Reduce Tracking Errors Research Articles

Fixed-Time Control with an Improved Sparrow Search Algorithm for Robotic Arm Performance Optimization

This paper presents an innovative approach that integrates a fixed-time control (FTC) algorithm with an improved sparrow search algorithm (ISSA) to enhance the trajectory tracking accuracy of a two-degree-of-freedom (two-DOF) robotic arm. The FTC algorithm, which incorporates barrier Lyapunov function (BLF) and adaptive neural network strategies, ensures rapid convergence, effective vibration suppression, and the robust handling of system uncertainties and input saturation. The ISSA, inspired by the foraging behavior of sparrows, improves search efficiency through dynamic weight adjustments and chaotic mapping, balancing global and local search capabilities. By optimizing control parameters, ISSA minimizes tracking errors. Simulation results demonstrate that the combined FTC and ISSA approach significantly reduces tracking errors and improves response speed compared to the use of FTC alone, underscoring its potential for achieving high-precision control in robotic arms and offering a promising direction for precise robotic control applications.

Linear Disturbance Observer-Enhanced Continuous-Time Predictive Control for Straight-Line Path-Following Control of Small Unmanned Aerial Vehicles

This paper studies the straight-line path-following problem on the lateral plane for fixed-wing unmanned aerial vehicles (FWUAVs) which are susceptible to uncertainties. Firstly, based on the natural frame’s location on the prescribed reference paths, the command yaw angle (which is the basis for yaw angle control system design) is solved analytically by combining it with the errors of path following, attack angle, sideslip angle, attitude angles, and geometric parameters of the prescribed reference paths. Secondly, by considering complicated dynamic characteristics, a linear extended state observer is designed to estimate uncertainties such as nonlinearities, couplings, and unmodeled dynamics whose estimated values are incorporated into the continuous-time predictive controllers for feedback compensation. Finally, numerical simulations are conducted to demonstrate the advantages of the proposed method, including reduced tracking errors and enhanced robustness in the closed-loop system, as compared to the conventional nonlinear dynamic inversion and sliding mode control approaches.

Multicolor wavefront sensing using Talbot effect for high-order harmonic generation

High-order harmonic generation (HHG) using femtosecond lasers is an efficient and cost-effective method for producing attosecond and femtosecond light in the extreme ultraviolet and soft x-ray regions. This technique generates high-brightness harmonic beams with stable spectra, intensity, and wavefronts, making it a valuable tool for applications such as nanoimaging, material metrology, and studies of ultrafast dynamics. Accurate wavefront measurement of HHG beams is essential for analyzing complex incident fields, understanding atomic responses, and enhancing applications such as attosecond-driven ultrafast processes. However, quantifying the wavefronts of each harmonic component remains a challenge. Here, we present a multicolor wavefront sensing for HHG beams using the Talbot effect, validated theoretically and experimentally. Our method reconstructs individual high-order harmonic wavefronts with a spectral resolution of 4.8 eV, capturing multiple harmonic wavelengths in a single scan along the propagation direction, without the need for additional spectrometers or complex calibrations. This approach surpasses conventional Talbot effect wavefront sensing, which typically relies on quasimonochromatic waves or wavelength-averaging. Additionally, we introduce a high-accuracy centroid detection strategy that reduces tracking errors to the thousandths of a pixel while maintaining high computational efficiency, paving the way for broader applications in imaging and metrology. Published by the American Physical Society 2024

Cognitive Radar Waveform Selection for Low-Altitude Maneuvering-Target Tracking: A Robust Information-Aided Fusion Method

In this paper, we introduce an innovative interacting multiple-criterion selection (IMCS) idea to design the optimal radar waveform, aimingto reduce tracking error and enhance tracking performance. This method integrates the multiple-hypothesis tracking (MHT) and Rao–Blackwellized particle filter (RBPF) algorithms to tackle maneuvering First-Person-View (FPV) drones in a three-dimensional low-altitude cluttered environment. A complex hybrid model, combining linear and nonlinear states, is constructed to describe the high maneuverability of the target. Based on the interacting multiple model (IMM) framework, our proposed IMCS method employs several waveform selection criteria as models and determines the optimal criterion with the highest probability to select waveform parameters. The simulation results indicate that the MHT–RBPF algorithm, using the IMCS method for adaptive parameter selection, exhibits high accuracy and robustness in tracking a low-altitude maneuvering target, resulting in lower root mean square error (RMSE) compared with fixed- or single-waveform selection mechanisms.

An Improved Quantum Particle Swarm Optimization Algorithm for Target Tracking Deployment in Spatial Sensor Networks

This paper presents a comprehensive review of the current research on spatial sensor networks and the node deployment methods employed for mobile target tracking. The study introduces particle swarm optimization (PSO) and its quantum behavior extension, detailing concepts such as the quantum state wave function and particle position representation. Subsequently, an improved Quantum Particle Swarm Optimization (QPSO) algorithm is proposed. This enhanced algorithm increases population diversity by incorporating quantum rotation gates and quantum mutation mechanisms, expands the search space through the superposition state and interference principles of quantum mechanics, and dynamically adjusts algorithm parameters to balance global exploration and local search. These modifications aim to improve both the convergence speed and accuracy of the algorithm. Simulation results demonstrate that the improved QPSO algorithm surpasses traditional mobile tracking deployment algorithms and the standard quantum behavior particle swarm optimization algorithm in terms of target tracking deployment within spatial sensor networks. Notably, it significantly enhances the tracking success rate and reduces tracking errors.

Effectiveness of Iterative Learning Control for Vision-Based Tracking in Repeated Tasks Under Varying Lighting Conditions

Among available techniques for lateral tracking in autonomous driving, none possesses the capability to learn from past behaviors and progressively reduce lateral errors. In contrast, our proposed iterative learning control (ILC) scheme significantly enhances tracking performance in vision-based classical control, particularly in challenging environmental conditions. Our vision-based control system incorporates real-time semantic segmentation using the ENet model for unconstructed road area extraction. Linear regression estimates steering adjustments, while a visual PID controller maintains the vehicle’s position at the road’s centerline. This control system’s performance varies with lighting conditions, notably in dense shade, where the vehicle tends to deviate from the desired path. To assess ILC’s potential in error reduction over successive trials, we examined various ILC structures and compared them with a pure PID controller. Despite challenges in directly comparing PID and ILC designs due to changing lighting conditions during experiments, ILC consistently reduced tracking errors and improved path alignment with each iteration. Notably, the degree of error reduction became more pronounced with a greater number of learning gains in the ILC design. Our experimental results underscore the overall effectiveness of ILC in tracking the desired path in autonomous driving scenarios, particularly in varying environmental conditions.

Adaptive Control for a Two-Axis Semi-Strapdown Stabilized Platform Based on Disturbance Transformation and LWOA-PID.

A two-axis semi-strapdown stabilized platform is a device designed to eliminate aircraft disturbances and ensure the stability of the sensor's orientation. A traditional two-axis semi-strapdown stabilization platform for aircraft can effectively control disturbance in pitch and yaw channel, but it cannot achieve ideal disturbance control in the roll channel. In order to solve this problem, an adaptive control method based on disturbance transformation and LWOA-PID is proposed. Disturbance transformation is the process of integrating the angular position disturbance of the roll from the previous moment into the combined disturbance of the pitch and yaw at the current moment. This is followed by decoupling the combined disturbance of the pitch and yaw at the current moment, thereby eliminating the disturbance caused by the roll from the previous moment. This process is repeated to achieve the goal of eliminating roll channel disturbances. To ensure the line of sight (LOS) pointing accuracy stability in the two-axis semi-strapdown stabilized platform system for aircraft, a whale optimization adaptive proportional-integral-derivative (LWOA-PID) controller based on Latin hypercube sampling is designed. It is then compared with the classical PID controller in Matlab/Simulink. The simulation results indicate that the disturbance conversion module proposed in this paper can eliminate the impact of roll axis disturbances on the LOS pointing accuracy of the two-axis semi-strapdown stabilized platform for aircraft. Compared to the classical PID controller, the LWOA-PID controller reduces tracking errors for step and sinusoidal signals by 50% and 75%, respectively. It also shortens optimization time by 37.5% compared to the WOA-PID while maintaining the same level of accuracy. Furthermore, when combined with the conversion module, the tracking error is reduced by an additional order of magnitude.

An asymmetrically variable wingtip anhedral angles morphing aircraft based on incremental sliding mode control: Improving lateral maneuver capability

This paper presents the design of an asymmetrically variable wingtip anhedral angles morphing aircraft, inspired by biomimetic mechanisms, to enhance lateral maneuver capability. Firstly, we establish a lateral dynamic model considering additional forces and moments resulting during the morphing process, and convert it into a Multiple Input Multiple Output (MIMO) virtual control system by importing virtual inputs. Secondly, a classical dynamics inversion controller is designed for the outer-loop system. A new Global Fast Terminal Incremental Sliding Mode Controller (NDO-GFTISMC) is proposed for the inner-loop system, in which an adaptive law is implemented to weaken control surface chattering, and a Nonlinear Disturbance Observer (NDO) is integrated to compensate for unknown disturbances. The whole control system is proven semi-globally uniformly ultimately bounded based on the multi-Lyapunov function method. Furthermore, we consider tracking errors and self-characteristics of actuators, a quadratic programming-based dynamic control allocation law is designed, which allocates virtual control inputs to the asymmetrically deformed wingtip and rudder. Actuator dynamic models are incorporated to ensure physical realizability of designed allocation law. Finally, comparative experimental results validate the effectiveness of the designed control system and control allocation law. The NDO-GFTISMC features faster convergence, stronger robustness, and 81.25% and 75.0% reduction in maximum state tracking error under uncertainty compared to the Incremental Nonlinear Dynamic Inversion Controller based on NDO (NDO-INDI) and Incremental Sliding Mode Controller based on NDO (NDO-ISMC), respectively. The design of the morphing aircraft significantly enhances lateral maneuver capability, maintaining a substantial control margin during lateral maneuvering, reducing the burden of the rudder surface, and effectively solving the actuator saturation problem of traditional aircraft during lateral maneuvering.

Position Control of Electro-hydraulic Servo System Based on Repetitive Control Strategy

Background: When performing repetitive work in an electro-hydraulic servo system, the expected tracking signals are often periodic signals, such as trigonometric functions. For this kind of electro-hydraulic servo system, repetitive control is one of the most ideal control strategies. Objective: The objective of this patent technology is to improve the position-tracking performance of the electro-hydraulic servo system and minimize tracking errors by designing and implementing a repetitive control strategy. Methods: The study models an electro-hydraulic servo system, designs a stabilizing controller, and develops a plug-in repetitive controller to enhance EHSS tracking. The regeneration spectrum is used as a stability criterion, and performance is evaluated using statistical metrics like Mean Square Error (MSE), Root Mean Square Error (RMSE), and standard deviation of the tracking error along with tracking performance and steady-state error. Results: The developed controller, validated through simulation analysis and real-time experiments, significantly reduces tracking error and enhances system position tracking accuracy, demonstrating its effectiveness. For instance, the repetitive control strategy outperforms PID and backstepping controllers at 30 mm with 0.5 Hz, achieving an error of 0.2 with an RMSE of 0.0924 and σ of 0.0878. Similar trends are observed at various test conditions, highlighting the consistent and robust performance of the designed repetitive controller. Additionally, the designed repetitive controller demonstrates an average improvement of 75.175% and 62.97% compared to the proportional- integral-derivative and backstepping controllers, respectively. Conclusion: The designed controller provides technical support for position control of the electrohydraulic servo system, achieves position control requirements, and significantly improves positioning accuracy and response.

The Sliding Mode Control for Piezoelectric Tip/Tilt Platform on Precision Motion Tracking

This paper presents the design of a sliding mode controller to compensate hysteresis nonlinearity and achieve precision motion tracking for a novel piezoelectric tip/tilt platform driven by a PZT actuator. The sliding mode control scheme is based on the unique physical characteristics of the piezoelectric tip/tilt platform. The proposed scheme effectively guides the platform state onto a predefined sliding surface and ensures its sustained movement along this manifold. This approach reduces tracking errors compared to conventional methodologies. The stability of the sliding mode control scheme is demonstrated by the Lyapunov theory framework. It achieves precise motion control with minimal tracking error on a piezoelectric tip/tilt platform. The properties of the controller have been confirmed through experimental tests. The proposed control scheme enhances the robust tracking and stability performance on the piezoelectric tip/tilt platform, outperforming traditional control schemes. Compared with the P562.6CD produced by PI Germany, the proposed innovative approach not only boosts the platform’s resolution by 32% but also implements a 33% reduction in cost.

A Novel Robust H∞ Control Approach Based on Vehicle Lateral Dynamics for Practical Path Tracking Applications

This paper proposes a robust lateral control scheme for the path tracking of autonomous vehicles. Considering the discrepancies between the model parameters and the actual values of the vehicle and the fluctuation of parameters during driving, the norm-bounded uncertainty is utilized to deal with the uncertainty of model parameters. Because some state variables in the model are difficult to measure, an H∞ observer is designed to estimate state variables and provide accurate state information to improve the robustness of path tracking. An H∞ state feedback controller is proposed to suppress system nonlinearity and uncertainty and produce the desired steering wheel angle to solve the path tracking problem. A feedforward control is designed to deal with road curvature and further reduce tracking errors. In summary, a path tracking method with H∞ performance is established based on the linear matrix inequality (LMI) technique, and the gains in observer and controller can be obtained directly. The hardware-in-the-loop (HIL) test is built to validate the real-time processing performance of the proposed method to ensure excellent practical application potential, and the effectiveness of the proposed control method is validated through the utilization of urban road and highway scenes. The experimental results indicate that the suggested control approach can track the desired trajectory more precisely compared with the model predictive control (MPC) method and make tracking errors within a small range in both urban and highway scenarios.

Design and Implementation of Extremum-Seeking Control Based on MPPT for Dual-Axis Solar Tracker

The increase in the production efficiency of photovoltaic technology depends on its alignment in relation to the solar position. Solar tracking systems perform the tracking action by implementing control algorithms that help the reduction of tracking errors. However, conventional algorithms can reduce the life of actuators and mechanisms due to control action, significantly reducing operation times and profitability. In this article, an unconventional control scheme is developed to address the mentioned challenges, presenting the design and implementation of an extremum-seeking control to perform maximum power point tracking for a two-axis solar tracker instrumented with a solar module. The proposed controller is governed by the dynamics of a classic proportional-integral scheme and assisted by sensorless feedback. Also, it has an anti-wind-up-type configuration for the integral component and counts with a variable amplitude for the dither signal. The proposal is validated experimentally by comparison between a fixed system and a two-axis system in azimuth-elevation configuration. In addition, two performance indices are defined and analyzed, system energy production and tracking error. The results show that the proposal allows producing up to 27.75% more than a fixed system, considering the tracker energy consumption due to the tracking action and a pointing accuracy with ±1.8° deviation. Finally, an analysis and discussion are provided based on the results, concluding that the proposed algorithm is a viable alternative to increase the performance of tracked photovoltaic systems.

Dynamic Modelling and Optimal Sliding Mode Control of the Wearable Rehabilitative Bipedal Cable Robot with 7 Degrees of Freedom

Although robot-assisted physiotherapy has gained increasing attention in recent years, the use of wearable rehabilitation robots for lower limbs has shown reduced efficiency due to additional equipment and motors located at the center of the joint, increasing complexity and load on disabled patients. This paper proposes a novel rehabilitation approach by eliminating motors and equipment from the center of joints and placing them on a fixed platform using cable-based power transmission. A proposed model of a 14 cable-driven bipedal robot with 7 degrees of freedom has been used to model a lower limb rehabilitation robot corresponding to it. The dynamic equations of the robot are derived using the Euler-Lagrange method. The sliding mode control technique is utilized to offer accurate control for tracking desired trajectories, ensuring smoothness despite disturbances, and reducing tracking errors. This approach is employed to help prevent patients from falling and support them in maintaining balance during rehabilitative exercises. To ensure that cables exert positive tension, the sliding mode controller was combined with quadratic programming optimization, minimizing path error while constraining the controller input torque to be non-negative. The performance of the proposed controller was assessed by considering several control gains resulting in K = 10 identified as the most effective one. The feasibility of this approach to rehabilitation is demonstrated by the numerical results in MATLAB simulation, which show that the RMSE amount of the right and left hip and thigh angles are 0.29, 0.37, 0.31, and 0.44, respectively which verified an improved rehabilitation process. Also, the correlation coefficient between the Adams and MATLAB simulation results for motor torque was found to be 0.98, indicating a high degree of correlation between the two simulation results.

Self-supervised learning for interventional image analytics: toward robust device trackers.

The accurate detection and tracking of devices, such as guiding catheters in live X-ray image acquisitions, are essential prerequisites for endovascular cardiac interventions. This information is leveraged for procedural guidance, e.g., directing stent placements. To ensure procedural safety and efficacy, there is a need for high robustness/no failures during tracking. To achieve this, one needs to efficiently tackle challenges, such as device obscuration by the contrast agent or other external devices or wires and changes in the field-of-view or acquisition angle, as well as the continuous movement due to cardiac and respiratory motion. To overcome the aforementioned challenges, we propose an approach to learn spatio-temporal features from a very large data cohort of over 16million interventional X-ray frames using self-supervision for image sequence data. Our approach is based on a masked image modeling technique that leverages frame interpolation-based reconstruction to learn fine inter-frame temporal correspondences. The features encoded in the resulting model are fine-tuned downstream in a light-weight model. Our approach achieves state-of-the-art performance, in particular for robustness, compared to ultra optimized reference solutions (that use multi-stage feature fusion or multi-task and flow regularization). The experiments show that our method achieves a 66.31% reduction in the maximum tracking error against the reference solutions (23.20% when flow regularization is used), achieving a success score of 97.95% at a faster inference speed of 42 frames-per-second (on GPU). In addition, we achieve a 20% reduction in the standard deviation of errors, which indicates a much more stable tracking performance. The proposed data-driven approach achieves superior performance, particularly in robustness and speed compared with the frequently used multi-modular approaches for device tracking. The results encourage the use of our approach in various other tasks within interventional image analytics that require effective understanding of spatio-temporal semantics.

Perfect Tracking Control of Linear Sliders Using Sliding Mode Control with Uncertainty Estimation Mechanism

This paper aims to achieve precise position control of a stage used in semiconductor exposure apparatus. The demand for smart devices, such as smartphones, is rapidly expanding, and their performance is expected to continue to improve. To manufacture these devices, it is necessary to miniaturize semiconductor devices and improve productivity. The precise control of semiconductor exposure apparatus is important for the manufacture of ultra-small semiconductor devices. The stage of semiconductor exposure apparatus uses a linear motor, and this paper performs high-precision perfect tracking control of this stage. Perfect tracking control is a control method that always follows the command value while the command value changes moment by moment, and requires high accuracy. In high-precision positioning, uncertainty in the stage model has a significant impact. Therefore, this paper proposes a method to reduce tracking errors due to the influence of uncertainty by performing uncertainty compensation using sliding mode control with the estimated value of uncertainty. The estimation of uncertainty uses a method that combines Kernel LMS with an observer. Instead of the widely used Gaussian kernel, this paper uses a generalized Gaussian kernel that allows for finer parameter settings. Furthermore, this paper proposes a method to adaptively optimize the shape parameter of the generalized Gaussian kernel. Our simulations and experiments confirm that the proposed method improves tracking performance compared to conventional sliding mode control.

An improved nonsingular adaptive super twisting sliding mode controller for quadcopter.

This paper presents an improved nonsingular adaptive super twisting sliding mode control for tracking of a quadrotor system in the presence of external disturbances and uncertainty. The initial step involves developing a dynamic model for the quadrotor that is free from singularities, achieved through the utilization of the Newton-Quaternion formalism. Then, the super twisting algorithm is used to develop a novel sliding mode control that mitigates chattering. Particle Swarm Optimization (PSO) is employed for the adjustment of the controller gains. Moreover, to maintain stable control of the quadcopter, even in scenarios where the upper limit of disturbances is unknown, an adaptive rule grounded in Lyapunov stability is applied. Simulation results demonstrate that the proposed controller reduces tracking errors to 0.1% for roll, 0.05% for pitch, and 2.2% for altitude, outperforming other state-of-the-art sliding mode controllers. Additionally, the proposed controller effectively rejects disturbances, maintaining minimal steady-state errors of 0.01° for roll, 0.02° for pitch, and 0.001° for yaw, significantly better than conventional controllers. These results highlight tracking and disturbance rejection capabilities of the proposed controller, making its real-time implementation for quadrotor Unmanned Aerial Vehicles (UAVs) feasible.

Adaptive Supplementary Control of VSG Based on Virtual Impedance for Current Limiting in Grid-Connected and Islanded Microgrids

By applying virtual synchronous generator (VSG) method in high penetration level microgrids, current limiting issue under fault condition has become an important challenge. The main objective of this paper is to propose a novel current limiting strategy which has the capability of voltage tracking error reduction to avoid voltage controller saturation. This purpose is obtained by adaptive virtual impedance-based reference voltage correction during fault condition. Furthermore, positive and negative peak detection-based current limiting method implemented in double loop control system prepares soft transition ability. Moreover, this current limiting method generates the adaptive term of virtual impedance part. In contrast to conventional VSG methods, the proposed approach provides high quality voltage and current for microgrid in both grid-connected and islanded modes during fault conditions. The offline and hardware in the loop (HIL) simulation results confirm that the peak current of the inverter is restricted to the threshold value under symmetrical and asymmetrical faults for two operating modes of microgrid.

Control moment coefficient methodology validation for eVTOL sizing

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.

A suboptimal control scheme based on integrated real-time nonlinear estimation-identification approach for developed flexible joint manipulators structure

As the safety of human-robot interaction is of great interest in various applications, the flexibility of machine joints becomes increasingly important. In this paper, a general model is developed for electrically driven flexible-joint robots (ED-FJR), in which the coupled phenomena of stiffness-damping and friction in the joints are modeled as nonlinear and time-varying parameters. Because the output torque of the actuator mounted on the link cannot be measured, its state variables are estimated by the suboptimal estimator. Furthermore, the unknown parameters of joint flexibility are identified by the identification algorithm based on time-varying nonlinear least-squares error (TV-NLS), which are then used in the proposed control algorithm to compensate for negative effects and errors. The state-dependent Riccati equation (SDRE) method is developed in this paper using the combined estimator-identifier approach. The novel proposed method for a 3-degree-of-freedom (3-DOF) mechanical arm with electrically driven flexible joints is implemented and validated. The obtained results show that the system's performance has improved by 83% in terms of modeling accuracy. Furthermore, when compared to other methods, the proposed algorithm reduces tracking error by 59%, making it easier to reach the target point.

Liquidity Risk, Return Performance, and Tracking Error: Synthetic vs. Physical ETFs

As the global ETF market continues to grow, the significance of understanding replication strategies has become increasingly apparent. This study examines the compensation of synthetic exchange-traded funds (ETFs) due to their greater risk exposure than physical ETFs, using ETFs listed on developed European markets from 2009 to 2020. This is the first study to investigate liquidity risk related to the replication strategy of ETFs. We investigate the difference in systematic liquidity risk between synthetic and physical ETFs using a liquidity-adjusted capital asset pricing model (LCAPM). Our findings suggest that synthetic ETFs have higher liquidity risks than physical ETFs and offer additional returns within the low-liquidity group. We also analyze the tracking performance of ETFs based on their type and find that the synthetic replication method reduces tracking errors within the high-liquidity group. Specifically, the enhanced tracking performance of synthetic ETFs becomes more prominent during periods of liquidity shocks than in regular periods. These findings shed light on key considerations for resolving puzzles in tracking errors.