concepts of optimal and predictive control of nonlinear dynamic systems. The formalisation, verification, and validation of the research hypotheses were carried out using a computer experiment and numerical analysis of electromechanical control systems. The proposed approach focuses on electrical dynamics and the optimisation of control parameters in the model predictive framework. The present study aims at improving the methods and means of energy-efficient and precision control of asynchronous electric drives, the results of which were previously reported in Ref. [31]. In the course of this article, an asynchronous machine with the technical characteristics given in Table 1, which correspond to typical parameters for electric motors with the rated power of 370 W, is considered as a controlled electromechanical object. It offers a balanced trade-off between model simplicity and realistic dynamic behaviour, making it well-suited for detailed control algorithm development and parametric optimisation. The following notations are used in Table 1: \(P_{N}\)--nominal power; \(Z_{p}\)--number of pole pairs; \(n_{N}\)--nominal speed; \(T_{N}\)--nominal torque; \(J_{M}\)--total moment of inertia of the asynchronous machine and the load machine, as well as the coupling between the two machines and the torque sensor; \(R_{1}\)--stator winding resistance; \(R_{2}\)--equivalent rotor winding resistance; \(L_{\sigma}\)--stray inductance in the inverse gamma equivalent diagram; \(L_{\mu}\)--magnetisation inductance in the inverse gamma equivalent diagram; \(P_{1}\)--\(P_{6}\)--coefficients of the magnetisation inductance polynomial \(L_{\mu}(I_{1d})=P_{1}I_{5}^{5}+P_{2}I_{4}^{4}+P_{3}I_{1d}^{3}+P_{4}I_{1d}^{2}+P_ {5}I_{1d}+P_{6}\), where \(I_{1d}\) is the d-component of the stator current vector \(L_{1}\); \(C_{1}\), \(C_{2}\)--coefficients for setting the torque dependence on speed reference trajectory; \(\omega_{2,1}\), \(\omega_{2,2}\)--the initial and final values of the speed reference trajectory, respectively. The functional basis for the parametric optimisation of predictive control algorithms based on the criteria for reducing computational costs and increasing the accuracy of task execution is the developed computer model in the MATLAB and Simulink simulation environment. The GRAMPC toolbox [32] is used as the framework for the MPC algorithm implementation. In order to reduce computational time and improve the accuracy of electric drive control, a set of parameters was selected for optimisation within the GRAMPC predictive algorithm, specifically the number of sampling points over the prediction horizon (\(N_{horizon}\)), the maximum number of gradient search iterations (\(N_{MaxGradIter}\)), the weighting coefficients of the cost function (\(P_{Cost}\)), the prediction horizon (\(T_{horizon}\)), and the maximum optimisation search step (\(LineSearchMax\)). For each of these parameters, numerical simulations with variable combinations were conducted to determine the impact on the following:  
* Accuracy of system operation in accordance with a given reference trajectory;
* Computation time;
* Energy consumption. To objectively assess the effectiveness of various combinations of parameters, the taxonomic method of multicriteria analysis (MCDM) was applied.