In this work, issues related to the application of the D-decomposition technique to selection of the controller parameters for a drive system with flexibility are presented. In the introduction the commonly used control structures dedicated to two-mass drive systems are described. Then the mathematical model as well as control structure are introduced. The considered structure has only basic feedbacks from the motor speed and PI type controller. Due to the order of the closed-loop system, the free location of the system’s poles is not possible. Large oscillations can be expected in responses of the plant. In order to improve the characteristics of the drive, the tuning methodology based on the D-decomposition technique is proposed. The initial working point is selected using an analytical formula. Then the value of controller proportional gain is decreasing, until the required value of overshoot is obtained. In the paper different advantages of the D-decomposition technique are presented, for instance calculation of global stability area for the selected gain and phase margin, the impact of parameter changes, and additional delay evident in the system. Theoretical considerations are confirmed by simulation and experimental results.

In this paper the D-decomposition technique is investigated as a source of non-linear boundaries used with the Genetic Algorithm (GA) search of a PI voltage compensator gains of the boost converter operating in Continuous Conduction Mode (CCM). The well known and appreciated boost converter has been chosen as a test object due to its right-half plane zero in the control-to-output ($c2o$) voltage transfer function. The D-decomposition, as a technique relying on the frequency sweeping, clearly indicates not only the global stability but, in its extended version, regions satisfying the required gain (GM) and phase (PM) margins. Such results are in form of easy to interpret functions $K_I=f\left(K_P\right)$. The functions are easy to convert to the GA constraints. The GA search, with three different performance indexes as the fitness functions, is applied to a control structure with time delays basing on identified $c2o$ voltage transfer functions. The identification took place in an experiment and in simulation. Outcomes of the identification are compared to mathematically derived formula taking into account certain parasitics. A complete set of practically useful mathematical formulas together with their validation in simulation and experiment is included.

Commonly used variants of the proportional-integral, PI, and the integral-proportional, IP, compensator gains selections, merged with the D-decomposition technique are presented in this paper. The motivation to this work is the willingness to check whether such a combination can lead to unified and perhaps simplified approach in this matter. Therefore, the D-decomposition technique has been effectively combined with the frequency- and the time-domain driven requirements regarding the control dynamics. Criteria such as the gain- and phase-margins, (GM, PM), the sensitivity, MS, the pole placements by means of the (σ, ωd) and the (ξ, ωn), and the overshoot with the rise time (δ, tr) are considered. It has been shown that the control design effort can be reduced by the means of the D-decomposition to intuitive judgements in the proportional and integral gains coordinates (KP, KI) with parametric curves. As such it can be thought of as a promising scenario in a case considered. The analyses are presented and discussed in details. They are conducted basing on example of output voltage closed loop control of the Dual Active Bridge, DAB, converter. The circuit operates under the phase shift control scheme. The control-to-output transfer function identification and the control circuit delays are included in the analyses. The case analysis have shown that the time domain requirements are less effectively met with the PI regulator when compared to its IP configuration. This is due to the commonly used simplifications during conversion between the (ξ,ωn) and the (δ, tr) in presence of uncompensated zero of the closed loop transfer function. The paper contains complete and intelligible approach to dedicated mathematical investigations verified experimentally.

This paper presents a systematic and innovative data–driven framework for constructing Mutual Information–enhanced NARX–NN Digital Twins (DTs) of power electronic converters, demonstrated on a DC–DC boost converter in continuous conduction mode under closed–loop voltage control. A Digital Twin Instance (DTI) of the inductance current is built via time–delay embedding of hidden dynamic attractors. Sampling frequency is optimized using self–Mutual Average Information (sMAI) to capture intra–cycle Pulse Width Modulation (PWM) dynamics. Input preselection uses correlation analysis and Variance Inflation Factor (VIF), followed by delay assignment via sMAI and cross-MAI (cMAI). The False Nearest Neighbours (FNN) criterion determines the minimal embedding dimension. Two NARX–NN configurations (4D and 5D) are trained on a high–fidelity MATLAB–SIMULINK model including parasitics, filtering, and non–idealities. Although thermal and voltage variations are excluded to isolate modelling effects, the 5D model outperforms the 4D under both nominal and perturbed loads. In the frequency domain (up to 50 kHz), it improves amplitude tracking. Experimental validation via offline transfer learning reduces steady–state error to approximately $\pm \,1\%$ and transient errors to a few percent, peaking at -13% in unseen saturation case. The resulting DTIs are lightweight (<1 GFLOPS), delay-aware, and interpretable, enabling scalable real–time integration into converter–centric smart grid digital twin architectures without solving differential equations.

The article presents a method for estimating the Boost converter inductance current using a NARX neural network. The model works basing on selected sampled and calculated time series, without the involvement of any algebraic equations describing the circuit. The proposed solution enables the estimation of the current in static and dynamic states across the entire load range of the converter, as well as under dynamically changing levels of the supply voltage - this under closed loop output voltage control. The proposed approach can serve as a foundation for further work on the digital twin of the converter. All considerations are based on experimentally verified simulation model.

The paper presents the application of the D-decomposition method to the selection of parameters of the speed control structure of the drive system with an elastic coupling. After an introduction where the issue of control structures of drive systems with an elastic joint is briefly presented, the main point of the paper is described. Then the mathematical model of the two-mass drive system is demonstrated. Next, the control structure with PI controller and additional feedback from the shaft torque is shown. Next, the idea of a D-decomposition is discussed. Then the simulation and experimental results showing the properties of the presented methodology are demonstrated.