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This paper focuses on solving the problem of the thrust ripple of the permanent magnet linear synchronous motor (PMLSM) to improve the machining accuracy and stability of the precision platform. The air gap magnetic field model of the permanent magnet magnetic field and the armature permanent magnet magnetic field are established using the equivalent magnetization method and the equivalent current method. The mathematical model of the linear motor is then derived using Clark and Park coordinate transformation. Also, the dynamic equation of the linear motor is developed considering the influence of electromagnetic thrust, detent force, and friction force. The error expressions resulting from thrust ripple are provided. To eliminate the thrust ripple and enhance the accuracy of the linear motor, a linear thrust observer is utilized to compensate for the low-frequency thrust ripple. The compensation current for the thrust ripple is then incorporated into the servo system using a new sliding mode controller. Additionally, a double T-Notch filter is designed to eliminate the interference signal caused by occasional resonance at a specific frequency, thereby ensuring the stability of the system output. Finally, experimental validation is conducted to verify the effectiveness of the proposed strategy, and the results demonstrate a significant improvement in thrust fluctuation and tracking accuracy. [ABSTRACT FROM AUTHOR]

Currently, there are demands for machine tools with higher dynamic performance as a result of their high machining accuracy and efficiency in designing complex parts in the manufacturing industry. The motion delays in each of the motion axes cause dynamic tracking errors or tool tracking errors which greatly affect the surface quality of machined parts; hence, tuning the dynamic parameters like the position gains of the motion axis causing the defect is as good as eliminating the error source rather than tuning the parameters of all the motion axes. This work proposes a decoupling method to identify the particular motion axis that greatly affects or causes the tool tracking error by using the ISO BK3 kinematic test, and this involves orientation contour error estimation and motion axis error computation based on inverse kinematics of the machine tool transformation. An experiment was carried out on an industrial machine tool with a tilting rotary table to verify the simulation results; the feed servo system model of the motion axes was constructed using MATLAB Simulink tools. The results obtained show that the tool tracking errors are greatly influenced by some dynamic parameters like the feedrate and the position gains emanating from a particular motion axis with dynamic deficiency, and the proposed decoupling method robustly identifies the individual motion axes greatly affecting the dynamic tracking error which makes it very relevant to tune only the dynamic parameters of those particular motion axes instead tuning all. Moreover, this method is simple and robust, and its implementation can help improve the dynamic performance of machine tools in the manufacturing industry. [ABSTRACT FROM AUTHOR]

We analyze the effect of leverage on tax-managed public equity strategies for different types of investors by running back-tests on hypothetical portfolios. We found the average 130/30 long/short portfolio funded with cash generates 2.7 times more capital losses than the average long-only portfolio over the first 10 years. For an investor with a sufficient supply of short- and long-term gains, these additional losses translate to average pre-liquidation tax alpha ("TA") of 4.41% per year. Liquidation reduces TA by about half, while a lack of short-term capital gains to offset reduces TA by approximately 40%. In combination, those investor characteristics may render a long-only loss harvesting portfolio or a low-cost ETF more desirable than a long/short tax-managed equity portfolio after costs and fees are taken into consideration. Leverage can also be used to revitalize an ossified portfolio whose loss-generating capacity has diminished. [ABSTRACT FROM AUTHOR]

In the original iterative learning control (ILC) algorithm, it is commonly assumed that the target signal remains constant throughout iterations. However, this assumption may not be satisfied in practical industrial applications. Therefore, this paper proposes a novel ILC approach for non-normal and biased measured targets, in which the target is not predetermined by a fixed curve or formula but generated from the generation system. The iterative learning control problem is first formulated, followed by algorithm implementation through mechanism analysis, process determination, and assessments for feasibility and convergence. The proposed algorithm is simulated subsequently. Results demonstrate that application of this algorithm can effectively minimize expected error between non-normal and biased measured targets and output. After a sufficient number of iterations, the tracking error will originate solely from the trajectory itself. [ABSTRACT FROM AUTHOR]

An analysis of the tracking error was performed without taking into account the pulsations of the electric motor supply voltage and taking into account the pulsations of the electric motor supply voltage. The results of the calculation of the constant tracking error are presented, taking into account the influence of pulsations, which is a consequence of the pulse width modulation (PWM) process. Ref. 7, fig. 2.

Abstract In the feedrate scheduling of complex curve direct interpolation, dynamic constraints such as axis acceleration and jerk are related to the actual state of the tool. Most existing methods convert dynamic constraints to velocity constraints at sampling points. However, it cannot guarantee the dynamic constraints are satisfied between sampling points. Addressing the issue, this paper proposes a dynamic look-ahead feedrate scheduling method based on sliding mode velocity control, which generates the motion command considering dynamic constraints in every interpolation cycle. To dynamically generate commands based on the current tool state, the acceleration and deceleration method based on sliding mode velocity control has been proposed, which can control tool state to transition to the command state with any initial state. To ensure sufficient distance for acceleration and deceleration, this paper uses braking distance to dynamically estimate the look-ahead distance. Then the minimum value within the look-ahead interval is selected as the command velocity for this scheduling cycle and the actual motion command is determined based on the dynamic constraints of each axis. Simulation and experiment results prove that compared with the existing method, this method effectively reduces the overshoot of dynamic constraints without significantly increasing the machining time. The analysis of real-time computation time has demonstrated the potential of the method proposed in this paper for real-time applications.

Tracking errors are caused by the amplitude attenuation and phase lag of the servo system to the command. Based on the mechanism, this study proposes the method of command correction which magnifies the amplitude and advances the phase of the command according to the amplitude attenuation and phase lag of the servo system. Firstly, the command is decomposed into stable components and unstable components using Fourier series fitting and Hilbert-Huang transform. Then, the frequency-domain characteristics of the servo system are used to calculate the amplitude attenuation and phase lag of each component. Finally, the stable components and unstable components of the command are corrected by amplifying the amplitude and advancing the phase to compensate for the attenuation and lag caused by the servo system. The experimental results show that the corrected command reduced the average tracking error of the X-axis of the butterfly-shaped trajectory by 66.58 % and the maximum tracking error by 72.28 %. Moreover, the contour error of the butterfly-shaped trajectory was reduced significantly. The proposed method is suitable for the tracking errors and contour error controlling of a trajectory with a drastic curvature change. • The commands are modified in the frequency domain, thereby offsetting command attenuation and lag by the servo system. • By combining Fourier series and Hilbert-Huang frequency analysis techniques, reasonable commands decomposition is realized. • Stable components and highly variable frequency components of the commands are processed separately in this study. [ABSTRACT FROM AUTHOR]

Using a unique database that includes publicly disclosed fund holdings at the end of the quarter as well as the holdings in all non-publicly disclosed months, we found that some funds could alter their portfolios in publicly disclosed months to artificially increase their Active Share scores and consequently appear more active and take advantage of the positive relationship between Active Share and money flows. We show how, consistent with non-informed trades, these funds erode their future performance. However, these funds reach their objective of increasing future money flows. Moreover, we find that window-dresser funds can be identified by controlling the level of tracking error. The funds with high Active Share scores and low tracking errors have the highest levels of Active Share window dressing and the worst future returns. However, compared with less active funds, they are able to capture higher money flows. [ABSTRACT FROM AUTHOR]

The stability of each train, high control accuracy, and minimum safe separation distance are important indexes to measure the performance of the cooperative control system of multiple trains. In this article, aiming at the problem of low accuracy of multiple trains cooperative control with nonlinear running resistance and external disturbance, the distributed cooperative robust adaptive control scheme for multiple trains with RBFNN position output constraints based on train running curve tracking is proposed. Multiple different control techniques are offered for different trains, and that they are based on local knowledge of position, speed, and acceleration. The leading train's speed and position precisely match the planned operation curve, while the following train keeps the tracking interval at the minimum safe distance between two trains. In order to reduce the influence of the uncertainty of basic resistance parameters and external interference on the cooperative control of multiple trains, the parameter uncertainties are compensated by adding a robust adaptive law to the multiple trains control based on position output constraints. The lumped exogenous disturbances (additional resistance, external interference, measurement noise, etc.) are estimated using an RBFNN approximator for the unknown term of the cooperative system. The stability of the cooperative operation of multiple trains is confirmed using the Lyapunov stability theorem. The performance of the proposed scheme was evaluated by the cooperative control system of multiple trains in predecessor following (PF) and bidirectional control (BC) modes. [ABSTRACT FROM AUTHOR]

The contour following task of a multi-axis servo system is one of the most important applications of modern computer numerical control (CNC) machining. Reducing the contour error is an important content in the multi-axis contour following task. A common method to solve this problem is the cross-coupling control (CCC). Since the traditional CCC method cannot meet the requirements of tracking accuracy and contour control accuracy at large curvature positions in free-form curve machining, the main contribution of this paper is to propose a novel integrated control strategy based on arc length parameters for contour error compensation, which consists of a double-circle weighted approximation contour error estimation model based on arc length parameters module, an improved cross-coupling position command shaping controller (CPCSC) module, and an improved position error compensator (PEC) module. To improve the accuracy of contour error estimation for large free-form curvature trajectories, a double-circle weighted approximation contour error estimation model based on arc length parameters is proposed. The method first finds the nearest interpolation point by backtracking method and calculates the backward reference points by using the method based on arc length parameters. Then, the obtained backward reference points are used as the expected instruction points by the double-circle weighted approximation method, and the estimated value of contour error is calculated. Moreover, an improved structure of CPCSC is proposed. Compared with the traditional biaxial CCC structure, the advantage of this new structure is that the compensator design and stability analysis in its CCC are relatively simple, and it can be easily implemented on most current systems by reprogramming the reference position command subroutine. In addition, an improved PEC method is further proposed to reduce contour error. The main advantage of this module is that it can simultaneously improve tracking and contouring performances by compensating position errors in advance. The feasibility of the proposed integrated control strategy is verified by serval non-uniform rational B-spline (NURBS) parametric curve contour following experiments. Moreover, the results of comparative experiments indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy of biaxial contour following tasks compared with none-CCC method and CCC method, and has better contour control performance in large curvature positions. [ABSTRACT FROM AUTHOR]

The index tracking problem consists of constructing a portfolio that has the closest performance of a given index as possible, with fewer assets in its composition. When considering a large number of assets, including all of them on the solution may incur high transaction fees, harming the accumulated returns in the long term. The constraint that limits the portfolio size imposes a combinatorial nature on the problem and the computation of the optimal solution becomes infeasible as the universe of assets grows. To get around this issue, pure and hybrid metaheuristics have been proposed in the literature to achieve good solutions in practical time. Different from pure metaheuristics, hybrid metaheuristics do not need any constraint handling or solution repairing approaches since they often use general-purpose solvers to adjust portfolio weights. This work presents a comparison between pure and hybrid genetic algorithms, which is one of the most popular heuristics applied in the portfolio selection field. We considered linear and nonlinear index tracking models in the experiments, where the GA that obtained the best performance in a single period optimization strategy, was selected to backtest in a dynamic index tracking approach. The results showed that hybrid GAs can compute good or even better solutions than the CPLEX solver and pure GAs, in a shorter time. [ABSTRACT FROM AUTHOR]

Abstract Passive investments such as exchange-traded funds (ETFs) provide an opportunity to invest in indexes, asset classes, and sectors with low maintenance costs and high transparency. Today ETFs dominate the world, with nearly 50% of the investment in the USA coming through ETFs. Numerous studies on specific aspects on ETFs have been done earlier; however, considering the scarcity of thorough summaries in the existing body of literature, this bibliometric and systematic review aims to adopt a methodical approach with the goal of delivering qualitative and quantitative understanding of ETFs, while highlighting general research trends. The authors analyzed 2058 articles associated with ETFs from the Scopus database during the last 50 years, i.e., from 1973 till date. The search was initially conducted using title, keyword, and abstract, yielding 2058 articles, which were narrowed to only include research papers and review papers, resulting in a final count of 958 items. The most important authors, highest cited articles, prominent journals, important themes, and associated countries have been identified using bibliometric research. The numerical and visual representations of the analysis show that ETFs are a widely studied research area, and the enormous rise in publications in 2020, 2021, and 2022 demonstrates that researchers are quite interested in the topic. According to affiliation statistics, most research is focused in the USA together with other developed nations, opening new options for the research on ETFs in relation to developing economies. The current analysis reconciles numerous exchange-traded fund studies associated with volatility, liquidity, risk-return trade-off, and tracking errors and identifies possible research gaps. Some of the emerging topics that evolved in passive investments include the use of machine learning, AI, and the emergence of ETFs associated with ESG and sustainability. This research will help lawmakers, scholars, and regulators understand the core principles of ETFs and identify areas that deserve additional investigation.

In order to enhance the efficiency of agricultural machinery in orchard rows and minimize harm to personnel caused by pesticide spraying, this study developed a GNSS-based (Global Navigation Satellite System) automatic navigation driving system for tracked orchard sprayers. The tracked sprayer was used as a platform for this research. We constructed both a crawler hydraulic platform and spraying working parts based on orchard operation requirements. Additionally, we designed the hydraulic and electrical sub-control process of the crawler platform. By utilizing the motion model of the tracked mobile platform, we designed a linear path tracking control method using position deviation and heading deviation as state quantities. This allows the research platform to automatically initiate and terminate, travel in a straight line between rows, and complete spraying operations. Experimental verification confirmed that the tracked sprayer designed in this study successfully achieves automatic driving. The best automatic driving performance is achieved at a speed of 1.0 m/s. When the sprayer's speed is 1.2 m/s, the maximum value of the straight-line path tracking accuracy of the platform's automatic driving is better than 5.6 cm, with a standard deviation of 2.8 cm. This system effectively meets the requirements of automatic operation for an automatic spraying machine, thereby establishing a foundation for the implementation of automatic spraying operations in orchards. [ABSTRACT FROM AUTHOR]

By the evolution of context-aware application, indoor location positioning gains much more attention worldwide. Radio Frequency Identification (RFID) is one such wireless positioning technology adopted widely. Moreover, enhancing the tracking accuracy and thus reducing the tracking error remains a challenging task in RFID based indoor environment. So as to overcome this aspect, a localization and tracking method depending on virtual reference tag (VRT) is employed in the indoor environment. This research work includes four modules like (i) data collection and Received Signal Strength Indication (RSSI) estimation;(ii) Optimal allocation of VRT using Spider Monkey Optimization (SMO) at which the allocation of VRT is made by considering number of tags, environmental factors (humidity and temperature), and SNR. Based on this data, the RFID reader allocates VRT for each grid so as to increase the tracking accuracy; (iii) Artificial Neural Network (ANN) module-based localization at which the localization of unknown tags is made; and (iv) tracking of moving target tag is carried based on Aquila Swarm Optimization-Long short-term memory (ASO-LSTM) approach. The optimization at this stage is employed to choose optimal position which enhances the accuracy of tracking. Thus, finally the location estimation is carried by this approach. The simulation is carried in NS3.26 network simulator and the performance are estimated in terms of SNR, tracking error, mean error, tracking accuracy, mean time, and standard deviation. The performance value is then compared with traditional models to show the enhancement of proposed mode over the other conventional techniques. [ABSTRACT FROM AUTHOR]

Passive investments such as exchange-traded funds (ETFs) provide an opportunity to invest in indexes, asset classes, and sectors with low maintenance costs and high transparency. Today ETFs dominate the world, with nearly 50% of the investment in the USA coming through ETFs. Numerous studies on specific aspects on ETFs have been done earlier; however, considering the scarcity of thorough summaries in the existing body of literature, this bibliometric and systematic review aims to adopt a methodical approach with the goal of delivering qualitative and quantitative understanding of ETFs, while highlighting general research trends. The authors analyzed 2058 articles associated with ETFs from the Scopus database during the last 50 years, i.e., from 1973 till date. The search was initially conducted using title, keyword, and abstract, yielding 2058 articles, which were narrowed to only include research papers and review papers, resulting in a final count of 958 items. The most important authors, highest cited articles, prominent journals, important themes, and associated countries have been identified using bibliometric research. The numerical and visual representations of the analysis show that ETFs are a widely studied research area, and the enormous rise in publications in 2020, 2021, and 2022 demonstrates that researchers are quite interested in the topic. According to affiliation statistics, most research is focused in the USA together with other developed nations, opening new options for the research on ETFs in relation to developing economies. The current analysis reconciles numerous exchange-traded fund studies associated with volatility, liquidity, risk-return trade-off, and tracking errors and identifies possible research gaps. Some of the emerging topics that evolved in passive investments include the use of machine learning, AI, and the emergence of ETFs associated with ESG and sustainability. This research will help lawmakers, scholars, and regulators understand the core principles of ETFs and identify areas that deserve additional investigation. [ABSTRACT FROM AUTHOR]

In the applications of multi-axis computer-numerical-control (CNC) precision machining, one of the important issues in the multi-axis contour following task is to reduce the contour error in the machining process. A popular method to solve this problem is the cross-coupling control (CCC). As the traditional CCC method cannot meet the requirements for tracking accuracy and contour control accuracy for large curvature positions, a novel integrated control strategy of cross-coupling contour error compensation, which consists of an improved real-time contour error estimation algorithm based on arc length parameters, an improved position error compensator (PEC) and a single neuron cross-coupling controller, is proposed. To improve the accuracy of contour error estimation for large curvature trajectories, an improved real-time estimation algorithm of contour error based on arc length parameters is proposed. The method first finds the nearest interpolation point by backtracking method and calculates the backward reference point by using the method based on arc length parameters. Then, the obtained backward reference point is used as the desired command point by arc approximation method to find the estimated value of contour error. Moreover, a single-neuron adaptive cross-coupling controller is designed, which continuously adjusts the weights through a single-neuron learning algorithm to reach the effect of improving the control accuracy. In addition, an improved PEC method is further presented, which improves the tracking accuracy by compensating the tracking error in advance. The feasibility of the proposed integrated control strategy is verified with several non-uniform rational B-spline (NURBS) parametric curve contour following experiments. Moreover, experimental results indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy of biaxial contour following tasks compared with None CCC method and CCC method and has better contour control performance in large curvature positions. [ABSTRACT FROM AUTHOR]

In machine tools, the trajectory error of the tool center point (TCP) is caused due to the dynamic positioning error of feed drive systems according to the relationship in spatial structure and motion. The dynamic positioning error of the feed drive system includes axial dynamic error and lateral dynamic error. To analyze the influence of the lateral dynamic error on the trajectory error of the TCP of multi-axis machine tools, in this study, circular and butterfly trajectories were designed as the set trajectories of a machine tool with three linear axes. In addition, the tracking error models were constructed both considering the lateral dynamic error and without considering the lateral dynamic error, and the difference between the two models was quantified. The Sobol method was then used to analyze the sensitivity of the lateral dynamic error of the feed drive system to the tracking error of the TCP. Finally, experiments were performed on a three-axis machine tool. The results show the maximum lateral dynamic error in the direction perpendicular to the motion direction is 0.026 mm. The lateral dynamic error detrimentally affects the tracking error and contour error of the TCP in multi-axis machine tools. [ABSTRACT FROM AUTHOR]

A new multifunctional proportional control triaxial stress loading apparatus is presented in this study, which can apply an output force on coal rock to simulate the conditions of triaxial stress loading, aiming at solving the problems of excessive consideration of static indices in the design and the incompleteness of the simulation and test verification system for the test parts at the performance analysis stage. This apparatus mainly combines the configuration of a triaxial stress loading system which can meet the stress loading requirements under different operating conditions, with the effective integration of multiple pressure loading operations based on the electrohydraulic proportional control method. In this context, a pressure and position combined control strategy based on the sliding mode is proposed to control the vertical and longitudinal loading hydraulic cylinders. Then, a co-simulation mode including the triaxial stress loading hydraulic system is established to verify the control strategy, system response characteristics and selection of the controller parameters. Furthermore, a multifunctional stress loading experimental platform is developed, and the stress loading characteristics with the proposed strategy are tested and analyzed. The results show that the triaxial stress loading hydraulic system can meet the response characteristics, the fluctuating deviation of the constant loading test can be restricted to 8.5%, the tracking error of the variable loading test is small, the minimum response time of instantaneous loading can reach 2.8 s, and the stress loading effect is noticeable. The experimental platform fully indicates that the stress loading system with the state perception and processing method as the core can meet a variety of verification indices of constant, variable and instantaneous loading tests. This research provides technical support for the smooth, synchronous control and intelligent operation of various types of hydraulic actuator machines. • A new multifunction proportional control triaxial stress loading apparatus is presented. • A state perception and processing method is illustrated to realize the effective integration of multipleloading operations. • A viable control strategy and controller are designed to the force control that rejecting the fluctuate deviation. • The coupled position and pressure loading controller are designed utilizing a sliding mode control method. • Experiment results are executed to verify the control effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This study aims to determine the analysis of factors that affect the performance of stock and bond-based ETFs on the Indonesian stock exchange. This research was conducted on stock and bond-based ETFs listed on the Indonesian stock exchange for the period 2019-2021. The sampling technique used in this research is purposive sampling. The samples in this study were 13 stock-based ETFs and 1 bond-based ETF sourced from Bloomberg, the Indonesian stock exchange website, ETF prospectus and asset management website. The data analysis method used is panel data regression analysis with the EViews program tool. The results of this study indicate that Risk affects the performance of stock and bond-based ETFs, Tracking Errors affect the performance of stock and bond-based ETFs, Expense Ratio has no significant impact on the performance of stock and bond-based ETFs. Key Words: ETFs, Risk, Tracking Error, Expense Ratio, Stock, Bond

Machine tools with high dynamic performance are in high demand currently in the manufacturing industry due to their high machining accuracy and efficiency in manufacturing complex parts. Though the S-shaped test piece shows much improvement over the standard cone-frustum test piece even under the non-machining dynamic performance test, however, the S-shaped test piece is still under development and there has been a call for a new test piece better than it. Therefore, the Scone test piece, which combines the geometric and the kinematic features of the S-shaped and the cone-frustum test pieces, has been proposed; this work objectively validates the dynamic performance of the five-axis machine tool based on the trajectory of the Scone test piece. The RTCP trajectory test is used to build the R-test process which involves the simultaneous movement of all five axes, and the results of the S-shaped and the cone-frustum part trajectory test are compared to that of the Scone part; an experiment was conducted on an industrial five-axis machine tool, with a tilting rotary table, to verify the simulation results. According to the results obtained, the Scone test is more sensitive to the dynamic tracking errors of the machine tool than the cone-frustum and the S-shaped tests under the same conditions; hence, the Scone trajectory based on the kinematic test can better reflect the dynamic performance of the five-axis machine tool. [ABSTRACT FROM AUTHOR]

This manuscript presents a control law based on the kinematic control concept and the input–output linearization approach. More specifically, the given approach has the structure of a two-loop controller. A rigorous closed-loop system analysis is presented by using known theory on perturbed systems. By assuming that the desired velocity in the body frame is persistently exciting, the uniform bound of the tracking error in earth coordinates is ensured. A simulation study using practical mobile robot parameters shows the viability of the introduced approach. In addition, two known trajectory tracking controllers are simulated in order to compare the performance of the proposed technique. Better tracking accuracy is obtained with the proposed control approach, even if uncertainties in the knowledge of the friction coefficients are presented. [ABSTRACT FROM AUTHOR]

In the manufacturing industry, there is an extensive use of high-precision motion control techniques to achieve high performance in the feed drive system. This study deals with the simple adaptive control (SAC) technique for simultaneous high-precision motion and energy-saving of the feed drive system. The application of the SAC requires that the "almost strictly positive real (ASPR)" property is satisfied and there is a command general tracking solution for the plant and the reference model. This paper presents to use the jerk-based augmented output signal for the ASPR property. The proposed approach allows the SAC to track the desired signal at high frequencies more precise and is achieved by placing the zeros of the system at effective locations. To verify the feasibility of the proposed approach, simulation and experiment are conducted. The results are compared with those of the commonly used parallel feedforward compensation (PFC) approach. Experimental results revealed that the proposed approach reduced the tracking error by about 80% compared to PFC without any additional control input. Moreover, the proposed approach has been proved to be energy-efficient by about 21% than PFC under similar tracking conditions. [ABSTRACT FROM AUTHOR]

The research article examines the performance of the five most traded equity ETFs on the basis of disintegration hypotheses and tracking errors. The study tests the disintegration hypotheses with respect to the most recent COVID-19 crisis. The study does not support the disintegration hypotheses in the case of Indian ETFs. It is discovered that 3 out of 5 ETFs are consistently co-integrated with their underlying index before, during, and after the COVID-19 financial crisis. Additionally, it was discovered that, prior to the financial crisis, 2 out of 5 were not co-integrated with their underlying index. However, during the financial crisis, only one ETF was not co-integrated with its benchmark index. However, after the pandemic crisis period, all the ETFs are co-integrated with the benchmark index. Moreover, during the financial crisis, the tracking error of these five exchange-traded funds increased and became more volatile compared to the pre-crisis and post-crisis periods. [ABSTRACT FROM AUTHOR]

Active fund performance is assessed relative to specified benchmarks. Fund managers aim to generate portfolio returns higher than the benchmarks while adhering to constraints such as tracking errors (TE) and asset weight restrictions. For each TE, the maximum active portfolio return and associated absolute portfolio risk traces out a hyperbolic TE frontier in risk/return space. The locus of all possible active portfolio coordinates for a given level of TE traces out a closed, distorted ellipse in risk/return space. Attempts to optimize active portfolio performance at a given TE include the maximum active return portfolio, the maximum active return portfolio with the same absolute risk as the benchmark and the tangent portfolio (maximal risk adjusted return or Sharpe ratio (SR)). Using the maximum SR approach, the locus of maximal, active portfolio SRs for different TEs is roughly parabolic with a clearly defined maximum at a unique TE. We derive a solution for identifying these global maximum SR portfolios and find that these occur at feasible TEs (i.e. ≤ 15 % – within the range of most active portfolios) but only if inter-asset correlations are relatively low ( < 0.30). For asset correlations > 0.35 , maximal SRs occur at unrealistically high TEs ( > 15 %). [ABSTRACT FROM AUTHOR]

In view of that the tracking error originates from the amplitude attenuation and phase lag of the setpoints frequency component caused by the servo control system at each moment, this paper puts forward the idea of obtaining the setpoints time-frequency response (STFR) by solving the amplitude attenuation and phase lag of each frequency component of the setpoints at each moment. First, the feasibility of the proposed idea is proved theoretically; Then, the setpoints time-frequency transform is carried out and the solving method of STFR and setpoints time-frequency response error (STFRE) is established; Finally, taking the servo control system as the object, the STFR and STFRE are solved, and the corresponding relationship with the output time-frequency transformation and tracking error is analyzed to verify the proposed method. The contributions of the proposed method are: the method achieves the solution of STFR based on the amplitude attenuation and phase lag of the servo system; it avoids the limitation that only harmonic wavelet bases must be used in the existing method and can be applied to the solution of the time-frequency response of actual setpoints; it can separate the setpoints loss or tracking error caused by amplitude attenuation and phase lag; it can determine the redundancy or lack of strategies such as filters for certain setpoints and servo control system. [ABSTRACT FROM AUTHOR]

Background: Dynamic tumor motion tracking is used in robotic radiosurgery for targets subject to respiratory motion, such as lung and liver cancers. Different methods of measuring tracking error have been reported, but the differences among these methods have not been studied, and the optimal method is unknown. Purpose: The purpose of this study was to assess and compare tracking errors encountered with individual patients using different evaluation methods for method optimization. Methods: We compared the beam's eye view (BEV), machine learning (ML), log (addition error: AE), and log (root sum square: RSS) methods. Log (AE) and log (RSS) were calculated from log files. These tracking errors were compared, and the optimal evaluation method was ascertained. A t‐test was performed to evaluate statistically significant differences. Here, the significance level was set at 5%. Results: The mean values of BEV, log (AE), log (RSS), and ML were 2.87, 3.91, 2.91, and 3.74 mm, respectively. The log (AE) and ML were higher than BEV (p < 0.001), and log (RSS) was equivalent to the BEV, suggesting that the log (RSS) calculated with the log file method can substitute for the BEV calculated with the BEV method. As RSS error calculation is simpler than BEV calculation, using it may improve clinical practice throughput. Conclusion: This study clarified differences among three tracking error evaluation methods for dynamic tumor tracking radiotherapy using a robotic radiosurgery system. The log (RSS) calculated by the log file method was found to be the best alternative to BEV method, as it can calculate tracking errors more easily than the BEV method. [ABSTRACT FROM AUTHOR]

Leveraged and inverse exchange-traded funds seek daily returns equal to fixed multiples of indexes' returns, but the ensuing rebalancing costs create a tension between a high correlation with the index and a low average deviation from the leveraged index' performance. With proportional trading costs, we find that the optimal replication policy is robust to the index' dynamics and obtain a sufficient statistic for index replication performance, the implied spread, which is insensitive to risk-premia and enables comparisons of funds tracking different factors of an index. Overall, the impact of trading costs on replication performance is comparable to or higher than the effect of management fees. [ABSTRACT FROM AUTHOR]

Contour tracking accuracy is the key performance index of a multi-axis motion control system. In the previous design of the contour error feedback controller, the independent design idea of the tracking controller and contour controller of each logic axis is often adopted, which is not easy to realize the optimal control of tracking accuracy and contour accuracy. The coupling increment of each controller is inevitable in motion control compensation, which impacts the control system's stability. Here, we propose a predictive control method for contour error. At first, through the state space model of the feed system, the system dynamics are judged to predict the contour accuracy in the future finite time domain. Besides, the linear quadratic performance index function of contour error is established, and the performance of the control objective is continuously optimized during the limited time domain with the form of rolling optimization. A closed-loop solution is obtained, which is most suitable for the current motion situation and could add to the system to realize the optimal control considering the trajectory contour and the tracking stability of each servo axis in the subsequent few sampling cycles. Finally, utilizing comparative experiments on the three-axis motion control platform, it is verified that the proposed contour predictive control strategy not only effectively reduces the tracking error but also significantly improves the contour accuracy, which is suitable for application in a complex industrial environment. [ABSTRACT FROM AUTHOR]

Lower limb disability is one of the major problems facing human lives. To restore the missing functionality and aesthetic features of an amputee's locomotion, finding the optimal design of a human knee prosthesis is crucial. This paper focuses on the design optimization of a four bar knee mechanism capable of reproducing the complex flexion/extension knee joint motion in the sagittal plane with variable instantaneous centre of rotation positions. Thus, an optimization approach with appropriate constraints is formulated to consider the degree of compatibility between the instantaneous centre of rotation trajectories of the human reference knee joint and the four bar knee mechanism. To solve this highly nonlinear optimization problem, an algorithm based on a multiobjective modified imperialist competitive method, where all the constraints are managed with a penalty method, is proposed. The results obtained by the multiobjective modified imperialist competitive method show that it is possible to obtain a small tracking error. The obtained results prove the effectiveness of the proposed optimization approach for the optimal synthesis of a four bar knee mechanism compared with that of other literature techniques. [ABSTRACT FROM AUTHOR]

Whenever additional states of a plant can be measured, closing nested feedback loops can be exploited in a variety of ways. The goal here is to reduce the bandwidth of feedback controllers and thus reduce the amplification of sensor noise that can otherwise spoil the expected performance when the actuator saturates. This can be particularly relevant for demanding tracking specifications and large plant uncertainties. In this context, the current work proposes a novel model-matching control architecture with a feedforward controller and two feedback controllers, which is accompanied by a new robust design method in the frequency domain of Quantitative Feedback Theory (QFT). The use of a feedforward controller reduces the amount of feedback to the minimum necessary to constrain the spread of the tracking error responses as specified. Furthermore, this amount of feedback is quantitatively distributed along the frequency between the inner and outer loops to reduce the total sensor noise at the control input as much as possible. A theoretical example illustrates the method and highlights the advantages of the new architecture over two other previously feasible QFT solutions: one with double feedback and another with single feedback plus feedforward. The importance of choosing the correct switching frequency between loops is also demonstrated. Finally, the angle of rotation of a commercial servo motor is successfully controlled using the motor speed as an internal measure. [ABSTRACT FROM AUTHOR]

In most conventional robotic arms, the motors are installed on the rotating shafts within the arm, which means that the shape and size of the motors must be considered in the design of the arm, while the weight of the motors increases the torque on the supporting joints generated during arm movements. This paper presents a dual-axis robotic arm with the motors installed on the base of the device to overcome these issues. Movement around the first axis is driven by a gear, while that of the second axis is driven by a belt. Trajectory tracking is controlled by an adaptive sliding mode controller (ASMC). In simulations and experiments, the proposed robotic arm outperformed arms using PID control and sliding mode control (SMC) in terms of tracking accuracy and stability.

This article proposes a methodology for the optimal selection of the control strategy for two-axis solar tracking systems, that simultaneously reduces tracking error and energy consumption in existing solar tracking systems, improving their overall performance. Begins with the characterization of the tracking system, then the constraint definition helps to pre-select the possible controllers. Subsequently, a selection stage is carried out from a heuristic approach, based on a multibody simulation analysis and an experimental analysis, and the feasible controllers for the application of the tracker are defined. Finally, a comparative analysis is carried out to find the best control strategy for the existing tracker and the solar application. The optimal selection approach was implemented in a solar tracking system for low-power photovoltaic applications. Based on the defined constraints, six control strategies were pre-selected, which were simulated and implemented in the physical system. The multibody simulation process allows the designer to know the dynamics of each controller, and in turn determine an approximation of the best configuration of the elements that compose it. This, with the aim of validating that each proposal is compatible with the application of the solar tracker, and that it can be taken to the real experimental environment. From the experimental results, the MPC controller shows the best performance. Well, although it has a greater error than other alternatives, its value is still below the permissible precision level (less than 2°) and in turn has the lowest energy consumption 0.7867 Wh. That is, a reduction ranging from 34 to 76% with respect to each performance of the alternatives considered. In addition, the dynamics of the control actions it performs are smoother, thus reducing wear on the actuators.Thus, the results obtained to support that with the proposed methodology the overall performance of solar tracking systems can be increased, significantly reducing tracking error and energy consumption.

Efficient and accurate state estimation is the basis for the safety and stability of the integrated energy system (IES). Particle filter has high precision and strong adaptability to nonlinear systems,and it has been applied to state estimation of power systems. To improve the precision of state estimation in IES,a forecasting-aided state estimation method based on improved particle filter is proposed. Firstly,a regional IES model including an electricity-heat-gas network is constructed. Secondly,the particle filter algorithm is applied to the electricity-heat-gas network. The prediction step of the particle filter is improved because of the tracking error problem of traditional particle filtering algorithm,which is based on particle filter theory. Finally,the improved particle filter algorithm is verified by using the classical IES example. The results show that this method can effectively solve the tracking error problem of the traditional particle filter algorithm,which can improve the precision of state estimation in IES.

The dish concentrator is an indispensable optical device for solar dish/stirling power system, which requires accurate tracking sun’s position. However, both the foundation settlement caused by long-term service and installation error can cause the support column tilt, thus destroying the vertical relationship between the column axis (i.e. azimuth axis) and ground plane resulting tracking errors. In this paper, a tracking error model of dish concentrator with elevation–azimuth dual-axis tracking considering column tilt is developed, the radial error angle θ1and circumferential error angle φ1are used to describe column tilt angle and tilt direction. The concentrator tracking error and focused spot position under column tilt error are analyzed using several dimensional evaluation indexes for the whole year, every day and every moment, and are verified by a novel virtual experiment of the concentrator tracking and optical simulation. When θ1is constant, the tracking performance is worst throughout the year at φ1of 90° and 270°, while the influence of column tilt can be effectively reduced at φ1of 0° or 180°. The maximum daily tracking error can reach 1.91∼3.49 mrad in whole year at θ1=0.1° and φ1in 0°∼360°, so θ1should be controlled within 0.1°.

Wind-induced tracking deviations of heliostats can be analyzed through numerical simulations or experimental studies on a full-scale heliostat. However, these methods are relatively costly and often, simpler estimations are necessary and sufficient. One simpler approach is to use an analytical model that describes the wind-induced tracking deviations and which requires only a few input parameters that can be determined through straightforward measurements at the full-scale heliostat. Therefore, this paper presents the derivation of an analytical model and describes the development process in a detailed way to clarify the necessary assumptions and simplifications. For verification purposes, the developed model is furthermore applied to measurement data of a field study. It is shown that the results of the model application agree well with the expectations and that the measured heliostat response matches the predicted response well, provided the underlying assumptions of the model fully apply to the investigated heliostat. Overall, no unexplainable inconsistencies are identified and the results support the model well. Thus, a method is provided which allows the estimation and prediction of wind-induced tracking deviations with comparatively little effort. In addition, the developed model helps to identify and analyze those parameters that have the greatest impact on the wind-induced tracking deviations of different types of heliostats. • Estimation of wind-induced tracking deviations of heliostats with little effort. • Only few and easy-to-determine input parameters for analytical model required. • Model developed for T-type and Stellio type heliostats, further applications possible. • Model confirmed through measurement data of a full-scale field study. [ABSTRACT FROM AUTHOR]

A multirod solar laser approach is here proposed to attain uniform and stable multibeam emission under non-continuous solar tracking. A Fresnel lens was used as the primary concentrator. The laser head was composed of a second-stage aspherical lens with a light-guide homogenizer and a third-stage conical pump cavity with six Nd:YAG rods. The solar laser system was optimized through numerical analysis in both Zemax® and LASCAD™ software to obtain six 1064 nm laser beams of similar multimode power. To investigate the effect of the homogenizer on the laser performance, the laser head was compared with a similar one that only used the aspherical lens in the second stage. The approach with the light guide attained a slightly lower efficiency than the one without the light guide; however, the tracking error width at 10% laser power loss was higher and, most importantly, only a 2.17% coefficient of variation of the laser power emitted by the six rods at the tracking error angle of ±0.5° was obtained. This is 4.2 times better than the 52.31% obtained with the laser head without the homogenizer and 76 times better than that of the previous numerical work. The light guide is thus essential to ensure uniform and stable solar laser power extraction from all rods even under non-continuous solar tracking, making this prototype the ideal for multibeam laser applications where uniformity and stability of the laser power are indispensable. This renewable multibeam solar laser may replace the classical lamp- and diode-pumped lasers, therefore ensuring a sustainable laser power production pattern for both space and terrestrial applications. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for the preliminary design of electric Vertical Takeoff and Landing (eVTOL) aircraft that utilizes the new Control Moment Coefficient (CMC) to size electric motors and to determine the rotor location and incidence angle. The CMC is determined for both thrust and arm length in eVTOL aircraft design, and is used to measure the moment produced by the rotors in the roll, pitch, and yaw axes. Analyzing its dimensionless value thus allows insights into an eVTOL aircraft's controllability. To test our methodology, two eVTOL aircraft were used in flight tests, one of which had up to 126% higher CMC values than the other. The results of the flight tests showed that a higher CMC value yielded many benefits, including an increased margin of safety between the rotors and the saturation level, reduced tracking error, and reduced control effort (or energy consumption). Furthermore, the 126% increase in the dimensionless CMC related to the pitch resulted in a 30% increase in the Pulse-Width Modulation -- PWM margin of safety of the rotors at the saturated level while still maintaining a reasonable tracking error and a 97% decrease in the pitch control effort. Our research suggests that incorporating higher CMCs into the preliminary design of an eVTOL aircraft can significantly improve its safety and controllability. We hope that our findings will encourage further exploration of this promising approach in future. [ABSTRACT FROM AUTHOR]

Aiming at the problem of deviations in the construction process of full-section vertical shaft boring machines, based on dynamic model, a control strategy (an error sign integral robust controller, RISE) was proposed. Firstly, according to the working principle of the tunneling machine, the three-dimensional deflection problem in tunneling space was decomposed into two-dimensional problems in the vertical plane. Then, the deviation correction scheme which involved alternating coordination of the propulsion and support systems under deflection states was planned. A dynamic model of shaft boring machine correction was established by using Lagrange energy and the unknown environmental disturbances were taken into account. An error sign integral robust controller was designed by using this model, and its stability was verified by the Lyapunov method. Finally, a section of the trajectory of the whole correction process was modeled and verified on MATLAB/Simulink. The control effect of the error sign integral robust controller was verified. The simulation results indicate that comparing with the proportional integral derivative (PID) controller and the feedback linearized controller(FLC), the error sign integral robust controller can reduce the tracking error of the maximum correction angle by 83.3% and 68. 6%, and reduce the tracking error of the maximum correction displacement by 86.8% and 66.4%. The results indicate that the error sign integral robust controller has a higher level of control accuracy for the correction trajectory. [ABSTRACT FROM AUTHOR]

Contour error compensation is an active research topic in five-axis CNC machining, especially in the manufacturing of sculptured surface parts. Nevertheless, current methods are mainly based on the mirror compensation principle, and fail to obtain a desired level of accuracy when processing parts with tight curvature feature. To address this issue, a global toolpath modulation-based contour error pre-compensation method is developed in this paper, which incorporates the error compensation issue into the stage of toolpath planning with a linear analytical solution. In this method, the nominal toolpaths used to machine the products is first expressed by dual B-spline curves, and then the instantaneous tracking error model of each individual drive is built with respect to control points of splined path. Afterward, the satisfaction condition of the spline control points for eliminating the contour error is yielded, which provides a possibility for compensating contour error in a global manner, and the neighbor-dependent coupling issue in error compensation between adjacent cutter location points is capable of being handled as well. On this basis, by applying the least-squares technique, the complicated contour error pre-compensation problem is further converted into a solution of simpler linear equation system. For enhancing its robustness when processing long toolpaths, an adaptive piecewise modulation strategy is also developed. Finally, both experiment and simulation are conducted to validate the proposed method, and the results demonstrate that the proposed method can significantly improve contour precision at low computational costs when compared with the existing pre-compensation method. [ABSTRACT FROM AUTHOR]

In a portfolio with multiple asset classes, each having its own benchmark, an alpha-seeking manager must decide how much tracking error (TE) to incur in each asset class, subject to given TE constraints. This paper helps practitioners clarify how to formulate this TE-allocation problem from a top-down perspective. By reconciling with a conceptual bottom-up formulation, we discover that the validity of the top-down model relies crucially on how one specifies the correlation structure of the asset classes' alphas. We propose a method for estimating this correlation structure that helps users of the top-down model avoid misallocation of TEs. [ABSTRACT FROM AUTHOR]

The main goal of the article is to examine the tracking efficiency of a homogenous sample of 14 ETFs listed on European exchanges, replicating the performance of Euro Stoxx 50 Index—a benchmark index for blue chips from the euro area. This study provides some insights into the tracking quality of European ETFs over the long time horizon (2012–2021 period) including data from entire business cycle: both economic prosperity and COVID-19 crisis. The study has been made applying different tracking error calculation techniques and return intervals—daily, weekly and monthly. Passive investing may be a highly desirable, cheap and accurate method for long or short term investments in the largest 50 cap companies in the euro zone. Hence, this unique research may help to succeed in ETF selection process. The study reveals that ETFs are very effectively managed by keeping the TEs below 0.3% (for ETFs with accumulating share classes) and below 1% (for ETFs with distributing share classes). This shows that the ETFs with accumulating share classes perform much better—the average TE for three different methods is 0.11% for accumulating share classes ETFs and 0.33% for distributing share classes ETFs. It proofs, that it is not important whether to use the standard deviation of the difference between the return of an ETF and that of its benchmark index, or the standard error of regression in TE assessment, both methods give very similar results. However, TE calculation method signifies, if the average of the absolute difference between the return of an ETF and that of the index is used. Additionally, it is found that time intervals used in TE calculations matter—the shift from monthly to daily intervals results in reduction of TE levels. Using shorter intervals brings lower TE values of European ETFs. [ABSTRACT FROM AUTHOR]

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In order to enhance the efficiency of agricultural machinery in orchard rows and minimize harm to personnel caused by pesticide spraying, this study developed a GNSS-based (Global Navigation Satellite System) automatic navigation driving system for tracked orchard sprayers. The tracked sprayer was used as a platform for this research. We constructed both a crawler hydraulic platform and spraying working parts based on orchard operation requirements. Additionally, we designed the hydraulic and electrical sub-control process of the crawler platform. By utilizing the motion model of the tracked mobile platform, we designed a linear path tracking control method using position deviation and heading deviation as state quantities. This allows the research platform to automatically initiate and terminate, travel in a straight line between rows, and complete spraying operations. Experimental verification confirmed that the tracked sprayer designed in this study successfully achieves automatic driving. The best automatic driving performance is achieved at a speed of 1.0 m/s. When the sprayer’s speed is 1.2 m/s, the maximum value of the straight-line path tracking accuracy of the platform’s automatic driving is better than 5.6 cm, with a standard deviation of 2.8 cm. This system effectively meets the requirements of automatic operation for an automatic spraying machine, thereby establishing a foundation for the implementation of automatic spraying operations in orchards.