Time-varying Angle Research Articles

Filtered Extended State Observer Based Line-of-Sight Guidance for Path Following of Unmanned Surface Vehicles With Unknown Dynamics and Disturbances

This paper investigates the path following problem for an underactuated unmanned surface vehicle (USV) in the presence of ocean currents, model uncertainties and input saturation. Firstly, a novel filtered extended state observer (FESO) based line-of-sight (LOS) guidance law is proposed. The FESO is employed to estimate the time-varying sideslip angle caused by ocean, wind and wave disturbances, which is incorporated into the proposed LOS guidance scheme. Then the path following control system is developed to keep the USV moving on the desired path by combining adaptive fuzzy technique with sliding mode method, where adaptive fuzzy technique is applied to deal with model uncertainties. Besides, an auxiliary system is designed to solve the issue of actuator saturation. By using Lyapunov's stability theory, the closed-loop system is shown to be semiglobally uniformly ultimately bounded (SGUUB). Lastly, the comparison simulation results demonstrate the correctness and effectiveness of the proposed scheme.

High-Gain Observer-Based Line-of-Sight Guidance for Adaptive Neural Path Following Control of Underactuated Marine Surface Vessels

This paper presents an adaptive neural network dynamic surface control law with time-varying sideslip compensation, which includes a geometric kinematic control design and a dynamic control design, for path following of underactuated marine surface vessels (MSVs) in the presence of unmeasured states, model uncertainties, unknown ocean environmental disturbances, and input saturation. First, a high gain observer based line-of-sight guidance law, capable of estimating and compensating the time-varying sideslip angle induced by the unknown time-varying ocean disturbances, is proposed to generate the desired heading for the dynamic control system of the MSV. Next, considering the input saturation, adaptive neural network dynamic surface velocity control laws, in which the model uncertainties and unknown ocean environmental disturbances of the system are compensated by adaptive radial basis function neural network and the problem of input saturation is solved by introducing auxiliary dynamic systems, are designed to realize the dynamic control target of the path following. The proposed control strategy of path following compensates the ocean environmental disturbances from the perspective of both the geometric kinematics and the dynamics, and all error signals of a closed-loop control system are proven to be uniformly ultimately bounded. The simulations validate the effectiveness of the proposed control strategy for path following of MSVs.

Subspace Estimation From Incomplete Observations: A High-Dimensional Analysis

We present a high-dimensional analysis of three popular algorithms, namely, Oja's method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations. We show that, with proper time scaling, the time-varying principal angles between the true subspace and its estimates given by the algorithms converge weakly to deterministic processes when the ambient dimension $n$ tends to infinity. Moreover, the limiting processes can be exactly characterized as the unique solutions of certain ordinary differential equations (ODEs). A finite sample bound is also given, showing that the rate of convergence towards such limits is $\mathcal{O}(1/\sqrt{n})$. In addition to providing asymptotically exact predictions of the dynamic performance of the algorithms, our high-dimensional analysis yields several insights, including an asymptotic equivalence between Oja's method and GROUSE, and a precise scaling relationship linking the amount of missing data to the signal-to-noise ratio. By analyzing the solutions of the limiting ODEs, we also establish phase transition phenomena associated with the steady-state performance of these techniques.

Estimation of Ground Reaction Forces Using Low-Cost Instrumented Forearm Crutches

Instrumented crutches are useful for many rehabilitation tasks, including monitoring the correctness of crutch use, analyzing gait properties for patients with lower-limb impairments, as well as providing sensory data for controlling lower-body robotic orthoses. In this paper, we describe the design and analysis of an instrumented crutch system equipped with low-cost accelerometer and pressure sensors to estimate all components of the ground reaction force(GRF), providing a well-defined and physically meaningful sensory output for practical applications. We propose an angle-dependent quadratic model to map pressure and inclination data to force components, which we identify using least-squares methods. Through systematic characterization experiments, we first show that our model can predict GRF vectors with less than 7% rms errors in all axes for fixed crutch angles used for training. Subsequently, we generalize the model to crutch angles other than those used for training, showing that rms estimation errors remain below 7% for all axes. Finally, we assess measurement accuracy and performance under dynamic loading conditions with time-varying crutch angles, showing that errors still remain below 8% under realistic conditions.

Surface currents from hourly variations of suspended particulate matter from Geostationary Ocean Color Imager data

ABSTRACTSurface currents in Korean coastal regions were obtained using the maximum cross-correlation method applied to hourly suspended particulate matter images from the Geostationary Ocean Color Imager. Preliminary current vectors were filtered out by applying a series of quality-control procedures. The current vectors resulting from the tests were compared with the currents from a numerical model with tide and wind field. It was found that the estimated currents were more similarly to the currents caused by both tide and wind. A high degree of discrepancy was detected in regions of strong tidal currents, where the fundamental assumption of horizontal movement was limited due to the dominant vertical tidal mixing in the shallow region. The hourly rotations of the current vectors within a day were clarified by a comparison of the time-varying orientation angles of tidal ellipses. This study emphasized how to understand the short-term surface flows from hourly high-resolution geostationary satellite images.

Finite-Time Observer Based Guidance and Control of Underactuated Surface Vehicles With Unknown Sideslip Angles and Disturbances

Suffering from complex sideslip angles, path following control of an under actuated surface vehicle (USV) becomes significantly challenging and remains unresolved. In this paper, a finite-time observer based guidance and control (FOGC) scheme for path following of an USV with time-varying and large sideslip angles and unknown external disturbances is proposed. The salient features of the proposed FOGC scheme are as follows: 1) time-varying large sideslip angle is exactly estimated by a finite-time sideslip observer, and thereby contributing to the sideslip-tangent line-of-sight guidance law which significantly enhances the robustness of the guidance system to unknown sideslip angles which are significantly large and time-varying; 2) a finite-time disturbance observer (FDO) is devised to exactly observe unknown external disturbances, and thereby implementing FDO-based surge and heading robust tracking controllers, which possess remarkable tracking accuracy and precise disturbance rejection, simultaneously; and 3) by virtue of cascade analysis and Lyapunov approach, global asymptotic stability of the integrated guidance-control system is rigorously ensured. Simulation studies and comparisons are conducted to demonstrate the effectiveness and superiority of the proposed FOGC scheme.

Robust Nonlinear Path Following Control of Underactuated MSV With Time-Varying Sideslip Compensation in the Presence of Actuator Saturation and Error Constraint

A robust nonlinear path following control scheme is proposed for the underactuated marine surface vehicle (MSV) under the condition of the unknown time-varying sideslip, time-varying error constraint, actuator saturation, and unknown compound disturbances including external environment disturbance and model uncertainties in this paper. First, integrating the time-varying barrier Lyapunov function and sideslip observer, an error-constrained and sideslip observer based line-of-sight (ECS-LOS) guidance law is established. The ECS-LOS guidance law can calculate the desired heading angle, estimate the time-varying sideslip angle, and deal with the error constraint problem. Second, the robust path following controller is developed via dynamic surface control technique to achieve attitude tracking and velocity tracking control. The unknown compound disturbances are estimated by means of disturbance observer and the actuator saturation is compensated by the auxiliary function. Stability analysis proves that the tracking error of MSV can converge into a small neighborhood around zero and the constraint requirements on the vessel position are not violated during operation, while guaranteeing all states in the closed-loop control system are uniformly ultimately bounded. In the end, simulation studies and comparisons are carried out to demonstrate the validity of the proposed control approach.

Spectral negentropy based sidebands and demodulation analysis for planet bearing fault diagnosis

Planet bearing vibration signals are highly complex due to intricate kinematics (involving both revolution and spinning) and strong multiple modulations (including not only the fault induced amplitude modulation and frequency modulation, but also additional amplitude modulations due to load zone passing, time-varying vibration transfer path, and time-varying angle between the gear pair mesh lines of action and fault impact force vector), leading to difficulty in fault feature extraction. Rolling element bearing fault diagnosis essentially relies on detection of fault induced repetitive impulses carried by resonance vibration, but they are usually contaminated by noise and therefor are hard to be detected. This further adds complexity to planet bearing diagnostics. Spectral negentropy is able to reveal the frequency distribution of repetitive transients, thus providing an approach to identify the optimal frequency band of a filter for separating repetitive impulses. In this paper, we find the informative frequency band (including the center frequency and bandwidth) of bearing fault induced repetitive impulses using the spectral negentropy based infogram. In Fourier spectrum, we identify planet bearing faults according to sideband characteristics around the center frequency. For demodulation analysis, we filter out the sensitive component based on the informative frequency band revealed by the infogram. In amplitude demodulated spectrum (squared envelope spectrum) of the sensitive component, we diagnose planet bearing faults by matching the present peaks with the theoretical fault characteristic frequencies. We further decompose the sensitive component into mono-component intrinsic mode functions (IMFs) to estimate their instantaneous frequencies, and select a sensitive IMF with an instantaneous frequency fluctuating around the center frequency for frequency demodulation analysis. In the frequency demodulated spectrum (Fourier spectrum of instantaneous frequency) of selected IMF, we discern planet bearing fault reasons according to the present peaks. The proposed spectral negentropy infogram based spectrum and demodulation analysis method is illustrated via a numerical simulated signal analysis. Considering the unique load bearing feature of planet bearings, experimental validations under both no-load and loading conditions are done to verify the derived fault symptoms and the proposed method. The localized faults on outer race, rolling element and inner race are successfully diagnosed.

ESO-Based Line-of-Sight Guidance Law for Path Following of Underactuated Marine Surface Vehicles With Exact Sideslip Compensation

This paper presents a novel extended state observer (ESO)-based line-of-sight guidance law for path following of underactuated marine surface vehicles in the presence of time-varying sideslip angle. A reduced-order ESO is employed to identify the vehicle sideslip angle caused by constant ocean disturbances when following a curved path or time-varying ocean disturbances. This guarantees that the sideslip angle can be timely and exactly estimated, and thus contributes to following the desired path with higher accuracy regardless of external disturbances induced by wind, waves, and ocean currents. The input-to-state stability of the closed-loop system is established via cascade theory. It is proven that the transient learning process can be shorten by increasing the bandwidth of the ESO. Both simulation and experimental results are provided to validate the effectiveness of the method.

Dynamic Chemically Driven Dewetting, Spreading, and Self-Running of Sessile Droplets on Crystalline Silicon.

A chemically driven dewetting effect is demonstrated using sessile droplets of dilute hydrofluoric acid on chemically oxidized silicon wafers. The dewetting occurs as the thin oxide is slowly etched by the droplet and replaced by a hydrogen-terminated surface; the result of this is a gradual increase in the contact angle of the droplet with time. The time-varying work of adhesion is calculated from the time-varying contact angle; this corresponds to the changing chemical nature of the surface during dewetting and can be modeled by the well-known logistic (sigmoid) function often used for the modeling of restricted growth, in this case, the transition from an oxidized surface to a hydrogen-terminated silicon surface. The observation of the time-varying contact angle allows one to both measure the etch rate of the silicon oxide and estimate the hydrogenation rate as a function of HF concentration and wafer type. In addition to this, at a certain HF concentration, a self-running droplet effect is observed. In contrast, on hydrogen-terminated silicon wafers, a chemically induced spreading effect is observed using sessile droplets of nitric acid. The droplet spreading can also be modeled using a logistical function, where the restricted growth is the transition from hydrogen-terminated to a chemically induced oxidized silicon surface. The chemically driven dewetting and spreading observed here add to the methods available to study dynamic wetting (e.g., the moving three-phase contact line) of sessile droplets on surfaces. By slowing down chemical kinetics of the wetting, one is able to record the changing profile of the sessile droplet with time and gather information concerning the time-varying surface chemistry. The data also indicates a chemical interface hysteresis (CIH) that is compared to contact angle hysteresis (CAH). The approach can also be used to study the chemical etching and deposition behavior of thin films using liquids by monitoring the macroscopic droplet profile and relating this to the time-varying physical and chemical interface phenomena.

Kinematic Origins of Motor Inconsistency in Expert Pianists

For top performers, including athletes and musicians, even subtle inconsistencies in rhythm and force during movement production decrease the quality of performance. However, extensive training over many years beginning in childhood is unable to perfect dexterous motor performance so that it is without any error. To gain insight into the biological mechanisms underlying the subtle defects of motor actions, the present study sought to identify the kinematic origins of inconsistency of dexterous finger movements in musical performance. Seven highly-skilled pianists who have won prizes at international piano competitions played a short sequence of tones with the right hand at a predetermined tempo. Time-varying joint angles of the fingers were recorded using a custom-made data glove, and the timing and velocity of the individual keystrokes were recorded from a digital piano. Both ridge and stepwise multiple regression analyses demonstrated an association of the inter-trial variability of the inter-keystroke interval (i.e., rhythmic inconsistency) with both the rotational velocity of joints of the finger used for a keystroke (i.e., striking finger) and the movement independence between the striking and non-striking fingers. This indicates a relationship between rhythmic inconsistency in musical performance and the dynamic features of movements in not only the striking finger but also the non-striking fingers. In contrast, the inter-trial variability of the key-descending velocity (i.e., loudness inconsistency) was associated mostly with the kinematic features of the striking finger at the moment of the keystroke. Furthermore, there was no correlation between the rhythmic and loudness inconsistencies. The results suggest distinct kinematic origins of inconsistencies in rhythm and loudness in expert musical performance.

Amplitude and frequency demodulation analysis for fault diagnosis of planet bearings

The vibration signals of planet bearings feature more complex amplitude modulation and frequency modulation (AM-FM) than those of fixed-axis bearings, due to the effects of time-varying vibration transfer path, load zone passing and time-varying angles between gear pair mesh lines of action and impact force vector, in addition to that of bearing fault. Their Fourier spectra have a complex sideband structure, leading to difficulty in feature extraction and fault diagnosis. In order to address this issue, a joint amplitude and frequency demodulation analysis method is proposed to reveal the fault features, by considering the modulation characteristics. To thoroughly understand planet bearing vibration characteristics, the explicit equations for amplitude and frequency demodulated spectra of outer race, rolling element and inner race fault cases are derived, and the fault symptoms are summarized respectively. The signal is firstly decomposed into intrinsic mode functions (IMFs) by empirical mode decomposition (EMD), thus meeting the mono-component requirement by instantaneous frequency calculation. Then a sensitive component with the instantaneous frequency fluctuating around the resonance frequency is chosen for further frequency demodulation analysis. Finally, planet bearing fault can be diagnosed by matching the peaks identified in amplitude and frequency demodulated spectra with the theoretical fault characteristic frequencies. The proposed method is validated with both numerical simulated and lab experimental signal analyses.

Bistatic ISAR distortion and defocusing analysis

Bistatic inverse synthetic aperture radar (ISAR) is an efficient geometric configuration of ISAR to image targets traveling along radar transmitter's line of sight, but it has the problem of defocusing and distortion because of the time-varying bistatic angle. In this paper, we derive the defocusing term and the distortion term by expanding the bistatic angle using first-order Taylor expansion. In addition, necessary constraints to neglect the defocusing term are provided via point spread function analysis, and a novel method to eliminate distortion based on linked scatterers is proposed. Simulation results validate our theoretical analysis and show the effectiveness of our method.

Defocusing and distortion elimination for shipborne bistatic ISAR

ABSTRACTShipborne bistatic inverse synthetic aperture radar (ISAR), with a stationary and visible transmitter on land and a mobile and stealthy receiver on a ship with complex 3-D rotations is a strategic asset which can provide complementary information to monostatic ISAR. However, it must first overcome the serious problems of defocusing and distortion due to the time-varying bistatic angle. In this letter, an improved cubic chirplet decomposition method is proposed to solve the defocusing problem. By decomposing the ISAR echo into cubic chirplet atoms and estimating the parameters for each term, higher-order defocusing terms can be eliminated. Moreover, a novel method based on linked scatterers is put forward to solve the distortion problem. The method utilizes ‘linked scatterers’ from monostatic ISAR image to calculate and compensate the distortion angle. The effectiveness of the proposed methods is verified by the simulation results.

Complex function projective synchronization in drive-response complex-variable dynamical networks with coupling time delays

This paper investigates complex function projective synchronization (CFPS) in drive-response complex-variable dynamical networks, which means that the complex-variable chaotic systems in networks may evolve in different directions with a time-varying intersection angle in a complex plane and can be synchronized up to a complex scaling function. Hybrid feedback control schemes are proposed to achieve CFPS in drive-response complex-variable networks with both constant coupling delay and time-varying coupling delay. Based on Lyapunov stability theory and the linear matrix inequality, some sufficient conditions are derived by adopting an appropriate Lyapunov–krasovskii energy function. Finally, the numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method and further reveal that the synchronization is independent of the coupling delay.

Vibration signal models for fault diagnosis of planet bearings

Rolling element bearings are key components of planetary gearboxes. Among them, the motion of planet bearings is very complex, encompassing spinning and revolution. Therefore, planet bearing vibrations are highly intricate and their fault characteristics are completely different from those of fixed-axis case, making planet bearing fault diagnosis a difficult topic. In order to address this issue, we derive the explicit equations for calculating the characteristic frequency of outer race, rolling element and inner race fault, considering the complex motion of planet bearings. We also develop the planet bearing vibration signal model for each fault case, considering the modulation effects of load zone passing, time-varying angle between the gear pair mesh and fault induced impact force, as well as the time-varying vibration transfer path. Based on the developed signal models, we derive the explicit equations of Fourier spectrum in each fault case, and summarize the vibration spectral characteristics respectively. The theoretical derivations are illustrated by numerical simulation, and further validated experimentally and all the three fault cases (i.e. outer race, rolling element and inner race localized fault) are diagnosed.

3D Wideband Non-Stationary Geometry-Based Stochastic Models for Non-Isotropic MIMO Vehicle-to-Vehicle Channels

Actual vehicle-to-vehicle (V2V) channel measurements have shown that the wide-sense stationary (WSS) modeling assumption is valid only for very short time intervals. This fact motivates us to develop non-WSS V2V channel models. In this paper, we propose a novel three-dimensional (3D) theoretical non-WSS regular-shaped geometry-based stochastic model (RS-GBSM) and the corresponding sum-of-sinusoids (SoS) simulation model for non-isotropic scattering wideband multiple-input multiple-output (MIMO) V2V fading channels. The movements of the transmitter (Tx), scatterers, and receiver (Rx) result in the time-varying angles of departure (AoDs) and angles of arrival (AoAs) that make our models non-stationary. The proposed RS-GBSMs, combining line-of-sight (LoS) components, a two-sphere model, and multiple confocal elliptic-cylinder models, have the ability to study the impacts of vehicular traffic density (VTD) and non-stationarity on channel statistics, and jointly consider the azimuth and elevation angles by using the von Mises Fisher (VMF) distribution. The proposed RS-GBSMs are sufficiently generic and adaptable to model various V2V scenarios. Based on the proposed 3D non-WSS RS-GBSMs, important local channel statistical properties are derived and thoroughly investigated. The impacts of VTD and non-stationarity on these channel statistical properties are investigated by comparing them with those of the corresponding WSS model. The proposed non-WSS RS-GBSMs are validated by measurements in terms of the channel stationary time. Finally, numerical and simulation results demonstrate that the 3D non-WSS model is more practical to characterize real V2V channels.

Stirring turbulence with turbulence

We stir wind-tunnel turbulence with an active grid that consists of rods with attached vanes. The time-varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer-Ohkitani-Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial-range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the largest eddies of the wind-tunnel turbulence. A large mismatch of these times creates a highly intermittent random flow with interesting but quite anomalous statistics.

An Investigation of Nonlinear Flow Oscillations in a High-Pressure Centrifugal Pump

High-pressure multistage pumps and their coupled piping systems, typically used in the process and power generation industry, can experience dangerous system-level instabilities. This can occur at flow coefficients well away from the surge limit and in the absence of cavitation. Such a pumping system and a related new kind of instability are the focus of this paper. A system-wide instability was observed at 0.05 times rotor frequency for flow coefficients near maximum head rise but at negative slope, thus on the stable side of the head rise characteristic. A previous study based on system-level experiments concluded that this instability differs from classical surge, cavitation surge, rotating stall, and rotating cavitation, but the underlying mechanism and necessary flow conditions remain unknown. This paper investigates the root cause of the system-wide pump instability, employing a systematic analysis of the impact of geometry changes on pump stability and performance. It is found that the upstream influence of the unsteady flow separation in the return channel leads to a time-varying incidence angle change on the volute tongue which causes periodic ingestion of low-stagnation pressure fluid into the diffuser passages. This sets up a limit cycle, promoting the system-wide instability. With the instability mechanism determined, the pump is redesigned to remove the flow separation while maintaining performance at design conditions. Unsteady numerical simulations demonstrate improved efficiency and pressure recovery at low flow coefficients. A time accurate calculation also indicates stable operation at all relevant flow conditions. The paper resolves a long-standing pump stability problem and provides design guidelines for reliable and improved performance, important to the chemical processing and power generation industry.

Kinetic measures of restabilisation during volitional stepping reveal age-related alterations in the control of mediolateral dynamic stability

Research examining age-related changes in dynamic stability during stepping has recognised the importance of the restabilisation phase, subsequent to foot-contact. While regulation of the net ground reaction force (GRFnet) line of action is believed to influence dynamic stability during steady-state locomotion, such control during restabilisation remains unknown. This work explored the origins of age-related decline in mediolateral dynamic stability by examining the line of action of GRFnet relative to the centre of mass (COM) during restabilisation following voluntary stepping. Healthy younger and older adults (n=20 per group) performed three single-step tasks (varying speed and step placement), altering the challenge to stability control. Age-related differences in magnitude and intertrial variability of the angle of divergence of GRFnet line of action relative to the COM were quantified, along with the peak mediolateral and vertical GRFnet components. The angle of divergence was further examined at discrete points during restabilisation, to uncover events of potential importance to stability control. Older adults exhibited a reduced angle of divergence throughout restabilisation. Temporal and spatial constraints on stepping increased the magnitude and intertrial variability of the angle of divergence, although not differentially among the older adults. Analysis of the time-varying angle of divergence revealed age-related reductions in magnitude, with increases in timing and intertrial timing variability during the later phase of restabilisation. This work further supports the idea that age-related challenges in lateral stability control emerge during restabilisation. Age-related alterations during the later phase of restabilisation may signify challenges with reactive control.