Minimum Tracking Error Research Articles

H ∞ prescribed tracking performance-based fractional-order sliding mode control for disturbed discrete-time systems: an LMI approach

This paper presents a novel approach to the design of a discrete-time Fractional-Order Sliding Mode Control (FSMC) system for Single Input Single Output (SISO) applications, utilising the Autoregressive with exogenous input (ARX) method for system modelling. The proposed methodology emphasises the Prescribed Performance Control (PPC) to ensure minimal tracking errors through a transformation of tracking errors based on a specified performance function. A Fractional-Order Quasi-Sliding Mode Control (FQSMC) is subsequently developed to maintain the tracking error within predetermined bounds, effectively addressing the chattering phenomenon commonly associated with the traditional sliding mode control. The integration of fractional calculus enhances the smoothness of the output while ensuring accurate tracking, making it ideal for real-world applications. Additionally, a novel Linear Matrix Inequality (LMI) observer is introduced to bolster the system's resilience against uncertainties and disturbances without complicating the computational process. The effectiveness of the proposed Prescribed Performance Fractional-Order Quasi-Sliding Mode Control (PP-FQSMC) is validated through extensive MATLAB simulations and experimental studies conducted on a Tank system. Results demonstrate that the PP-FQSMC significantly outperforms traditional methods, with maximum tracking errors of 1.6 × 10−4 compared to 0.2 for the PP-QSMC and a Root Mean Square Tracking Error (RMSTE) of 1.3 × 10−3 compared to 1.2 × 10−4 for the PP-QSMC, ensuring strong tracking performance and stability. The findings indicate that the proposed controller effectively mitigates chattering in control signals while maintaining a smooth output. It showcases its potential for practical applications in environments characterised by model inaccuracies, time delays, and external disturbances.

Non-Commodity Agricultural Price Hedging with Minimum Tracking Error Portfolios: The Case of Mexican Hass Avocado

Non-Commodity Agricultural Price Hedging with Minimum Tracking Error Portfolios: The Case of Mexican Hass Avocado

Design and Modeling of a Long Range Motion Compliant Nanopositioning Stage Driven by a Normal Stressed Electromagnetic Actuator

Compliant nanopositioning stages with built-in ultra-precision actuators are frequently integrated into production and analysis instruments comprising ultra-high precision motion generation systems. These stages are essential nanotechnology and advanced material analysis components, providing precise positioning capabilities for various applications. However, in the practical engineering field, there is a lack of compliant nanopositioning stages that can achieve a long-range motion while maintaining accuracy, reliability, and compact size, which is the inspiration for this research. This paper investigates the design, modeling, and experimental testing of a long-range motion-compliant nanopositioning stage driven by a normal stressed electromagnetic actuator (NSEA). The nanopositioning stage components’ structural framework and working principle, including NSEA, bridge type distributed compliant (BTDC) mechanism, and the guiding mechanism, are fully examined to derive an analytical model. The analytical model is utilized in the sections that follow. Factors affecting the stroke and natural frequency of the nanopositioning stage are also illustrated. The optimization process of the nanopositioning stage is conducted in pursuit of a high-precision stage by specifically looking into the electromagnetic, BTDC mechanism, and guiding mechanism parameters. This optimization procedure also takes into account various design constraints, including stiffness, saturation flux density, and stress. Furthermore, the finite element analysis is used to verify the analytical model, and the results are discussed. The prototype is fabricated with reference to the analytical and finite element analysis results, and the experimental tests are conducted, including motion and natural frequency tests. In addition, a control system, which adopts both a proportional-integral-derivative controller and a damping controller, is designed to create a closed-loop system. Finally, the tracking performance of the stage was investigated, and a very minimal tracking error was observed. Overall, the comprehensive models and experimental tests proved the stage to be a good model which achieved the objective of the research.

Self-organizing feature selection fuzzy neural network-based terminal sliding mode control for uncertain nonlinear systems

A composite terminal sliding mode controller (CTSMC) for a kind of uncertain nonlinear system (UNS) is developed in this study. The primary aim of the design is to enhance the control performance of the CTSMC by learning its unknown parameters using a newly fuzzy neural network (FNN). Firstly, the stability and convergence of CTSMC for UNS with known parameters are demonstrated. Secondly, since some parameters of actual UNS are unmeasurable, a self-organizing feature selection fuzzy neural network (SOFSFNN) is intended to approach these unknown parts. Finally, the CTSMC using SOFSFNN is applied to UNS. The outcomes demonstrate that it has minimal tracking error, good robustness, and the ability to dynamically modify the network structure.

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.

A dynamic target tracking framework of UGV for UAV recovery under random disturbances

PurposeDynamically tracking the target by unmanned ground vehicles (UGVs) plays a critical role in mobile drone recovery. This study aims to solve this challenge under diverse random disturbances, proposing a dynamic target tracking framework for UGVs based on target state estimation, trajectory prediction, and UGV control.Design/methodology/approachTo mitigate the adverse effects of noise contamination in target detection, the authors use the extended Kalman filter (EKF) to improve the accuracy of locating unmanned aerial vehicles (UAVs). Furthermore, a robust motion prediction algorithm based on polynomial fitting is developed to reduce the impact of trajectory jitter caused by crosswinds, enhancing the stability of drone trajectory prediction. Regarding UGV control, a dynamic vehicle model featuring independent front and rear wheel steering is derived. Additionally, a linear time-varying model predictive control algorithm is proposed to minimize tracking errors for the UGV.FindingsTo validate the feasibility of the framework, the algorithms were deployed on the designed UGV. Experimental results demonstrate the effectiveness of the proposed dynamic tracking algorithm of UGV under random disturbances.Originality/valueThis paper proposes a tracking framework of UGV based on target state estimation, trajectory prediction and UGV predictive control, enabling the system to achieve dynamic tracking to the UAV under multiple disturbance conditions.

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.

Optimization of a fractional-order interval type-2 fuzzy PID controller based on BBO for real-time applications

This paper addresses the development of a robust controller for a nonlinear system to minimize the tracking errors and reduce the effects of external noise and disturbances. To achieve this, the biogeography-based optimization (BBO) algorithm is utilized for an optimally robust interval type 2 fractional-order fuzzy proportional integral derivative controller (BB0-IT2FO-FPID) is proposed. The proposed method offers several advantages. Firstly, the proposed controller is optimized to achieve robustness and minimize tracking errors. Secondly, it effectively handles external noise and disturbances, making it suitable for real-world applications. Thirdly, the use of the BBO algorithm enhances the controller's performance by dynamically adjusting its parameters based on system requirements. The performance of the proposed controller is validated by applying it to control a robotic manipulator, which presents challenges due to its nonlinear characteristics and interacting multi-input multi-output (MIMO) dynamics. Additionally, a real-time evaluation of the proposed controller is conducted by applying it to the speed control of a direct current (DC) machine. The effectiveness of the proposed controller is verified through simulation and practical experiments and comparisons with other optimized controllers, namely FO fuzzy type 1 PID (T1FO-FPID) and FOPID. The simulation and practical results demonstrate the superior performance of the BBO-IT2FO-FPID controller in the presence of system uncertainties and different types of disturbances.

Game theory based finite-time formation control using artificial potentials for tethered space net robot

The Tethered Space Net Robot (TSNR) is an innovative solution for active space debris capture and removal. Its large envelope and simple capture method make it an attractive option for this task. However, capturing maneuverable debris with the flexible and elastic underactuated net poses significant challenges. To address this, a novel formation control method for the TSNR is proposed through the integration of differential game theory and robust adaptive control in this paper. Specifically, the trajectory of the TSNR is obtained through the solution of a real-time feedback pursuit-evasion game with a dynamic target, where the primary condition is to ensure the stability of the TSNR. Furthermore, to minimize tracking errors and maintain a specific configuration, a robust adaptive formation control scheme with Artificial Potential Field (APF) based on a Finite-Time Convergent Extended State Observer (FTCESO) is investigated. The proposed control method has a key advantage in suppressing complex oscillations by a new adaptive law, thus precisely maintaining the configuration. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.

Passivity-based Rieman Liouville fractional order sliding mode control of three phase inverter in a grid-connected photovoltaic system.

Photovoltaic (PV) system parameters are always non-linear due to variable environmental conditions. The Maximum power point tracking (MPPT) is difficult under multiple uncertainties, disruptions and the occurrence of time-varying stochastic conditions. Therefore, Passivity based Fractional order Sliding-Mode controller (PBSMC) is proposed to examine and develop a storage function in error tracking for PV power and direct voltage in this research work. A unique sliding surface for Fractional Order Sliding Mode Control (FOSMC) framework is proposed and its stability and finite time convergence is proved by implementing Lyapunov stability method. An additional input of sliding mode control (SMC) is also added to a passive system to boost the controller performance by removing the rapid uncertainties and disturbances. Therefore, PBSMC, along with globally consistent control efficiency under varying operating conditions is implemented with enhanced system damping and substantial robustness. The novelty of the proposed technique lies in a unique sliding surface for FOSMC framework based on Riemann Liouville (R-L) fractional calculus. Results have shown that the proposed control technique reduces the tracking error in PV output power, under variable irradiance conditions, by 81%, compared to fractional order proportional integral derivative (FOPID) controller. It is reduced by 39%, when compared to passivity based control (PBC) and 28%, when compared to passivity based FOPID (EPBFOPID). The proposed technique led to the least total harmonic distortion in the grid side voltage and current. The tracking time of PV output power is 0.025 seconds in PBSMC under varying solar irradiance, however FOPID, PBC, EPBFOPID, have failed to converge fully. Similarly the dc link voltage has tracked the reference voltage in 0.05 seconds however the rest of the methods either could not converge, or converged after significant amount of time. During solar irradiance and temperature change, the photovoltaic output power has converged in 0.018 seconds using PBSMC, however remaining methods failed to converge or track fully and the dc link voltage has minimum tracking error due to PBSMC as compared to the other methods. Furthermore, the photovoltaic output power converges to the reference power in 0.1 seconds in power grid voltage drop, whereas other methods failed to converge fully. In addition power is also injected from the PV inverter into the grid at unity power factor.

A dual-axis solar tracking system with minimized tracking error through optimization technique

A dual-axis solar tracking system with minimized tracking error through optimization technique

Particle swarm optimization based leader-follower cooperative control in multi-agent systems

Multi-agent systems (MAS) have attracted significant attention in recent years due to their wide applications in cooperative control, formation control, synchronization of complex networks, and distributed coordination. A fundamental problem in MAS is the leader-follower consensus or cooperative tracking, where the followers are required to track the state trajectory of the leader agent. To solve the leader-follower consensus problem, we propose a novel evolutionary computation approach to design the optimal distributed control protocols for leader-follower MAS. First, we formulate the design of distributed control gains for leader-follower consensus as an optimization problem to minimize tracking errors. Then, we leverage particle swarm optimization as an efficient evolutionary technique for distributed gain optimization in multi-agent networks. Finally, we guarantee stability for the closed-loop dynamics under directed communication topologies based on algebraic graph theory. The simulation results indicate that the proposed method yields a diminished tracking error, expedites the convergence process, and minimizes the requisite control effort while enhancing computational efficiency. Furthermore, these results exemplify the method's versatility when applied to nonlinear dynamic scenarios, directed network topologies, fluctuating disturbances, and optimization across multiple domains.

A comparative study of entry guidance for Mars robotic and human landing missions

Human desire to explore Mars has persisted throughout history, and especially, it is required to achieve precise and safe landings on the Martian surface. The atmospheric entry phase plays a crucial role in ensuring mission success, and active research on entry guidance methods continues. This paper presents a comparative study between the two primary types of entry guidance methods: (1) path planning-tracking and (2) predictor–corrector methods by applying them to solve two distinct Mars atmospheric entry guidance problems: (a) robotic entry and (b) human entry missions. Optimization approaches are adopted for the path planning-tracking method. After generating an optimal reference trajectory based on a mission concept-defined cost function, the receding horizon control method is employed to minimize tracking errors. In the predictor–corrector method, two parameterized entry guidance approaches are explored and analyzed. A well-known numerical predictor–corrector method that utilizes a parameterized bank angle profile for entry trajectory generation is tested to demonstrate its robustness against random dispersions. On the other hand, another predictor–corrector type guidance method that assumes a polynomial shape to shape an altitude profile over range-to-go is adopted to show its range control capability. Numerical simulations reveal the pros and cons of each type of entry guidance method, and a suitable guidance method for each Mars entry mission is identified depending on the mission concept and requirements. The analysis results provide future work.

Tracking bacteria at high density with FAST, the Feature-Assisted Segmenter/Tracker.

Most bacteria live attached to surfaces in densely-packed communities. While new experimental and imaging techniques are beginning to provide a window on the complex processes that play out in these communities, resolving the behaviour of individual cells through time and space remains a major challenge. Although a number of different software solutions have been developed to track microorganisms, these typically require users either to tune a large number of parameters or to groundtruth a large volume of imaging data to train a deep learning model-both manual processes which can be very time consuming for novel experiments. To overcome these limitations, we have developed FAST, the Feature-Assisted Segmenter/Tracker, which uses unsupervised machine learning to optimise tracking while maintaining ease of use. Our approach, rooted in information theory, largely eliminates the need for users to iteratively adjust parameters manually and make qualitative assessments of the resulting cell trajectories. Instead, FAST measures multiple distinguishing 'features' for each cell and then autonomously quantifies the amount of unique information each feature provides. We then use these measurements to determine how data from different features should be combined to minimize tracking errors. Comparing our algorithm with a naïve approach that uses cell position alone revealed that FAST produced 4 to 10 fold fewer tracking errors. The modular design of FAST combines our novel tracking method with tools for segmentation, extensive data visualisation, lineage assignment, and manual track correction. It is also highly extensible, allowing users to extract custom information from images and seamlessly integrate it into downstream analyses. FAST therefore enables high-throughput, data-rich analyses with minimal user input. It has been released for use either in Matlab or as a compiled stand-alone application, and is available at https://bit.ly/3vovDHn, along with extensive tutorials and detailed documentation.

Penalized enhanced portfolio replication with asymmetric deviation measures

Passive investment strategies, such as those implemented by Exchange Traded Funds (ETFs), have gained increasing popularity among investors. In this context, smart beta products promise to deliver improved performance or lower risk through the implementation of systematic investing strategies, and they are also typically more cost-effective than traditional active management. The majority of research on index replication focuses on minimizing tracking error relative to a benchmark index, implementing constraints to improve performance, or restricting the number of assets included in portfolios. Our focus is on enhancing the benchmark through a limited number of deviations from the benchmark. We propose a range of innovative investment strategies aimed at minimizing asymmetric deviation measures related to expectiles and quantiles, while also controlling for the deviation of portfolio weights from the benchmark composition through penalization. This approach, as compared to traditional minimum tracking error volatility strategies, places a greater emphasis on the overall risk of the portfolio, rather than just the risk relative to the benchmark. The use of penalization also helps to mitigate estimation risk and minimize turnover, as compared to strategies without penalization. Through empirical analysis using simulated and real-world data, we critically examine the benefits and drawbacks of the proposed strategies in comparison to state-of-the-art tracking models.

SIMPLIFIED EXPONENTIAL REACHING LAW BASED SLIDING MODE CONTROL OF TWO-LINK PLANAR ROBOT

Robotics has gained attention for its ability to perform industrial tasks like welding, machining, position con- trol, and other essential medical operations. Controllers are continuously being improved in design for simplicity, robustness, and performance accuracy. High-accuracy trajectory tracking is a challenging area in robot control due to nonlinearities and input couplings. To achieve high accuracy and precision, robots need accurate, and fast- processing controllers. This research focuses on applying the exponential reaching law (ERL) to control a two-link planar robot. The Euler-Lagrange approach was used for dynamic modeling, and the MATLAB/Simulink toolbox was used for the simulation. The result was obtained in terms of RMS error for the links, with and without the fric- tional disturbance, in the case of the proportional and derivative (PD) controller, reaching law based sliding mode controller (RSMC), and the simplified exponential reaching law based sliding mode controller (SSMC). RMSE with disturbance for SSMC (0.0753 rad, 0.0817 rad for link 1 and link 2 respectively), RSMC (0.0828 rad, 0.0852 rad) and PD (0.2784 rad, 0.1062 rad), and RMSE values without disturbance for SSMC (0.0743rad, 0.0811rad for link 1 and link 2 respectively), RSMC (0.0752 rad, 0.0815 rad) and PD (0.2579 rad, 0.1021 rad). Based on the result obtained, SSMC was found to be more accurate and robust as a result of having the minimum tracking error minimum change in RMSE respectively, as compared to the other controllers. It is evident that SSMC control scheme has proven to have an improved performance with simplicity and robustness.

Adaptive Robust Terminal Sliding Mode Control with Integral Backstepping Synthesized Method for Autonomous Ground Vehicle Control

Autonomous ground vehicles (AGVs) operating in complex environments face the challenge of accurately following desired paths while accounting for uncertainties, external disturbances, and initial conditions, necessitating robust and adaptive control strategies. This paper addresses the critical path-tracking task in AGVs through a novel control framework for multilevel speed AGVs, considering both structured and unstructured uncertainties. The control system introduced in this study utilizes a nonlinear adaptive approach by integrating integral backstepping with terminal sliding mode control (IBTSMC). By incorporating integral action, IBTSMC continuously adjusts the control input to minimize tracking errors, improving tracking performance. The hybridization of the terminal sliding mode method enables finite time convergence, robustness, and a chatter-free response with reduced sensitivity to initial conditions. Furthermore, adaptive control compensators are developed to ensure robustness against unknown but bounded external disturbances. The Lyapunov stability theorem is employed to guarantee the global asymptotic stability of the closed-loop system and the convergence of tracking errors to the origin within finite time. To validate the effectiveness of the proposed control scheme, high-fidelity cosimulations are conducted using CarSim and MATLAB. Comparative analysis is performed with other methods reported in the literature. The results confirm that the proposed controller demonstrates competitive effectiveness in path-tracking tasks and exhibits strong efficiency under various road conditions, parametric uncertainties, and unknown disturbances.

Tracking ‘Pure’ Systematic Risk with Realized Betas for Bitcoin and Ethereum

Using the capital asset pricing model, this article critically assesses the relative importance of computing ‘realized’ betas from high-frequency returns for Bitcoin and Ethereum—the two major cryptocurrencies—against their classic counterparts using the 1-day and 5-day return-based betas. The sample includes intraday data from 15 May 2018 until 17 January 2023. The microstructure noise is present until 4 min in the BTC and ETH high-frequency data. Therefore, we opt for a conservative choice with a 60 min sampling frequency. Considering 250 trading days as a rolling-window size, we obtain rolling betas < 1 for Bitcoin and Ethereum with respect to the CRIX market index, which could enhance portfolio diversification (at the expense of maximizing returns). We flag the minimal tracking errors at the hourly and daily frequencies. The dispersion of rolling betas is higher for the weekly frequency and is concentrated towards values of β > 0.8 for BTC (β > 0.65 for ETH). The weekly frequency is thus revealed as being less precise for capturing the ‘pure’ systematic risk for Bitcoin and Ethereum. For Ethereum in particular, the availability of high-frequency data tends to produce, on average, a more reliable inference. In the age of financial data feed immediacy, our results strongly suggest to pension fund managers, hedge fund traders, and investment bankers to include ‘realized’ versions of CAPM betas in their dashboard of indicators for portfolio risk estimation. Sensitivity analyses cover jump detection in BTC/ETH high-frequency data (up to 25%). We also include several jump-robust estimators of realized volatility, where realized quadpower volatility prevails.

A Comparative Study of Various Intelligent Algorithms Based Nonlinear PID Neural Trajectory Tracking Controller for the Differential Wheeled Mobile Robot Model

This paper presents a comparative study of two learning algorithms for the nonlinear PID neural trajectory tracking controller for mobile robot in order to follow a pre-defined path. As simple and fast tuning technique, genetic and particle swarm optimization algorithms are used to tune the nonlinear PID neural controller's parameters to find the best velocities control actions of the right wheel and left wheel for the real mobile robot. Polywog wavelet activation function is used in the structure of the nonlinear PID neural controller. Simulation results (Matlab) and experimental work (LabVIEW) show that the proposed nonlinear PID controller with PSOlearning algorithm is more effective and robust than genetic learning algorithm; this is demonstrated by the minimized tracking error and obtained smoothness of the velocity control signal, especially when external disturbances are applied.

A Stable Path Following Algorithm Based on Adaptive Target Points for Unmanned Surface Vehicles

This study proposes a stable and robust path following algorithm for Unmanned Surface Vehicles (USVs). The main objective of this paper is to optimize a key parameter in the improved algorithm to minimize tracking errors. In this study, firstly a stability criterion is developed to limit this parameter and make stable navigation. This model determines the unique target points for each time step using the optimum and flexible parameter in contrast fixed value used in previous studies. The proposed stability criterion and the turning rate data obtained from the previous time step are used to determine this optimum parameter. It provides smooth and precise navigation at critical points like as sharp turning maneuvers. Moreover, it includes saturation for maximum turning rate to make realistic navigation. The proposed model in this study reduces tracking errors by around 20% compared to the conventional carrot-chasing algorithm. Finally, a numerical simulator for USVs in the Matlab environment has been included in the Appendix to support the work of other researchers.