Nonlinear Objective Research Articles

Optimized harmonic PWM implementation in a reduced switch count MLI with quadruple boosting using PSO for solar PV applications

Abstract The reduced switch multilevel inverters are used in many applications specially in renewable energy system. They have a smaller number of semiconductor devices, complexity and thus lower cost and power losses. A reduced-switch multilevel inverters (MLIs) with quadruple boosting capability have been investigated in this study by implementing an optimized harmonic pulse width modulation (OPWM) technique. As an example, a nine-level quadruple boosting inverter, operating at fundamental frequency, is analysed to reduce the dominant lower order harmonics such as third, fifth, and seventh-order harmonics in the output voltage along with control on fundamental component. The particle swarm optimization (PSO) algorithm is employed to obtain the optimize the switching angles using a constrained nonlinear objective function. The computational results have been used to simulate the nine-level quadruple boost inverter and results shows a significant reduction in lower order harmonics. The simulation results have been verified on a prototype of nine-level quadruple boost inverter.

Distributed planning method for detection array of UAV formation with bearing-only sensor network

Abstract Unmanned aerial vehicle (UAV) formations for bearing-only passive detection are increasingly important in modern military confrontations, and the array of the formation is one of the decisive factors affecting the detection accuracy of the system. How to plan the optimal geometric array in bearing-only detection is a complex nondeterministic polynomial problem, and this paper proposed the distributed stochastic subgradient projection algorithm (DSSPA) with layered constraints to solve this challenge. Firstly, based on the constraints of safe flight altitude and fixed baseline, the UAV formation is layered, and the system model for bearing-only cooperative localisation is constructed and analysed. Then, the calculation formula for geometric dilution of precision (GDOP) in the observation plane is provided, this nonlinear objective function is appropriately simplified to obtain its quadratic form, ensuring that it can be adapted and used efficiently in the system model. Finally, the proposed distributed stochastic subgradient projection algorithm (DSSPA) combines the idea of stochastic gradient descent with the projection method. By performing a projection operation on each feasible solution, it ensures that the updated parameters can satisfy the constraints while efficiently solving the convex optimisation problem of array planning. In addition to theoretical proof, this paper also conducts three simulation experiments of different scales, validating the effectiveness and superiority of the proposed method for bearing-only detection array planning in UAV formations. This research provides essential guidance and technical reference for the deployment of UAV formations and path planning of detection platforms.

Multispheroidal model of magnetic field of uncertain extended energy-saturated technical object

Problem. The implementation of strict requirements for magnetic silence of elongated energy-saturated technical objects – such as naval vessel and submarines is largely determined by the adequacy of mathematical models to the signatures of a real magnetic field. Aim. Simplification of mathematical modeling of the magnetic field of an uncertain extended energy-saturated object based on the development and application of a multispheroidal model of its magnetic field instead of the well-known multidipole model. Methodology. Coordinates of the geometric location and magnitudes of spatial extended spheroidal harmonics of spheroidal sources of multispheroidal model of magnetic field calculated as magnetostatics geometric inverse problems solution in the form of nonlinear minimax optimization problem based on near field measurements for prediction far extended technical objects magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field COMSOL Multiphysics software package used. Nonlinear minimax optimization problems solutions calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction far magnetic field magnitude of extended technical objects based on designed multispheroidal model of the magnetic field in the form of spatial prolate spheroidal harmonics in prolate spheroidal coordinate system using near field measurements with consideration of extended technical objects magnetic characteristics uncertainty. Originality. For the first time the method for design of multispheroidal model of magnetic field of uncertain extended energy-saturated technical object based on magnetostatics geometric inverse problems solution and magnetic field spatial spheroidal harmonics calculated in prolate spheroidal coordinate system taking into account of technical objects magnetic characteristics uncertainties developed. Practical value. It is shown the possibility to reduce the number of spheroidal sources of the magnetic field for adequate modeling of the real magnetic field based on the developed multispheroidal model compared to the number of well-known dipole sources of the magnetic field in the multidipole model of the magnetic field. References 48, figures 4.

Distributed Nonfragile Guaranteed Cost Filter Design for Nonlinear Systems With Sensor Networks

This paper addresses the distributed filter design issue of nonlinear systems in sensor networks. Furthermore, by considering the synthesized filter gain fluctuations, the nonfragile design scheme is developed to improve the implementation robustness and applicableness. Since the nonlinear system model is more practical and general to describe the real‐world dynamical systems, the nonlinear objective system measured by a sensor network grouped by sensor nodes is investigated. Moreover, in order to solve this theoretical filtering problem, the control theory and system theory are applied with control model transformation. More precisely, all the filters are supposed to be designed with the measurement of each sensor in the sensor network. Firstly, the distributed filtering problem is converted to the stability of filtering error system. Then, sufficient convex optimization conditions are accordingly established to ensure the desired H∞ disturbance attenuation level with the desired guaranteed cost performance. Then, distributed filter gains can be derived by means of convex optimization method. Finally, the illustrative simulation of a nonlinear system with four sensor nodes is given to demonstrate the usefulness and correctness of our filter design.

Solving economic emission dispatch of combined heat and power units problem using enhanced Tasmanian devil optimization strategy in power systems

ABSTRACT Economic load dispatch (ELD) is a general procedure to distribute essential loads among the available generation units to minimize operational costs. Different problems presented in the ELD are generated because of inequality and equality constraints of the system. The double objective-based combined economic emission dispatch (CEED) issues presented in the power system are considered for the environmental impacts and accumulated by the gaseous pollutants emission in the fossil-fueled power plants. Moreover, the purpose and importance of the multi-objective combined heat and power economic emission dispatch has to be considered since the co-generation system with two major objectives like fuel cost and emission mass, must be reduced. Thus, the non-convex and non-linear objective functions require the best optimization technique to resolve the issues. Hence, this paper presented an efficient CEED framework by developing novel optimization strategy. The enhanced Tasmanian devil optimization (ETDO) algorithm is developed in this work by enhancing the Tasmanian devil optimization (TDO) algorithm through the parameter regularization, and enhanced fitness function. Various complex benchmark datasets are considered in this work for the experimental verification. In addition, various standard power system problems of CEED are rectified with the help of the proposed ETDO to attain better efficacy than the previous systems. The objective function of the proposed ETDO-based heat and power unit optimization in the CEED problem is to reduce the overall fuel cost and emission. The performance analysis of the developed ETDO algorithm is varied based on iterations. Overall, the cost function analysis is performed using the developed model that shows as 16.3%, 8.8%, 12.7%, and 6.8% improved than HGSO, ESO, EVO, and TDO at the 50th iteration. This experimental analysis shows that the proposed ETDO for solving CEED issues performs well in complex environments and large-scale emission applications. Further experiments on the proposed ETDO are held by varying the total heat and power units to measure the reliability and robustness of the system.

An optimization-free approximation Framework for Connected and Automated Vehicles Eco-Trajectory Planning Under limited computing capacity

The trajectory planning problem (TPP) has become increasingly crucial in the research of next-generation transportation systems, but it presents challenges due to the non-linearity its constraints. One specific case within TPP, namely the Eco-trajectory Planning Problem (EPP), poses even greater computational difficulties due to its nonlinear, high-order, and non-convex objective function. This paper proposes an optimization-free framework to address the eco-trajectory planning problem of connected and automated vehicles (CAVs) under a limited computing capacity scenario. The framework consists of an offline module and an online module. In the offline module, an optimal eco-trajectory batch is constructed by solving a sequence of simplified optimization problems to minimize fuel consumption, considering various initial and terminal system states. Each candidate trajectory in the batch yields the lowest fuel consumption subject to a specific travel time from the vehicle entry to the departure from the intersection. In the online module, an approximation framework is proposed, which greatly improves the computational efficiency of planning and only suffers from a limited extent of optimality losses through a batch-based selection process because optimization and calculation are pre-computed in the offline module. Numerical tests are presented and discussed to evaluate the computational quality and efficiency of the optimization-free approximation framework under a mixed-traffic flow environment that incorporates human-driving vehicles (HDV) and connected and automated vehicles (CAVs) with different market penetration rates (MPR) and the stochasticity of HDVs.

Nonlinear convolutional sparse filtering with Gaussian fitting for rolling bearings compound fault diagnosis

The operational precision, stability, and lifespan of servo motors are directly influenced by the healthy operation of rolling bearings. Early diagnosis of bearing faults holds significant importance in enhancing the reliability of servo motors and preventing substantial economic losses and personal injuries. However, strong noise interference in industrial environments poses challenges to bearing fault diagnosis. Additionally, the difficulty in detecting single faults in bearings often leads to the occurrence of compound faults. To achieve compound fault diagnosis under intense noise interference in industrial environments, this paper proposes the nonlinear convolutional sparse filtering (NCSF). First, generalized sigmoid and Z-score normalization are utilized to amplify fault features and reduce the influence of irrelevant interference. Subsequently, multidimensional filters are learned based on a nonlinear objective function to achieve the separation of compound faults. Then, the Gaussian function is utilized to fit the trained filters, reducing the impact of low-frequency noise. Finally, the filtered signals are envelope demodulated to analyze fault types. The capability of NCSF to distinguish compound faults amid noise interference is confirmed by both experimental and simulation results. The proposed NCSF is an effective method to realize compound fault diagnosis under strong noise interference.

A High-Quality and Convenient Camera Calibration Method Using a Single Image

Existing camera calibration methods using a single image have exhibited some limitations. These limitations include relying on large datasets, using inconveniently prepared calibration objects instead of commonly used planar patterns such as checkerboards, and requiring further improvement in accuracy. To address these issues, a high-quality and convenient camera calibration method is proposed, which only requires a single image of the commonly used planar checkerboard pattern. In the proposed method, a nonlinear objective function is derived by leveraging the linear distribution characteristics exhibited among corners. An algorithm based on enumeration theory is designed to minimize this function. It calibrates the first two radial distortion coefficients and principal points. The focal length and extrinsic parameters are linearly calibrated from the constraints provided by the linear projection model and the unit orthogonality of the rotation matrix. Additionally, a guideline is explored through theoretical analysis and numerical simulation to ensure calibration quality. The quality of the proposed method is evaluated by both simulated and real experiments, demonstrating its comparability with the well-known multi-image-based method and its superiority over advanced single-image-based methods.

Ensembled snake optimiser to solve multiobjective mixed energy generation scheduling

This paper presents Ensembled Snake Optimiser (ESO), to optimise the scheduling of mixed energy generation from coordinated thermal, hydro, pumped-storage hydro, and solar units. It tackles operational constraints while minimising non-convex and non-linear objectives. To reduce the pollutants emitted and operating cost of thermal and solar units, the mixed energy generation scheduling problem uses committed hydro, thermal, and solar units to generate power, pumped-storage hydro units to maintain water levels, and hydro units to maximise available water volume. Utilising the water volume and actively exceeding the power-generating limit are the primary obstacles to satisfy the load requirement. The heuristics are utilised to satisfy the load demand and water volume constraints. The binary-optimistic approach commits solar units. The snake optimisation algorithm tends to get trapped in the local minima while solving complex engineering optimisation problems, which leads to sluggish convergence behaviour. A local search, simplex search, and extended opposition-based learning are investigated to improve its exploitation aspect, convergence behaviour, and procure good solutions. Three electric power systems are undertaken for the simulation studies. ESO gives better results. The significant cost savings for integrated energy scheduling are ranging from 10–15%. The rapid convergence behaviour and whisker box plots justify ESO’s robustness.

Method for prediction magnetic silencing of uncertain energy-saturated extended technical objects in prolate spheroidal coordinate system

Aim. Development of method for prediction by energy-saturated extended technical objects magnetic silencing based on magnetostatics geometric inverse problems solution and magnetic field spatial spheroidal harmonics calculated in prolate spheroidal coordinate system taking into account of technical objects magnetic characteristics uncertainties. Methodology. Spatial prolate spheroidal harmonics of extended technical objects magnetic field model calculated as magnetostatics geometric inverse problems solution in the form of nonlinear minimax optimization problem based on near field measurements for prediction far extended technical objects magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field COMSOL Multiphysics software package used. Nonlinear minimax optimization problems solutions calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction extended technical objects far magnetic field magnitude based on extended technical objects spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system using near field measurements with consideration of extended technical objects magnetic characteristics uncertainty. Originality. The method for prediction by extended technical objects magnetic cleanliness based on spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of magnetic characteristics uncertainty is developed. Practical value. The important practical problem of prediction extended technical objects magnetic silencing based on the spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of extended technical objects magnetic characteristics uncertainty solved. References 48, figures 2.

Centroid opposition-based backtracking search algorithm for global optimization and engineering problems

Evolutionary algorithms (EAs) have a lot of potential to handle nonlinear and non-convex objective functions. Particularly, the backtracking search algorithm (BSA) is a popular nature-based evolutionary optimization method that has attracted many researchers due to its simple structure and efficiency in problem-solving across diverse fields. However, like other optimization algorithms, BSA is also prone to reduced diversity, local optima, and inadequate intensification capabilities. To overcome the flaws and increase the performance of BSA, this research proposes a centroid opposition-based backtracking search algorithm (CoBSA) for global optimization and engineering design problems. In CoBSA, specific individuals simultaneously acquire current and historical population knowledge to preserve population variety and improve exploration capability. On the other hand, other individuals execute the position from the current population's centroid opposition to progress convergence speed and exploitation potential. In addition, an elite process based on logistic chaotic local search was developed to improve the superiority of the current individuals. The suggested CoBSA was validated on a set of benchmark functions and then employed in a set of application examples. According to extensive numerical results and assessments, CoBSA outperformed the other state-of-the-art methods in terms of accurateness, reliability, and execution capability.

Sparse-Coding Variational Autoencoders.

The sparse coding model posits that the visual system has evolved to efficiently code natural stimuli using a sparse set of features from an overcomplete dictionary. The original sparse coding model suffered from two key limitations; however: (1) computing the neural response to an image patch required minimizing a nonlinear objective function via recurrent dynamics and (2) fitting relied on approximate inference methods that ignored uncertainty. Although subsequent work has developed several methods to overcome these obstacles, we propose a novel solution inspired by the variational autoencoder (VAE) framework. We introduce the sparse coding variational autoencoder (SVAE), which augments the sparse coding model with a probabilistic recognition model parameterized by a deep neural network. This recognition model provides a neurally plausible feedforward implementation for the mapping from image patches to neural activities and enables a principled method for fitting the sparse coding model to data via maximization of the evidence lower bound (ELBO). The SVAE differs from standard VAEs in three key respects: the latent representation is overcomplete (there are more latent dimensions than image pixels), the prior is sparse or heavy-tailed instead of gaussian, and the decoder network is a linear projection instead of a deep network. We fit the SVAE to natural image data under different assumed prior distributions and show that it obtains higher test performance than previous fitting methods. Finally, we examine the response properties of the recognition network and show that it captures important nonlinear properties of neurons in the early visual pathway.

Simultaneous inversion of four physical parameters of hydrate reservoir for high accuracy porosity estimation

AbstractEstimation of the porosity of a hydrate reservoir is essential for its exploration and development. However, the estimation accuracy was usually less certain in most previous studies that simply assumed that there is a linear relationship between the porosity and single‐elastic wave velocities or other rock physical parameters, thus affecting the evaluation of the reserves. In the three‐phase Biot‐type equations that are fundamental to model a hydrate‐bearing reservoir, porosity, alongside hydrate saturation, mineral constituent proportions and hydrate–grain contact factor, is non‐linearly responded by density, compressional and shear wave velocities. To improve porosity estimation, we propose to invert simultaneously four‐parameter (porosity, hydrate saturation, mineral constituent proportions and hydrate–grain contact factor) using an iteratively nonlinear interior‐point optimization algorithm to solve a nonlinear objective function that is a summation of the squared misfits between the well log and three‐phase Biot‐type equation–modelled density, compressional and shear wave velocities. A test in Mount Elbert gas hydrate research well was conducted for the case of a gas hydrate stratigraphic test well where elastic wave velocities, density, porosity and mineral composition analysis data are available. The four‐parameter inversion yielded a lower root mean square error for porosity (0.0245) across the entire well‐logging section compared to previous estimations from the linear relationship, post‐stacked and pre‐stacked seismic traces as well as the pore‐filling effective medium theory model applied to other well cases. Additionally, the other three parameters demonstrated good agreement with well logs. Inversion tests conducted at three additional hydrate sites also produced accurate results. Consequently, the new method surpasses previous approaches in porosity estimation accuracy.

Unsupervised learning for efficiently distributing EVs charging loads and traffic flows in coupled power and transportation systems

With the escalating adoption of electric vehicles (EVs), the intricate interplay between power and traffic systems becomes increasingly pronounced. Understanding the distribution of charging loads and traffic flows are paramount for effective coordination. Traditionally, the distribution of EVs charging loads and traffic flows are obtained via solving the EVs traffic assignment problem with User Equilibrium (TAP-UE). Despite the general convexity of TAP-UE, the iterative nature of the prevailing solution process and the nonlinear objective function pose challenges, leading to prolonged solution times. This paper introduces a novel unsupervised learning-based framework aimed at efficiently distributing EVs charging loads and traffic flows without off-the-shelf solvers or a large dataset. Firstly, feasible paths are identified for each OD pair, eliminating the need for iterative procedures. Subsequently, the convexity-preserving reformulation of TAP-UE converts it into an unconstrained nonlinear optimization problem, leading to a properly designed loss function to guide neural networks in directly learning a legitimate OD demands-EVs loads-traffic flows mapping which satisfies the UE conditions. The incorporation of the Hessian matrix into the gradient update of network parameters, facilitated by the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm, enhances the convergence speed of the unsupervised learning process. Case studies are conducted to demonstrate the efficacy of the proposed framework.

Sparse Integer Programming Is Fixed-Parameter Tractable

We study the general integer programming problem where the number of variables n is a variable part of the input. We consider two natural parameters of the constraint matrix A: its numeric measure a and its sparsity measure d. We present an algorithm for solving integer programming in time [Formula: see text], where g is some computable function of the parameters a and d, and L is the binary encoding length of the input. In particular, integer programming is fixed-parameter tractable parameterized by a and d, and is solvable in polynomial time for every fixed a and d. Our results also extend to nonlinear separable convex objective functions. Funding: F. Eisenbrand, C. Hunkenschröder, and K.-M. Klein were supported by the Swiss National Science Foundation (SNSF) within the project “Convexity, geometry of numbers, and the complexity of integer programming” [Grant 163071]. A. Levin and S. Onn are partially supported by the Israel Science Foundation [Grant 308/18]. A. Levin is also partially supported by the Israel Science Foundation [Grant 1467/22]. S. Onn is also partially supported by the Dresner Chair at the Technion. M. Koutecký is partially supported by Charles University project UNCE 24/SCI/008, and by the project 22-22997S of the Grantová Agentura České Republiky (GA ČR).

Stochastic and robust truck-and-drone routing problems with deadlines: A Benders decomposition approach

Time-definite delivery service requires efficient and punctual delivery within specified deadlines. Enhancing the service level of delivery in last-mile logistics prompted the application of a truck-and-drone cooperative system. However, the inherent uncertainty in travel time contributes to frequent service delays. To address this challenge, our study addresses the stochastic and robust truck-and-drone routing problems with deadlines, aiming to minimize service delay risk under uncertainty. We leverage the sample average approximation (SAA) and robust optimization (RO) approaches to handle uncertainty in scenarios involving both big and small datasets. Benders decomposition (BD) algorithms are developed to solve the SAA and RO truck-and-drone routing problems efficiently. Numerical experiments showcase the algorithms’ effectiveness and reveal interesting insights. These findings suggest the importance of tailoring the approach to data availability for optimizing truck-and-drone delivery under uncertainty. Furthermore, the proposed model formulations and algorithms are generalized to address truck-and-drone routing problems under more complex scenarios, such as that with uncertainty of service time, or with nonlinear objective functions.

Solving Complex Optimisation Problems by Machine Learning

Most optimisation research focuses on relatively simple cases: one decision maker, one objective, and possibly a set of constraints. However, real-world optimisation problems often come with complications: they might be multi-objective, multi-agent, multi-stage or multi-level, and they might have uncertainty, partial knowledge or nonlinear objectives. Each has led to research areas with dedicated solution methods. However, when new hybrid problems are encountered, there is typically no solver available. We define a broad class of discrete optimisation problem called an influence program, and describe a lightweight algorithm based on multi-agent multi-objective reinforcement learning with sampling. We show that it can be used to solve problems from a wide range of literatures: constraint programming, Bayesian networks, stochastic programming, influence diagrams (standard, limited memory and multi-objective), and game theory (multi-level programming, Bayesian games and level-k reasoning). We expect it to be useful for the rapid prototyping of solution methods for new hybrid problems.

A novel application of artificial intelligence technology for outdoor high-voltage composite insulator

The distribution of the electric field plays a crucial role in evaluating the effectiveness of composite insulators. This research presents an innovative approach for optimizing the design of corona rings, aiming to decrease the electric field intensity in critical areas to satisfactory levels. The investigation examined the correlation among corona ring design variables and the intensity of the electric field close to the energized-end fitting in a 220 kV composite insulator equipped with a corona ring. Using design of experiment methods, the impact of three corona ring design parameters – corona ring diameter (R), ring tube diameter (Dr), and corona ring height (H) – was assessed. A novel nonlinear mathematical objective function was formulated, connecting the electric field magnitude to the structural parameters of the corona ring. Subsequently, the Bat algorithm, a bio-inspired optimization technique, was employed to enhance the initial corona ring design and mitigate the electric field intensity. Finally, the Finite Element Method (FEM) was utilized to simulate and evaluate the voltage distribution and electric field stress. The optimization process resulted in a substantial decrease in the highest electric field magnitude, by 58.6 % compared to the insulator with the threshold value, and 75 % when devoid of a corona ring. Additionally, the research highlighted the significant influence of ring tube thickness on the distribution of the electric field. The combination of experimental design and the Bat algorithm proved to be a powerful tool for optimizing the design of corona rings on transmission line composite insulators, providing precise solutions for optimizing corona discharge problems and enhancing the reliability of power transmission systems.

Optimization of air refractive index based on dispersive interferometry.

This study discusses the limitations of the multi-color method for air refractive index compensation and introduces the nonlinear objective refractivity optimization (NORO) to address these shortcomings. Utilizing a nonlinear objective function and the Davidon-Fletcher-Powel (DFP) optimization method, NORO provides precise, self-corrected geometric distance without the need for extensive environmental sensing or broad spectral coverage. Compared to the multi-color method, the NORO method reduces the minimum usable spectral range from 600 nm to 40 nm, achieving consistency with the empirical formula within 2.5 ppm using a 90 nm spectral range, significantly decreasing the dependence of algorithm accuracy on the spectral range. During a 4.5-hour long-term compensation, the relative residual compared to the empirical formula remains within 3 ppm, with a standard deviation of σE = 9.4 × 10-7. Additionally, in long-distance measurements compared with the empirical formula, the NORO method demonstrates an agreement within 1.89 × 10-7 m for distances up to 12 m, without requiring environmental parameter sensing.

Ultra-Fast Nonlinear Model Predictive Control for Motion Control of Autonomous Light Motor Vehicles

Advanced Driver Assistance System (ADAS) is the latest buzzword in the automotive industry aimed at reducing human errors and enhancing safety. In ADAS systems, the choice of control strategy is not straightforward due to the highly complex nonlinear dynamics, control objectives, and safety critical constraints. Nonlinear Model Predictive Control (NMPC) has evolved as a favorite option for optimal control due to its ability to handle such constrained, Multi-Input Multi-Output (MIMO) systems efficiently. However, NMPC suffers from a bottleneck of high computational complexity, making it unsuitable for fast real-time applications. This paper presents a generic framework using Successive Online Linearization-based NMPC (SOL-NMPC) for for the control in ADAS. The nonlinear system is linearized and solved using Linear Model Predictive Control every iteration. Furthermore, offset-free MPC is developed with the Extended Kalman Filter for reducing model mismatch. The developed SOL-NMPC is validated using the 14-Degrees-of-Freedom (DoF) model of a D-class light motor vehicle. The performance is simulated in matlab/Simulink and validated using the CarSim® software (Version 2016). The real-time implementation of the proposed strategy is tested in the Hardware-In-the-Loop (HIL) co-simulation using the STM32-Nucleo-144 development board. The detailed performance analysis is presented along with time profiling. It can be seen that the loss of accuracy can be counteracted by the fast response of the proposed framework.