Control Engineering Research Articles

Effects of hydrogen and methane anti-knocking characteristics on the efficiency and power output in argon power cycle engines

Argon Power Cycle (APC) combustion engine has a high efficiency, zero carbon emissions, and zero pollutant emissions, rendering it a promising way for achieving zero or carbon neutrality within the realm of internal combustion engine (ICE) technology. Previous studies have shown that while APCs significantly improve the thermal efficiency of ICEs, they also face serious knock problems due to their high temperatures and pressures, especially when hydrogen is used as a fuel. In this study, the anti-knocking characteristics of hydrogen, methane, carbon monoxide, and ammonia were first investigated in APC through thermodynamic calculations by Ignition Delay Time. Then, based on testbench experiments, hydrogen and methane fuels were selected to further investigate the effect of different fuel anti-knocking characteristics on the indicated thermal efficiency and power of APC combustion engine. Test results showed that when using hydrogen, the APC ICE exhibited a pronounced knock tendency, and the test engine could not operate stably when the excess oxygen ratio <2.1 at compression ratio = 9.6. The CA50 of the maximum efficiency point was delayed in APC than in air for both hydrogen and methane, specially H2 has an obvious lag at about 5–15 ° CA. In comparison, when using methane, the combustion control of engine is easier, and the peak indicated thermal efficiency 59% and the peak indicated mean effective pressure 0.92 MPa are higher than 54.3% and 0.60 MPa of using hydrogen. The use of hydrogen still needs an anti-knocking strategy while an extra carbon capture device is necessary to ensure a closed argon cycle if methane is employed.

Engineering Controls for Scaling CO2 Electrolyzers

The electrochemical CO2 reduction (CO2R) to ethylene on copper-based catalysts has garnered significant attention for its potential in sustainable industrial practices. While substantial progress has been achieved in the development of small-scale electrolyzers with geometric areas ranging from 1 to 5 cm2, the imperative to address larger scales for industrial decarbonization necessitates a shift in focus. There are inherent critical risks when scaling a nascent technology like CO2 electrolysis. There can be emergent phenomena observed only at larger scales, that can prevent it from reaching commercialization, such as change in local CO2 concentration, defects in the porous transport layer, and temperature gradients The optimized conditions for operating a 5 cm2 electrolyzer may not work well with a 25 cm2 electrolyzer leading to failures. Therefore, there is a need to develop a systematic way to test for these phenomena to address these challenges to successfully operate a CO2R electrolyzer at an industrially relevant scale. In this work, we highlight the performance of a Cu-based catalyst designed for the selective reduction of CO2 to ethylene across varying scales, ranging from 5 to 100 cm2. This investigation shows the changes in the electrolyzer performance at different scales. Our findings highlight the critical importance of implementing engineering controls to overcome challenges associated with the scaling of electrolyzers. Specifically, we explore the impact of anolyte flow rate, gasket compression, and electrochemical pulsing techniques on maintaining the desired selectivity of the electrocatalyst across different scales. By systematically adjusting these parameters, we demonstrate the ability to mitigate non-linear effects and uphold the efficiency of CO2 reduction to ethylene, even on larger electrode surfaces.This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

A novel scale-bridging method for MSMA linking continuum thermodynamics constitutive formulations to lumped system-level models

This work introduces a novel scale-bridging method between a continuum thermodynamics constitutive model and a lumped system-level model for magnetic shape memory alloys (MSMA). With this method, system models for real-time operations are generated based on virtual experiments using the constitutive model. The proposed method addresses the fact that, while constitutive models for MSMA typically only require small sets of parameters as input, their evaluation is still computationally expensive. System models for control engineering, however, require extensive experimental parameterization, while their evaluation is highly time-efficient. The proposed scale-bridging method has the potential to combine a small parameterization effort and a low computational cost of the real-time system model. Additionally, the constitutive model is utilized to investigate whether it can determine the individual behavior of MSMA samples. This is important since the inherent model parameters, while valid for ideal single crystals, deviate for non-ideal MSMA sample behavior. To this end, the MSMA constitutive model, based on a global variational principle originally proposed by Kiefer et al is supplemented by various extensions, including a more robust algorithmic treatment. A parameter identification procedure is introduced to optimize the constitutive model parameters based on an outer hysteresis curve for a particular load case. By conducting virtual experiments with the constitutive model, data sets are generated to parameterize Preisach hysteresis models as numerical approximations of the constitutive models. The resulting hysteresis models are compared with physical experiments using an MSMA test bench for different load cases. It is shown that the proposed scale-bridging method successfully generates hysteresis models derived from constitutive models. While maintaining accuracy comparable to strictly phenomenological models across various load cases (as validated through physical MSMA test bench experiments), these models require significantly less parameterization effort than classical system models. This translates to faster model creation and broader applicability.

Assessing the health risks of dermal exposure to heavy metals dust among nail salon technicians.

Nail salon technicians are susceptible to potential exposure to a diverse array of hazardous chemicals in the form of dust or vapors. One of the main routes of exposure is dermal contact. The aim of present study was to health risk assessment of dermal exposure to dust containing heavy metals in nail salon technicians. Dust sampling was done on the work surface of 20 available nail salon technicians. The concentration of five metals including cadmium, lead, chromium, nickel, and manganese were determined using ICP-MS. Afterwards, the United States Environmental Protection Agency (USEPA) guideline was used to estimate the potential health risks, including carcinogenic and non-carcinogenic risks, associated with the analyzed metals. Results indicated the mean concentrations of Pb, Cd, Ni, Cr and Mn were 0.7953±0.4373, 0.0952±0.0264, 0.7666±0.8629, 0.4900±0.5994 and 1.134±0.4736, respectively. The hazard quotient (HQ) of all metals was within the permissible value, while hazard index (HI) was greater than 1. The probability of cancer risk (CR) resulting from dermal exposure to Ni, Cd and Cr exceeded the acceptable risk levels (10-6-10-4), but CR calculated for Pb was less than allowable value. Implementation of engineering controls such as downdraft vented nail tables and portable source capture systems is necessary. Besides, the use of personal protective equipment such as disposable nitrile gloves, N95 respirator masks, and ensuring proper training on safe work practices is recommended.

Closed-Loop Control of Macrophage Engineering Enabled by Focused-Ultrasound Responsive Mechanoluminescence Nanoplatform for Precise Cancer Immunotherapy.

Macrophage engineering has emerged as a promising approach for modulating the anti-tumor immune response in cancer therapy. However, the spatiotemporal control and real-time feedback of macrophage regulatory process is still challenging, leading to off-targeting effect and delayed efficacy monitoring therefore raising risk of immune overactivation and serious side effects. Herein, a focused ultrasound responsive immunomodulator-loaded optical nanoplatform (FUSION) is designed to achieve spatiotemporal control and status reporting of macrophage engineering in vivo. Under the stimulation of focused ultrasound (FUS), the immune agonist encapsulated in FUSION can be released to induce selective macrophage M1 phenotype differentiation at tumor site and the near-infrared mechanoluminescence of FUSION is generated simultaneously to indicate the initiation of immune activation. Meanwhile, the persistent luminescence of FUSION is enhanced due to hydroxyl radical generation in the pro-inflammatory M1 macrophages, which can report the effectiveness of macrophage regulation. Then, macrophages labeled with FUSION as a living immunotherapeutic agent (FUSION-M) are utilized for tumor targeting and focused ultrasound activated, immune cell-based cancer therapy. By combining the on-demand activation and feedback to form a closed loop, the nanoplatform in this work holds promise in advancing the controllability of macrophage engineering and cancer immunotherapy for precision medicine.

Servo Control of a Current-Controlled Attractive-Force-Type Magnetic Levitation System Using Fractional-Order LQR Control

Recent research on fractional-order control laws has introduced the fractional calculus concept into the field of control engineering. As described herein, we apply fractional-order linear quadratic regulator (LQR) control to a current-controlled attractive-force-type magnetic levitation system, which is a strongly nonlinear and unstable system, to investigate its control performance through experimentation. First, to design the controller, a current-controlled attractive-force-type magnetic levitation system expressed as an integer-order system is extended to a fractional-order system expressed using fractional-order derivatives. Then, target value tracking control of a levitated object is achieved by adding states, described by the integrals of the deviation between the output and the target value, to the extended system. Next, a fractional-order LQR controller is designed for the extended system. For state-feedback control, such as fractional-order servo LQR control, which requires the information of all states, a fractional-order state observer is configured to estimate fractional-order states. Simulation results demonstrate that fractional-order servo LQR control can achieve equilibrium point stabilization and enable target value tracking. Finally, to verify the fractional-order servo LQR control effectiveness, experiments using the designed fractional-order servo LQR control law are conducted with comparison to a conventional integer-order servo LQR control.

Investigation on NOx control of a CI engine through the collective effect of hydrogen and biodiesel blend at modified compression ratio

The main challenges with using biodiesel in CI engines are higher NOx emissions and reduced brake thermal efficiency. These biodiesel-related issues can be handled by concurrently introducing gaseous fuels along with primary fuel into CI engines. This study examines the effects of hydrogen in a dual fuel mode operation with diesel and Calophyllum inophyllum biodiesel blend (B20) at different compression ratios on the engine's performance, combustion, and emission characteristics. A single-cylinder, 4-stroke, variable compression ratio engine operating at 1500 rpm was used for the research. A standard compression ratio (SCR) of 17.5 and a modified compression ratio (MCR) of 15.5 at a constant hydrogen flow rate of 6 L per minute (lpm) were used with diesel and B 20. The addition of hydrogen with diesel and B20 resulted in higher cylinder pressure and heat release rate when compared to pure diesel and B20 operation. This resulted in a shorter delay period (by an average of 9.4 % and 7.1 %) with lower peak pressure than pure diesel and B20 operation. During the dual fuel mode of H2 with B 20 at a modified compression ratio, the maximum heat release rate was decreased and its occurrence was retarded. NOx, UBHC, and CO emissions of the engine were decreased significantly by an average of 20.8% 43.7, %, and 22 % respectively with 37.7 % increase in smoke opacity. The increase in NOx emission with the use of H2 with diesel was reduced by operating H2 with B20 and at a reduced compression ratio. This lower emission was achieved with a compromise of a marginal decrease in engine brake thermal efficiency.

A multi-scale attention mechanism for detecting defects in leather fabrics

Defect detection is critical to industrial quality control in leather production engineering. The various sizes and locations of defects in leather, as well as significant differences within the same class and indistinctive variations between different classes of defects, contribute to the complexity of the problem. To address this challenge, we propose a Multi-Layer Residual Convolutional Attention (MLRCA) approach. MLRCA enhances its ability to capture both intra-class and inter-class differences by enhancing the semantic feature representation in the backbone network. To improve multiscale fusion effects, we also incorporate the MLRCA module into the feature pyramid network (FPN) and propose a new multi-layer residual convolution attention feature pyramid network (ML-FPN). This approach enables more accurate identification of leather defects at a more detailed level by selectively capturing contextual information from different domains. We then implement the Side-Aware Boundary Localization (SABL) detection head, which accurately locates defects and helps the network distinguish between similar defect categories for more precise positioning. To validate the effectiveness of our approach, we conducted ablation experiments on the created leather dataset. Comparative experiments demonstrate the excellent capability of our model to detect minor defects. The model achieved 83.4, 89.7, and 85.6 for the AP, AP50, and AP75 evaluation metrics. In addition, the model achieves 71.3, 89.9, and 88.9 for APS, APM, and APL. Our approach has been confirmed feasible through experimentation and provides new insights for automated leather defect detection methods.

The drug titration paradox: a control engineering perspective.

The drug titration paradox describes that, from a population standpoint, drug doses appear to have a negative correlation with its clinical effect. This paradox is a relatively modern discovery in anesthetic pharmacology derived from large clinical data sets. This review will interpret the paradox using a control engineering perspective. Drug titration is a challenging endeavor, and the medication delivery systems used in everyday clinical practice, including infusion pumps and vaporizers, typically do not allow for rapid or robust titration of medication being delivered. In addition, clinicians may be reluctant to deviate from a predetermined plan or may be content to manage patients within fixed goal boundaries. This drug titration paradox describes the constraints of how the average clinician will dose a patient with an unknown clinical response. While our understanding of the paradox is still in its infancy, it remains unclear how alternative dosing schemes, such as through automation, may exceed the boundaries of the paradox and potentially affect its conclusions.

Reverse engineering control of the relative phase and populations of two-level quantum systems

Reverse engineering control of the relative phase and populations of two-level quantum systems

Substantial Energy Band Modulation of Semiconducting Hexagonal GaTe Quantum Wells by Layer Thickness and Mirror Twin Boundaries.

Exploring emerging two-dimensional (2D) van der Waals (vdW) semiconducting materials and precisely tuning their electronic properties at the atomic level have long been recognized as crucial issues for developing their high-end electronic and optoelectronic applications. As a III-VI semiconductor, ultrathin layered hexagonal GaTe (h-GaTe) remains unexplored in terms of its intrinsic electronic properties and band engineering strategies. Herein, we report the successful synthesis of ultrathin h-GaTe layers on a selected graphene/SiC(0001) substrate, via molecular beam epitaxy (MBE). The widely tunable quasiparticle band gaps (∼2.60-1.55 eV), as well as the vdW quantum well states (QWSs) that can be strictly counted by the layer numbers, are well characterized by onsite scanning tunneling microscopy/spectroscopy (STM/STS), and their origins are clearly addressed by density functional theory (DFT) calculations. More intriguingly, distinctive 8|8E and 4|4P (Ga) mirror twin boundaries (MTBs) are identified in the ultrathin h-GaTe flakes, which can induce decreased band gaps and prominent p-doping effects. This work should deepen our understanding on the electronic tunability of 2D III-VI semiconductors by thickness control and line defect engineering, which may hold promise for fabricating atomic-scale vertical and lateral homojunctions toward ultrascaled electronics and optoelectronics.

Modulating charge distribution of MIL@CuFe-Se by in-situ interface engineering for high performance supercapacitors

Designing hybrid materials with ideal interfacial interactions derived from metal-organic frameworks (MOFs) remains significant but challenging for the realm of energy storage. Herein, a controllable dual interface engineering concept is proposed with the objective of eliminating the non-ideal effects by augmenting the interfacial contact area, enhancing the efficacy of charge transfer across interfaces. Specifically, electrode materials with dual interface (FeSe/Cu2Se and MIL/CuFe-Se) were well-designed by co-precipitation and in-situ selenide, where the FeSe/Cu2Se heterogeneous interface by in-situ selenitisation of CuFe prussian blue analogue (PBA) increases the surface roughness of nanocubes, enlarging the dual interfacial contact area of MIL/CuFe-Se and eliminating non-interfacial effects. Density Functional Theory (DFT) calculations confirm that the prepared electrodes exhibit both excellent rate performance and the ability to regulate interfacial charge transfer. Based on these advantages, the synthesised nanomaterials have a specific capacity of 913C/g at 1 A/g and a capacity retention of 86 % after 10,000 charge/discharge tests at 20 A/g. In addition, a hybrid supercapacitor (HSC) made of MIL@CuFe-Se (cathode) and activated carbon (AC, anode) has an energy density of 90 Wh kg−1 at 800 W kg−1 and a capacitance retention of 85.24 % after 10,000 cycles at 20 A/g. Remarkably, two MIL@CuFe-Se//AC HSC in series can illuminate a light emitting diode (LED) lamp, implying the potential application prospects. This study aims to identify a viable method for advancing the development of high-performance supercapacitor applications.

Predictability of human mobility during the COVID-19 pandemic in the United States.

Human mobility is fundamental to a range of applications including epidemic control, urban planning, and traffic engineering. While laws governing individual movement trajectories and population flows across locations have been extensively studied, the predictability of population-level mobility during the COVID-19 pandemic driven by specific activities such as work, shopping, and recreation remains elusive. Here we analyze mobility data for six place categories at the US county level from 2020 February 15 to 2021 November 23 and measure how the predictability of these mobility metrics changed during the COVID-19 pandemic. We quantify the time-varying predictability in each place category using an information-theoretic metric, permutation entropy. We find disparate predictability patterns across place categories over the course of the pandemic, suggesting differential behavioral changes in human activities perturbed by disease outbreaks. Notably, predictability change in foot traffic to residential locations is mostly in the opposite direction to other mobility categories. Specifically, visits to residences had the highest predictability during stay-at-home orders in March 2020, while visits to other location types had low predictability during this period. This pattern flipped after the lifting of restrictions during summer 2020. We identify four key factors, including weather conditions, population size, COVID-19 case growth, and government policies, and estimate their nonlinear effects on mobility predictability. Our findings provide insights on how people change their behaviors during public health emergencies and may inform improved interventions in future epidemics.

Unlocking ultra-high holographic information capacity through nonorthogonal polarization multiplexing

Contemporary studies in polarization multiplexing are hindered by the intrinsic orthogonality constraints of polarization states, which restrict the scope of multiplexing channels and their practical applications. This research transcends these barriers by introducing an innovative nonorthogonal polarization-basis multiplexing approach. Utilizing spatially varied eigen-polarization states within metaatoms, we successfully reconstruct globally nonorthogonal channels that exhibit minimal crosstalk. This method not only facilitates the generation of free-vector holograms, achieving complete degrees-of-freedom in three nonorthogonal channels with ultra-low energy leakage, but it also significantly enhances the dimensions of the Jones matrix, expanding it to a groundbreaking 10 × 10 scale. The fusion of a controllable eigen-polarization engineering mechanism with a vectorial diffraction neural network culminates in the experimental creation of 55 intricate holographic patterns across these expanded channels. This advancement represents a profound shift in the field of polarization multiplexing, unlocking opportunities in advanced holography and quantum encryption, among other applications.

Optimization of NOX emissions of a CRDI DIESEL engine using CMA-ES method

Engine calibration is the tuning of embedded parameters in the engine control unit (ECU) software to improve vehicle characteristics and meet legal requirements. Due to the stricter emission limits and rising customer expectations, current ECU software may include variables up to 30,000, which require very much time for engine calibration development. For this reason, automotive manufacturers continuously develop mathematical-based optimization methods to find optimum operating conditions for the engines. This study aimed to develop an online optimization algorithm to conduct automated dynamometer tests in the calibration development process. A modified covariance matrix adaptation (CMA) algorithm, which is an evolutionary strategy (ES) method belonging to meta-heuristic optimization, was integrated with an automation system for online calibration optimization. Some CMA method parameters such as step size and damping factor were initially revised to achieve the method to function efficiently in online engine calibration. Optimization was conducted at three different operating points of a 2-liter common rail direct injection (CRDI) diesel engine, where NOx emission mainly impacts the New European Driving Cycle (NEDC) results. The main injection timing, rail pressure, pilot injection quantity and timing, manifold pressure, and mass air flow were controlled in the optimization process. Optimization targets were determined according to the NOx-PM Pareto curve for each operating point. Covariance matrix adaptation was used to generate Pareto curves. Sixty-five measurements were taken for each operating point in the optimization process. Once optimization targets were determined, optimization occurred at each operating point. A total NOx emission reduction of 3.8% was obtained in the NEDC test, while fuel consumption and PM remained almost the same at steady-state operating points. The modified CMA-ES algorithm is expected to be an efficient method for online calibration optimization.

Controllable synthesis of carbon supported cobalt monoxide anode and high-voltage lithium cobalt oxide cathode with enhanced lithium-ion storage

Natural macromolecule amylose (AM) is employed to deoxygenate few-layered graphene oxide (GO) and modulate the surface interaction between GO sheets and Co2+ ions under mild hydrothermal conditions. The obtained Co2+ ions and AM molecule jointly decorated reduced graphene oxide (Co-AM/RGO) sample is further utilized to synthesize both anode and cathode materials with controlled microstructures. To synthesize anode material, the Co-AM/RGO can be directly converted to a hierarchical AM pyrolyzed carbon and RGO supported cobalt monoxide nanocomposite (CoO@AMC/RGO) after a simple inert gas protected thermal treatment. To synthesize cathode material, a carbon coated nano-sized lithium cobalt oxide sample (LiCoO2/C, LCO/C) can be obtained after a solid-state reaction in air by mixing lithium salt with the Co-AM/RGO. The CoO and LCO nanocrystals with significantly controlled sizes are well dispersed in the carbon matrices. The CoO@AMC/RGO anode shows a high reversible capacity of 785.25 mAh·g−1 after 500 cycles at 200 mA·g−1 and 608.25 mAh·g−1 after 700 cycles at 1000 mA·g−1, while the LCO/C cathode delivers a superior reversible capacity of 140.91 mAh·g−1 after 1000 cycles at 1000 mA·g−1 with a high cut-off voltage of 4.6 V. This work provides a new perspective for controllable engineering of electrode materials with enhanced lithium-ion storage performances.

Parallel dual adaptive genetic algorithm: A method for satellite constellation task assignment in time-sensitive target tracking

The evolution of satellite surveillance technology, bolstered by advanced onboard intelligent systems and enhanced attitude maneuver capabilities, has thrust mission scheduling and execution into the spotlight as a prominent and dynamic research field in recent years. As the demand intensifies for mission scheduling and execution to transition from static ground targets to time-sensitive moving targets, conventional scheduling methods often fall short of delivering satisfactory results for continuously tracking these dynamic targets with constellation. The paper introduces a rapid yet efficacious satellite constellation task assignment method, termed the Parallel Dual Adaptive Genetic Algorithm (PDA-GA), for the task assignment of multiple moving target tracking. Specifically, the dual adaptive mechanism isolates the genetic algorithm’s sensitivity to parameters, while the parallel mechanism increases the evolutionary process’s computation speed by deploying complex computations to the GPU. Based on the meticulous analysis of the relevant factors that need to be considered in real tracking scenarios, the proposed PDA-GA can improve the search quality and efficiency of the task assignment solution. We conduct an extensive array of contrast and ablation experiments to showcase the performance and efficiency of PDA-GA in conjunction with autonomous attitude control algorithms across five simulated tracking scenarios. Furthermore, to enable high-fidelity simulation of tracking scenarios, we introduce the Constellation Target Tracking Environment (CTTE), which is equipped with a physics engine and algorithms for multi-satellite task assignment and single-satellite attitude control. This endeavor lays a foundation for future research endeavors focused on autonomous tracking of multiple time-sensitive moving targets within large-scale constellation.

Optimal control for helicopter/turboshaft engine system based on hybrid variable speed

In order to address the limitation of fixed-ratio transmission (FRT), which compromises the attainment of both optimal main rotor speed and optimal power turbine speed, an optimal speed control method based on hybrid variable speed (HVS) is proposed. Firstly, based on the integrated performance calculation model of helicopter/turboshaft engine system, the distribution factors of variable speed are applied, and the integrated optimization method of optimal speed is proposed based on the minimum engine fuel flow. Subsequently, an online estimation technique employing a high-order filter is devised and engineered to achieve superior cascaded control of turboshaft engines. Finally, a novel real-time optimal speed control method based on hybrid variable speed is proposed. The simulation results under different operation conditions demonstrate that regardless of whether it is FRT or HVS, the optimal main rotor speed increases with forward velocity. In the case of HVS, turboshaft engine degradations have a significant impact on the optimal power turbine speed rather than optimal main rotor speed. Adopting an estimation method based on high-order filtering for gas turbine rotational acceleration proves more advantageous in mitigating high-frequency oscillation and continuous saltation of estimated values. Moreover, in comparison with the optimal speed control method of FRT, HVS-based approach enables simultaneous attainment of the optimal main rotor speed and power turbine speed, thereby enhancing the overall efficiency of the integrated helicopter/turboshaft engine system and significantly decreasing engine fuel consumption by over 2%. Consequently, there has been a remarkable enhancement in the overall performance of the integrated helicopter/turboshaft engine system.

Thermally and Mechanically Stable Perovskite Artificial Synapse as Tuned by Phase Engineering for Efferent Neuromuscular Control.

The doping of perovskites with mixed cations and mixed halides is an effective strategy to optimize phase stability. In this study, we introduce a cubic black phase perovskite CsyFA(1-y)Pb(BrxI(1-x))3 artificial synapse, using phase engineering by adjusting the cesium-bromide content. Low-bromine mixed perovskites are suitable to improve the electric pulse excitation sensitivity and stability of the device. Specifically, the low-bromine and low-cesium mixed perovskite (x = 0.15, y = 0.22) annealed at 373 K allows the device to maintain logic response even after 1000 mechanical flex/flat cycles. The device also shows good thermal stability up to temperatures of 333 K. We have demonstrated reflex-arc behavior with MCMHP synaptic units, capable of making sensory warnings at high frequency. This compositionally engineered, dual-mixed perovskite synaptic device provides significant potential for perceptual soft neurorobotic systems and prostheses.

Method of Equivalent Error as a Criterion of the Assessment of the Algorithms Used for Estimation of Synchrophasor Parameters Taken from the Power System.

The development of digital techniques in control engineering leads to the creation of innovative algorithms for measuring specific parameters. In the field of electric power engineering these parameters may be amplitude, phase and frequency of voltage or current occurring in the analyzed electric grid. Thus, the algorithms mentioned, applied in relation to the quoted parameters, may provide precise and reliable measurement results in the electric grid as well as ensure better grid monitoring and security. Signal analysis regarding its identification due to the type of interference is very difficult because the multitude of information obtained is very large. In order to indicate the best method for determining errors in measuring synchronous parameters of the measured current or voltage waveforms, the authors propose in this paper a new form of one error for all testing functions, which is called an equivalent error. This error is determined for each error's value defined in the applicable standards for each of selected 15 methods. The use of the equivalent error algorithm is very helpful in identifying a group of methods whose operation is satisfactory in terms of measurement accuracy for various types of disturbances (both in the steady state and in the dynamic state) that may occur in the power grid. The results are analyzed for phasor measurement unit (PMU) devices of class P (protection) and M (measurement).