Time-varying Position Research Articles

Structural response reconstruction of beam-like bridge based on equivalent loads under moving forces

Response reconstruction has advantages in enriching monitoring data with high quality and it is of great importance to bridge structural health monitoring. However, there still are many current difficulties with response reconstruction due to the complex operation of bridges, e.g., hard to deal with time-varying positions of vehicles and inefficient reconstruction for cases with a long time. According to the theory of equivalent load identification, this paper proposes a model-based method for reconstructing responses induced by moving forces. The proposed method introduces moving time windows to extract the measured responses in an orderly manner and re-organizes them into a matrix form. The measured responses, expressed in matrix form, then serve as the input data to identify both equivalent loads and structural initial conditions, but not to estimate the actual moving forces. Herein, the equivalent loads represent some concentrated loads with time-invariant acting positions and are employed to approximately re-express the main information of moving forces. Matrix regularization with a sparse penalty term is used to ensure the robustness of identified results. Since the structural inputs have been estimated, the structural responses happening at the validation sensors then can be calculated as a forward problem. In this process, the role of identified structural inputs is an intermediate variable connecting the measuring sensors and the validation sensors so that, the transmissibility function (TF) discussed in the proposed method is expressed in an implicit pattern. Compared to the response reconstruction methods developed from moving force identification (MFI), an obvious characteristic is that information on the actual moving forces is no longer necessary. Therefore, it can bring convenience in practical application such as the time-varying positions of moving vehicles are not needed in advance. In addition, the application of matrix regularization has the potential for efficient computation. To verify the feasibility and effectiveness of the proposed method, both numerical simulations and experimental studies are finally carried out. The illustrated results indicate that the proposed method can accurately reconstruct the structural response. In addition, some related issues are also discussed.

Wind farm structural response and wake dynamics for an evolving stable boundary layer: computational and experimental comparisons

Abstract. The wind turbine design process requires performing thousands of simulations for a wide range of inflow and control conditions, which necessitates computationally efficient yet time-accurate models, especially when considering wind farm settings. To this end, FAST.Farm is a dynamic-wake-meandering-based mid-fidelity engineering tool developed by the National Renewable Energy Laboratory targeted at accurately and efficiently predicting wind turbine power production and structural loading in wind farm settings, including wake interactions between turbines. This work is an extension of a study that addressed constructing a diurnal cycle evolution based on experimental data (Quon, 2024). Here, this inflow is used to validate the turbine structural and wake-meandering response between experimental data, FAST.Farm simulation results, and high-fidelity large-eddy simulation results from the coupled Simulator fOr Wind Farm Applications (SOWFA)–OpenFAST tool. The validation occurs within the nocturnal stable boundary layer when corresponding meteorological and turbine data are available. To this end, we compared the load results from FAST.Farm and SOWFA–OpenFAST to multi-turbine measurements from a subset of a full-scale wind farm. Computational predictions of blade-root and tower-base bending loads are compared to 10 min statistics of strain gauge measurements during 3.5 h of the evolving stable boundary layer, generally with good agreement. This time period coincided with an active wake-steering campaign of an upstream turbine, resulting in time-varying yaw positions of all turbines. Wake meandering was also compared between the computational solutions, generally with excellent agreement. Simulations were based on a high-fidelity precursor constructed from inflow measurements and using state-of-the-art mesoscale-to-microscale coupling.

Position constrained adaptive time-varying formation control of autonomous surface vessels with uncertain dynamics

This paper investigates the adaptive time-varying formation control problem of autonomous surface vessels (ASVs) with position constraints, uncertain dynamics and external disturbances under directed communication topology. Different from the existing studies, the nonlinear error transformation function is combined with formation control to achieve position constraints of ASVs. Based on dynamic surface control and backstepping method, a virtual control law is designed for each vessel. Radial basis function neural networks are employed to approximate the unknown nonlinear continuous function caused by ASVs’ model uncertainties, and the minimum learning parameter (MLP) method is applied to reduce computational complexity. Then, a time-varying formation position constrained controller and an adaptive law are proposed for each ASV. By using the Lyapunov stability theory, it is proved that all signals of the closed-loop ASV system are semi-global uniformly ultimately bounded and the position constrained objective can be achieved. Finally, simulation analyses are given to verify the effectiveness of theoretical results.

Adaptive controller based on barrier Lyapunov function for a composite Cartesian-delta robotic device for precise time-varying position tracking

This study presents the design of an adaptive event-driven controller for solving the trajectory tracking problem of a composite robotic device made up of a three-dimensional Cartesian and a parallel Delta robot. The proposed composite device has a mathematical model satisfying a standard Lagrangian structure affected by modeling uncertainties and external perturbations. The adaptive gain of the controller is considered to enforce the convergence of the tracking error while the state bounds are satisfied. The barrier Lyapunov function addresses the preconceived state constraints for both robotic devices by designing a time-varying gain that guarantees the ultimate boundedness of the tracking error under the effect of external perturbations. The event-driven approach considers that the Cartesian robot is moving into a predefined invariant zone near to the origin. In contrast, the delta robot can complete the tracking problem once the end-effector is inside the given zone. The suggested controller was evaluated using a virtual representation of the composite robotic device showing better tracking performance (while the restrictions are satisfied) than the performances obtained with the traditional linear state feedback controllers. Analyzing the mean square error and its integral led to confirming the benefits of using the adaptive barrier control.

Adaptive Neural Control of Connected Vehicular Platoons With Actuator Faults and Constraints

This paper focuses on the adaptive neural control problem for a connected vehicles platoon system with external disturbances, actuator fault and constraints. Then, the tangent barrier Lyapunov function is introduced into the control design to solve the time-varying position and velocity constraints in a vehicle platoon. Since the selected engine dynamics model is nonlinear, the neural network is adopted to approximate the unknown internal vehicle dynamics. Moreover, the actuator fault effect is addressed by the designed adaptive law designed based on the projection operator. It can be eventually confirmed that all the involved closed-loop signals are bounded based on the Lyapunov stability theory. Finally, a comparative simulation shows the effectiveness of the proposed control scheme.

Non-contact Ultrasonic Sonar-based Ranging Technique for In-motion 3D Railroad Tie Deflection Measurements

This paper presents an ultrasonic technique for non-contact surface deflection mapping of railroad ties using concepts of sonar-based ranging. The technique utilizes an array of capacitive ultrasonic transducers arranged along the length of the railroad tie at a lift-off distance of 3 in. from the rail surface to ensure contactless measurements. The transducer array is used in pulse-echo mode and distances from the transducers to the tie surface are measured by tracking the time-of-flight of the waves reflected from the tie surface. A reference-based cross-correlation operation is introduced to compute the time-of-flight, wherein one of the transducers is used as a reference for the distance measurements. The reference-based cross-correlation ensures accurate peak-detection for time-of-flight based differential distance measurements. An acoustic signal strength-based technique is utilized to differentiate between signals reflected from ties and those reflected from ballast. Laboratory scale tests were first performed as a proof-of-concept on a slender wooden beam to measure deflections in loaded and unloaded conditions. Dynamic tests were also performed on this beam to determine the ability to track time-varying positions. Field tests on a replica test track with wood ties were performed at the Rail Defect Testing Facility at University of California San Diego by mounting the prototype on a test-cart moved at walking speed. A dynamic assessment of the prototype was also performed to determine natural frequencies of the mounting beam that may be relevant for future uses at higher speeds. The results indicate the potential of this non-contact system to measure full-field tie deflections in 3D in-motion. This ability may potentially be used to detect conditions of poor tie support that may cause derailments.

Breathing characteristics of rotor cracks based on time-varying centroid position

Breathing characteristics of rotor cracks based on time-varying centroid position

Containment control for second-order multi-agent systems with intermittent sampled position data under directed topologies

This paper investigates the intermittent containment control problem for second-order multi-agent systems under directed communication topologies. In order to reduce energy consumption and overcome the difficulty of velocity measurement in engineering applications, an intermittent containment control protocol utilizing the present time-varying position data and sampled position data is proposed. Under the assumption on the existence of the directed spanning forest, a necessary and sufficient condition for the stability of the multi-agent system is obtained, which is derived by the coupling coefficients, the eigenvalues of the Laplacian matrix, the period length and the communication width. Finally, the correctness of the theoretical results is validated by experimental simulations.

RL-Ladder Circuit Models for Eddy-Current Problems With Translational Movement

This article proposes an adaptive equivalent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RL$ </tex-math></inline-formula> -circuit model for eddy-current devices with a single electrical port (one terminal voltage and current) and translational movement. The device is first characterized by means of frequency-domain finite-element computations in the relevant frequency and position intervals, for subsequently fitting constant-coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RL$ </tex-math></inline-formula> -ladder circuits of adjustable size (i.e., variable number of branches and loops). The accuracy of the ladder-circuit model is assessed in both the frequency and time domains. The time-varying position involves the force computation from the circuit and the coupling with the mechanical equation. By way of validation, we study the axisymmetric magnetic-levitation device of TEAM Workshop problem 28. Results exhibit good convergence to reference finite-element ones with increasing number of branches.

Global-Position Tracking Control for Three-Dimensional Bipedal Robots Via Virtual Constraint Design and Multiple Lyapunov Analysis

Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking.

Vehicle weight identification based on equivalent loads reconstructed from responses of beam-like bridge

Moving force identification (MFI) is an effective way for closely monitoring vehicle weight in a dynamic state. Time-varying position of vehicle is usually needed. This applying condition may limit the applicability because the measurement of time-varying position has certain difficulty. To tackle this problem, this study proposes an equivalent load-based method for identifying the gross weight of a vehicle moving on a beam-like bridge. The proposed method is developed based on an innovative concept of equivalent load and the application of force reconstruction. Herein, the equivalent loads are expressed as some concentrated loads whose acting positions are time invariant. Modal forces induced by the equivalent loads are equal to the ones caused by the vehicle-induced moving forces. Under the crucial assumption of equivalent loads, the first key step is to reconstruct the equivalent loads by using a force identification method that is implemented via matrix regularization. Since the equivalent loads have been estimated, the second step aims to introduce a practical strategy for identifying the vehicle weight from the sum of the identified equivalent loads rather than the sum of moving forces. Because of this, a highlight is that time-varying position of vehicle is not needed. To verify the effectiveness and feasibility of the proposed method, beam structures with single span are carried out for numerical simulations and experimental validations. Illustrated results show that the proposed method can be applied for identifying the gross weight of a vehicle moving on a beam-like bridge with high accuracy and strong robustness. Some related issues are discussed as well.

Robustifying Payload Carrying Operations for Quadrotors Under Time-Varying State Constraints and Uncertainty

Quadrotors find a vast potential use in delivery and disaster relief operations. Control becomes critical in such scenarios, especially when quadrotors have to manoeuvre through constrained spaces or deliver payloads at precise locations in the presence of external disturbances and parametric uncertainties stemming from uncertain payloads. Therefore, the controller has to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">guarantee a predefined tracking accuracy not to violate the state constraints</i> . On the other hand, conventional fixed-valued state constraints are not suitable in many scenarios such as (i) initial offset being well beyond the expected accuracy, (ii) system dynamics experiencing significant transients due to the dropping of the payload. However, to the best of the authors’ knowledge, state-of-the-art controllers do not provide any solution for an underactuated system like a quadrotor when the system needs to honour time-varying constraints under uncertainties. This work proposes a controller for quadrotors which is robust against external disturbances and parametric variations and guarantees a time-varying predefined position, velocity, attitude, and attitude-rate accuracy. The closed-loop system stability is established analytically, and the effectiveness of the proposed controller is validated experimentally compared to the state-of-the-art under a precision payload delivery scenario.

Non-linear Finite-Time Tracking Control of Uncertain Robotic Manipulators Using Time-Varying Disturbance Observer-Based Sliding Mode Method

In this paper, a time-varying chattering-free disturbance observer-based position tracking control law of serial robotic manipulators is presented to track a reference signal in a finite time. The key idea is to employ a positive-increasing function associated with the control/observer objectives to improve the control performance. First, the model of an uncertain robotic manipulator is presented as the case study of the proposed strategy. Then, the time-varying form of the robotic manipulator model is obtained to provide finite-time boundedness using the first-order sliding mode method. Moreover, without any knowledge about the upper bounds of the uncertainties, a reduced-order observer is presented to estimate the uncertainties in a finite time. Subsequently, a disturbance observer-based finite-time position tracking control law is designed. The time-varying gains are provided to converge the position tracking error to a neighborhood of zero in a finite time. Finally, comparative simulations are presented to show the effectiveness of the proposed scheme compared to other existing strategies.

Direct Current Motor Position Control by a Sliding Mode Controlled Dual Three-Phase AC-DC Power Converter

Direct voltage source (DC) and a DC/DC power converter can be used to control the position, speed or torque of a DC motor. In such an operational condition, a rectifier is needed to have a DC voltage source, if a three-phase voltage source is available only. The objective of this study is to replace a rectifier and DC/DC power converter with one AC/DC power converter such that its output would be equal to the voltage needed for control of DC motor. It is assumed that the control algorithm of a DC motor is selected, which means that the desired output voltage of the AC/DC converter as a time function or function of the motor state is known. First, the sliding mode methodology is applied to control the converter's three branches to make three-phase input current track source voltages multiplied by a time-varying gain. Then the gain is selected such that the converter output voltage is equal to the desired input of the DC motor. It is shown that this condition holds if the time-varying gain satisfies the first-order differential equation, which can be implemented as part of the controller. The application of the Lyapunov theory confirmed that the position regulation process has a stable equilibrium point at the origin and the time gain variation is bounded. The power efficiency is equal to one which is a desirable setting in the proposed controller. A numerical simulation demonstrates the application of the developed control methodology for both constant and time-varying angular position reference.

Numerical analysis of cylindrical shell stability interacting with inhomogeneous soil

The research is aimed at determining the critical buckling load of the spatial model shell - soil system in the case of inhomogeneous physical and mechanical soil properties along the longitudinal axis of the cylindrical shell in a nonlinear formulations of the task. Methods. The task is solved by a numerical method using a finite element complex ANSYS. Two calculated cases of the spatial model shell - soil system are compiled. The soil is divided into two equal parts with different physical and mechanical properties. The problem was solved in geometrically, physically and constructively nonlinear statement. Nonlinearity is due to the need to find the contact zone through an iterative process and determine the time-varying position of the shell. The soil is modeled by volumetric elements, each consisting of twenty nodes. The shell is modeled by flat elements, each consisting of four nodes. Contact elements of one-side action are used. Critical buckling load are determined relative to the actual load of its own weight. Results. Critical loads are obtained from two calculated cases of the spatial model shell - soil system. There is a comparative analysis of the results. An assessment of the stability margin of the shell relative to the actual load is given.

Investigation of tool-workpiece contact rate and milling force in elliptical ultrasonic vibration-assisted milling

Elliptical ultrasonic vibration-assisted milling (EUVAM) is widely used as an efficient processing method for hard-to-machining materials such as titanium alloy, superalloy, and hard-brittle materials. To uncover the mechanism of the intermittent cutting characteristics in EUVAM, the tool-workpiece contact rate model is developed by combining with the kinematic relationship between the tool edge and the workpiece in the process. According to the analysis of the contact rate model, the phenomenon that the contact rate increases rapidly with the time-varying tooth position angle in one-dimensional ultrasonic vibration assisted milling can be improved in EUVAM. In addition, considering the variation of window function and undeformed cutting thickness, a force model is established. And the experiment of EUVAM is performed to verify the model of ultrasonic milling force, and the influence of process parameters (amplitude, cutting speed, feed rate and cutting depth) on ultrasonic milling force is also analyzed.

Robust cooperative trajectory tracking control for an unactuated floating object with multiple vessels system

This paper proposes a robust cooperative trajectory tracking control scheme for an unactuated floating object with multiple vessels under environmental disturbances. The object and multiple vessels are connected by using towlines. The proposed control scheme consists of three parts: a virtual controller for the object, a control allocation algorithm and a distributed robust time-varying formation controller for vessels. The virtual controller is first designed to obtain the control forces of the object to track the reference trajectory. To compute the optimal tension of each towline, the control allocation algorithm is introduced. Then, the time-varying relative positions from the object to vessels are gained by using a nonlinear towline model and the towline attachment geometry. Furthermore, the distributed robust time-varying formation controller is devised for vessels based on dynamic surface control technique, an adaptive law and graph theory. It is proved that the tracking errors of the object and vessels are bounded. Simulations substantiate that the proposed method can achieve good cooperative control performance and robustness, and the unactuated object can track the reference trajectory with high accuracy.

Tracking surface waves in bi-static geometries with Doppler sensitive probe signals

This talk describes a method of estimating the position and velocity of surface waves that uses the delay and Doppler shift of observed scatter arrivals, and does not need a receiving array with high spatial resolution. This method is demonstrated using data collected during the at-sea KAM11 experiment, similar to data that has been previously analyzed using Doppler insensitive linear frequency modulated waveforms [e.g., M. Badiey, A. Song, and K. Smith, J. Acoust. Soc. Am. 132(4), EL290–EL295 (2012)]. An analysis of Doppler sensitive maximum length sequence transmissions is presented for the same experimental geometry as the previous studies. The Doppler sensitive analysis shows additional scatter arrivals previously not reported with distinct Doppler shifts. A simple travel time argument is then used to explain the observed Doppler of the scatter arrivals, and infer the time-varying position of waves traveling along the sea surface.

Formation Control With Time-Varying Formations, Bounded Controls, and Local Collision Avoidance

We present a formation control algorithm for double-integrator agents, where the formation is time-varying and the agents’ controls satisfy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> bounds (e.g., the controls can accommodate actuator saturation). We assume that each agent has relative-position-and-velocity feedback of its neighbor agents, where the communication structure is a quasi-strongly connected graph, and at least one agent has a measurement of its position and velocity relative to the leader (if applicable). The main analytic results provide sufficient conditions such that all agents converge to the desired time-varying relative positions with one another and the leader and have <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> bounded controls (if applicable). Next, we extend the formation control algorithm to include collision-avoidance terms that, for a set of initial conditions, prevent each agent from colliding with the agents in its neighbor set or colliding with the leader (if applicable). Finally, we present results from rotorcraft experiments that demonstrate the algorithm with time-varying formations and bounded controls. These experimental results include indoor experiments using a motion-capture system and outdoor experiments demonstrating the algorithm in a real-world environment with disturbances (e.g., wind) and only onboard feedback.

Cross-sectional and time-series momentum returns: Is China different?

We compare the performance of the time-series (TS) and cross-sectional (CS) momentum strategies in the US and China. The CS strategies by default are zero net investment strategies, whereas the TS strategies take on a time-varying net long position in risky assets. In the US, we confirm that the performance of the TS and CS strategies are not substantially different, as it is explained by a time-varying investment in risky assets. However, we find positive and significant return differences between the TS and CS strategies in China, after adjusting the CS strategies for a time-varying investment in risky assets. Our results suggest that in China, the difference between the performance of the TS and CS strategies might not be only limited to a time-varying investment in risky assets.