A multi-tone central divided difference frequency tracker with adaptive process noise covariance tuning

The problem of real-time frequency estimation of nonstationary multi-harmonic signals is important in many applications. In this paper, we propose a novel multi-frequency tracker based on a state-space representation of the signal with Cartesian filters and the second-order central divided difference filter (CDDF), which improves the performance of the extended Kalman filter (EKF) by using Stirling's interpolation method to approximate the mean and covariance of the state vector. A crucial element of the method is the adaptive scaling of the process noise covariance matrix appearing in the filter equations, as a function of the innovation sequence, which tunes the accuracy-reactivity trade-off of the filter. The proposed solution is evaluated against two approaches from the literature, namely the factorized adaptive notch filter (FANF) and the extended Kalman filter frequency tracker (EKFFT). Several experiments emphasize the estimation accuracy of the proposed method as well as the improved robustness with respect to initial errors and input signal complexity. The presented method appears to be particularly efficient with rapidly varying frequencies, thanks to the update mechanism that adjusts the filter parameters based on the amplitude of the estimation error.     

Development of fan‐shaped tracker for single particle tracking

With the development of super‐resolution fluorescence microscopy, complex dynamic processes in living cells can be observed and recorded with unprecedented temporal and spatial resolution. Single particle tracking (SPT) is the most important step to explore the relationship between the spatio‐temporal dynamics of subcellular molecules and their functions. Although previous studies have developed SPT algorithms to quantitatively analyze particle dynamics in cell, traditional tracking methods have poor performance when dealing with intersecting trajectories. This can be attributed to two main reasons: (a) they do not have point compensation process for overlapping objects; (b) they use inefficient motion prediction models. In this paper, we present a novel fan‐shaped tracker (FsT) algorithm to reconstruct the trajectories of subcellular vesicles in living cells. We proposed a customized point compensation method for overlapping objects based on the fan‐shaped motion trend of the particles. Furthermore, we validated the performance of the FsT in both simulated time‐lapse movies with variable imaging quality and in real vesicle moving images. Meanwhile, we compared the performance of FsT with other five state‐of‐the‐art tracking algorithms by using commonly defined measures. The results showed that our FsT achieves better performance in high signal‐to‐noise ratio conditions and in tracking of overlapping objects. We anticipate that our FsT method will have vast applications in tracking of moving objects in cell.     

Sag in drying coatings: Prediction and real time measurement with particle tracking

Sag is a coating phenomenon characterized by gravity-driven flow after deposition; excessive amounts of sag can lead to coating defects. In this work, a new method for evaluating and quantifying sag is investigated. The motion of micron-sized Lycopodium spores on an inclined coating surface is tracked during drying, and the resulting surface velocity data is used to determine sag length. This in situ particle tracking method is minimally invasive and permits real time measurements. Measured sag lengths and real time surface velocities in aqueous polyvinyl alcohol solution coatings compare well with a theoretical model. The model is also used to develop a predictive sag regime map, which anticipates the extent of sag given coating properties and process-specific parameters. This map also identifies viable processing windows and aids in intelligent coating design given specific process constraints. The predictions of the sag regime map are compared against experimental sag results from polyvinyl alcohol solution coatings as well as four commercial latex paints, revealing good agreement for coatings with Newtonian or ‘Newtonian-like’ rheologies.     

Study on maximum power point tracking of photovoltaic array in irregular shadow

Traditional maximum power point tracking (MPPT) methods can hardly find global maximum power point (MPP) because output characteristics curve of photovoltaic (PV) array may have multi local maximum power points in irregular shadow, and thus easily fall into the local maximum power point. To address this drawback, Considering that sliding mode variable structure (SMVS) control strategy have such advantages as simple structure, fast response and strong robustness, and P&O method have the advantages of simple principle and convenient implementation, so a new algorithm combining SMVS control method and P&O method is proposed, besides, PI controller is applied to reduce system chattering caused by switching sliding surface. It is applied to MPPT control of PV array in irregular shadow to solve the problem of multi-peak optimization in partial shadow. In order to verity the rationality of the proposed algorithm, the experimental circuit is built, which achieves MPPT control by means of the proposed algorithm and P&O method. The experimental results show that compared with the traditional P&O algorithm, the proposed algorithm can fast track the global MPP, tracking speed increases by 60% and the relative error decreased by 20%. Moreover, the system becomes more stable near the MPP, the fluctuations of output power is greatly reduced, and thus make full use of solar energy.     

A new class of nonlinear Rauch–Tung–Striebel cubature Kalman smoothers

In this paper, a new Rauch–Tung–Striebel type of nonlinear smoothing method is proposed based on a class of high-degree cubature integration rules. This new class of cubature Kalman smoothers generalizes the conventional third-degree cubature Kalman smoother using the combination of Genz׳s or Mysovskikh׳s high-degree spherical rule with the moment matching based arbitrary-degree radial rule, which considerably improves the estimation accuracy. A target tracking problem is utilized to demonstrate the performance of this new smoother and to compare it with other Gaussian approximation smoothers. It will be shown that this new cubature Kalman smoother enhances the filtering accuracy and outperforms the extended Kalman smoother, the unscented Kalman smoother, and the conventional third-degree cubature Kalman smoother. It also maintains close performance to the Gauss–Hermite quadrature smoother with much less computational cost.     

A new approach to contour error control in high speed machining

High speed machining technology attempts to maximize productivity through the use of high spindle speeds and axis traverse rates. The technology is dependent upon the development of suitable mechanical hardware, electrical drives and associated control software to ensure that all components are used to maximum advantage. The role of the control software is particularly demanding since one needs to maximize traverse rates while providing the necessary accuracy, and indeed providing a margin of safety to deal with unexpected changes in process, or system parameters. There have been relatively few improvements in commercial CAD or CAM systems that would help machine tool users to take maximum advantage of high speed machining; rather the majority of the approaches have been undertaken at the machine tool controller level. This paper uses circular interpolation and corner tracking to compare several such control techniques, (Cross Coupled Control (CCC), Zero Phase Error Tracking Control (ZPETC), and Realtime Frequency Modulated Interpolation (FMI)), each of which have been proposed in the literature order to improve machining accuracy. None of these approaches are found to be universally successful when used alone and the authors, in this paper, examine the use of these systems in combination. Particular attention is focused upon an extension of a simplified version of cross coupled control together with Frequency Modulated Interpolation. It is shown that the combined system performs extremely well, and is easily actuated at high frequencies with conventional hardware. A custom built high speed x-y table is used to confirm system performance with multiple constraints present.     

Asymptotic stability of general linear methods for systems of linear neutral delay differential-algebraic equations

This paper is concerned with numerical stability of general linear methods (GLMs) for a system of linear neutral delay differential-algebraic equations. A sufficient and necessary condition for asymptotic stability of GLMs solving such system is derived. Based on this main result, we further investigate the asymptotic stability of linear multistep methods, Runge–Kutta methods, and block θ-methods, respectively. Numerical experiments confirm our theoretical result.     

Robust distributed attitude synchronization of multiple three-DOF experimental helicopters

Multiple experimental three-degrees-of-freedom (three-DOF) helicopters that are equipped with active disturbance systems constitute an attractive platform to validate robust control strategies. In this paper, a distributed synchronization controller is developed for such a platform, where each helicopter is subjected to unknown model uncertainties and external disturbances, and the desired trajectories are generated online, communicated through a network and not accessible by all helicopters. The controller is composed of a continuous tracker and a continuous uncertainty and disturbance estimator (UDE). The tracker makes the nominal closed-loop system globally asymptotically stable, and the UDE output is used to reject total uncertainties. The conditions that ensure zero-error tracking for each helicopter are identified; for the case with nonzero error, explicit relationship inequalities between the involved design parameters and the ultimate bound of error are revealed. Experimental results of four cases demonstrate improved tracking and synchronization accuracy of using the UDE with small parameters.     

Utilizing sensor data to model students’ creativity in a digital environment

While creativity is essential for developing students’ broad expertise in Science, Technology, Engineering, and Math (STEM) fields, many students struggle with various aspects of being creative. Digital technologies have the unique opportunity to support the creative process by (1) recognizing elements of students’ creativity, such as when creativity is lacking (modeling step), and (2) providing tailored scaffolding based on that information (intervention step). However, to date little work exists on either of these aspects. Here, we focus on the modeling step. Specifically, we explore the utility of various sensing devices, including an eye tracker, a skin conductance bracelet, and an EEG sensor, for modeling creativity during an educational activity, namely geometry proof generation. We found reliable differences in sensor features characterizing low vs. high creativity students. We then applied machine learning to build classifiers that achieved good accuracy in distinguishing these two student groups, providing evidence that sensor features are valuable for modeling creativity.