Minimum Tracking Error Research Articles

A Heuristic Approach for Tracking Error and Energy Consumption Minimization in Solar Tracking Systems

This paper proposes a methodology for optimizing a class of robotic solar tracking systems with two degrees of freedom using a heuristic approach. The proposal allows a balance to be found between the energy consumption and tracking accuracy in the tracking system. The main purpose is the behavior modification of the system through the combination of two manipulation strategies, one associated with the energy savings and the other with the tracking error. The heuristic approach was implemented in a solar tracking system with the end effector connected to a solar measurement device. Four energy-saving strategies and three tracking strategies were developed, simulated, and implemented in the system. The simulation results show that the resulting strategy combination (tracking error and energy saving approach) led to 31.55% energy savings compared to the reference values, with a tracking error of 0.06°. Moreover, the experimental assessment of the same combination led to 26.98% energy is being saved, with an azimuthal tracking error of 0.062° and elevation tracking error of 0.071°. The preceding values support the aim of the presented proposal to significantly reduce energy consumption while concurrently achieving a competitive tracking error.

Optimal Path-Planning of Nonholonomic Terrain Robots for Dynamic Obstacle Avoidance Using Single-Time Velocity Estimator and Reinforcement Learning Approach

A single-time velocity estimator-based reinforcement learning (RL) algorithm, integrated with a chaotic metaheuristic optimization technique is proposed in this article for the optimal path-planning of the nonholonomic robots considering a moving/stationary obstacle avoidance strategy. The additional contribution of the present study is by employing the Terramechanics principles to incorporate the effects of wheel sinkage into the deformable terrain on the dynamics of the robot aiming to find the optimal compensating force/torque magnitude to sustain a robust and smooth motion. The designed systematic control-oriented system incorporates a cost function of weighted components associated with the target-tracking and the obstacle avoidance. The designed velocity estimator contributes to the finite-state Markov decision process (MDP) in order to train the transition probabilities of the problem objectives. Based on the obtained results, the optimal solution for the Q-learning in terms of the adjusting factor for the minimized tracking error and obstacle collision risk propagation profiles is found at 0.22. The results further confirm the promising capacity of the proposed optimization-based RL algorithm for the collision avoidance control of the nonholonomic robots on deformable terrains.

Model Predictive Virtual-Flux Control of Three-Phase Vienna Rectifier Without Voltage Sensors

In this paper, a finite-control-set model predictive virtual-flux control (FCS-MPVFC) for a three-phase Vienna rectifier is developed and implemented to achieve voltage sensorless control, which is very robust to distorted grid-side voltage operation. Firstly, by investigating the relationship between virtual-fluxes aroused from grid-side voltages and line voltages in $d$ - $q$ frame, the control object is directly associated with virtual-flux tracking error minimization. Secondly, the reference line virtual-flux is calculated based on the controllability of active/reactive power associated with the delay compensation and load angle. Thirdly, to enhance the steady-state performance, switching sequence rather than single switching vector is utilized during one sampling period. Furthermore, a redundant vector pre-selection is adopted to balance the neutral-point voltage. The proposed strategy is compared with the traditional finite-control-set model predictive current control (FCS-MPCC) method. Both simulated and experimental results verify the effectiveness of the proposed control algorithm.

Structural minimization of tracking error

The structural tracking error minimization (STEM) approach produces stable tracking portfolios out-of-sample in the crucial investment period

Joint Radio Resource Allocation and Control for Vehicle Platooning in LTE-V2V Network

To improve safety and efficiency of transportation system, an effective approach is vehicle platooning, in which a group of vehicles maintains a pre-defined moving pattern by minimizing tracking error of each vehicle. As a networked control process, platooning control relies on the cooperative awareness messages (CAM) periodically exchanged in the vehicle platoon. In meeting communication and control expectations, we propose to jointly optimize the radio resource allocation in LTE-vehicle-to-vehicle (V2V) network for the CAM transmission and control parameters of vehicle, in order to minimize the tracking error while guaranteeing the reliability requirements of V2V communication and string stability of platoon. To solve the formulated problem, we develop a sub-optimal solution. First, we present a tracking error based scheduling criterion and then obtain a radio resource allocation scheme by bipartite graph matching. Then, control parameters of vehicle are adapted to minimize the tracking error by heuristic gradient descent based method. Simulation results show that the proposed scheme can reduce the tracking error as well as ensure the platoon stability compared to the existing schemes.

Tracking and outperforming large stock-market indices

Enhanced index-tracking funds aim to achieve a small target excess return over a given financial benchmark index with minimum additional risk relative to this index, i.e., a minimum tracking error. These funds are attractive to investors, especially when the index is large and thus well diversified. We consider the problem of determining a portfolio for an enhanced index-tracking fund that is benchmarked against a large stock-market index subject to real-life constraints that may be imposed by investors, stock exchanges, or investment guidelines. In the literature, various solution approaches have been proposed to enhanced index tracking that are based on different linear and quadratic tracking-error functions. However, it remains an open question which tracking-error function should be minimized to determine good enhanced index-tracking portfolios. Moreover, the existing approaches may neglect real-life constraints such as the minimum trading values imposed by stock exchanges or may not devise good feasible portfolios within a reasonable computational time when the index is large. To overcome these shortcomings, we propose novel mixed-integer linear and quadratic programming formulations and novel matheuristics. To address the open question, we minimize different tracking-error functions by applying the proposed matheuristics and exact solution approaches based on the proposed mixed-integer programming formulations in a computational experiment using a set of problem instances based on large stock-market indices with up to more than 9,000 constituents. The results of our study suggest that minimizing the so-called tracking error variance, which is a quadratic function, is preferable to minimizing other tracking-error functions.

Dynamic Data Communications for Real-time Information Fusion

This paper studies dynamic data communications between airplanes and a control tower, where the control tower needs to monitor the state of each aircraft close to the airport or on the ground in real time. Given limited communication bandwidth, it is impossible for the control tower to communicate with all aircrafts at the same time. This paper focuses on the problem of optimal scheduling of data communications for the control tower to acquire information from aircrafts to minimize tracking errors. A dynamic learning problem with limited communication bandwidth is formulated in this paper where the objective is to minimize the total variance of real-time tracking. To solve the problem, a dynamic scheduling algorithm for data communications is proposed, which prioritizes data communications based on the tracking variances of the aircrafts, channel conditions and importance of the information. Our simulations demonstrate that our algorithm outperforms policies such as a round robin policy.

Optimal tracking performance for SIMO systems with packet dropouts and control energy constraints

In this study, the optimal tracking performance for single-input multiple-output (SIMO) systems under control energy constraints is investigated. The packet dropouts in the upstream channel and down channel are adequately considered. The minimal tracking error is obtained by searching through all stablising controllers. The main results of this study show that the optimal tracking performance in these kinds of system is closely dependent on the structure of the given plant and statistic characteristics of the reference signal. Furthermore, the packet dropouts in the communication channel will degenerate the tracking performance. Finally, a typical example is given to illustrate the theoretical results.

Modeling and forecasting (un)reliable realized covariances for more reliable financial decisions

We propose a new framework for modeling and forecasting common financial risks based on (un)reliable realized covariance measures constructed from high-frequency intraday data. Our new approach explicitly incorporates the effect of measurement errors and time-varying attenuation biases into the covariance forecasts, by allowing the ex-ante predictions to respond more (less) aggressively to changes in the ex-post realized covariance measures when they are more (less) reliable. Applying the new procedures in the construction of minimum variance and minimum tracking error portfolios results in reduced turnover and statistically superior positions compared to existing procedures. Translating these statistical improvements into economic gains, we find that under empirically realistic assumptions a risk-averse investor would be willing to pay up to 170 basis points per year to shift to using the new class of forecasting models.

Attitude Stabilization and Trajectory Tracking Control Strategy for Civil UAV

To remove the funitional payload variation, the attitude oscillation and trajectory tracking error of civil UAV in complex environment, a combined inner and outer control strategy for the civil UAV is designed based on the interval system control theory and dynamic tracking error minimization principle, which can guarantee the attitude stabilization in inner loop and the heading tracking in outer loop, thus solving the control effect deterioration and trajectory error drawback of the existing UAV with large scale model variation. The simulation results show that, the proposed combined control strategy can keep flight state's stabilization and effective trajectory tracking with good closed-loop robustness. This study is useful to develop effective and automatic civil UAV system's flight control strategy.

Double Vectors Model Predictive Torque Control Without Weighting Factor Based on Voltage Tracking Error

In order to reduce the computation burden and eliminate the weighting factor in conventional model predictive torque control (MPTC), this paper proposes an improved MPTC algorithm without the use of weighting factor. Based on the deadbeat direct torque and flux control, the reference voltage vector, which would be applied in the next period, is predicted to avoid testing all feasible voltage vectors, hence reducing the computation burden of conventional MPTC. Moreover, the torque and flux error-based cost function of conventional MPTC is replaced by the voltage vector tracking error-based cost function; thus, the weighting factor of stator flux in conventional MPTC, which is always necessary because of the different units between torque and flux, is eliminated. Furthermore, two voltage vectors, which include an active vector and a null vector, are applied during one control period to improve steady-state performance. The durations of the selected voltage vectors are determined based on the principle of voltage vector tracking error minimization. Moreover, to further improve the steady-state performance, a different vector selection way, in which the second voltage vector is not fixed as a null vector but selected in a border range, is introduced. The selection process of candidate voltage vectors is analyzed, and the duration is calculated. Simulation and experimental results both show the validity of the proposed control approach.

English

In this paper, a trajectory tracking control for a non-holonomic differential wheeled mobile robot (WMR) system is presented. A big number of investigations have been used the kinematic model of mobile robot which is a nonlinear model in nature, thus a hard task to control it. This work focuses on the design of fuzzy PID controller tuned with a firefly optimization algorithm for the kinematic model of mobile robot. The firefly optimization algorithm has been used to find the best values of controller's parameters. The aim of this controller is trying to force the mobile robot tracking a pre-defined continuous path with the least possible value of error. Matlab Simulation results show that a good performance and robustness of the controller. This is confirmed by the value of minimized tracking error and the smooth velocity especially concerning presence of external disturbance or change in initial position of mobile robot.

Enhanced index tracking in portfolio optimization with two-stage mixed integer programming model

Enhanced index tracking is a portfolio management which aims to construct the optimal portfolio to generate higher return than the benchmark index return at minimum tracking error without purchasing all the stocks that make up the index. The objective of this paper is to propose a two-stage mixed integer programming model to improve the existing single-stage mixed integer programming model for tracking FBMKLCI Index in Malaysia. The optimal portfolio performance of both models are determined and compared in terms of portfolio mean return, tracking error, excess return and information ratio. The results of this study indicate that the optimal portfolio of the proposed model generates weekly excess return over the benchmark FBMKLCI index return at minimum tracking error. Besides that, the proposed model is able to outperform the existing model in tracking the benchmark index.

Adaptive Gain Control Method of a Phase-Locked Loop for GNSS Carrier Signal Tracking

The global navigation satellite system (GNSS) has been widely used in both military and civil fields. This study focuses on enhancing the carrier tracking ability of the phase-locked loop (PLL) in GNSS receivers for high-dynamic application. The PLL is a very popular and practical approach for tracking the GNSS carrier signal which propagates in the form of electromagnetic wave. However, a PLL with constant coefficient would be suboptimal. Adaptive loop noise bandwidth techniques proposed by previous researches can improve PLL tracking behavior to some extent. This paper presents a novel PLL with an adaptive loop gain control filter (AGCF-PLL) that can provide an alternative. The mathematical model based on second- and third-order PLL was derived. The error characteristics of the AGCF-PLL were also derived and analyzed under different signal conditions, which mainly refers to the different combinations of carrier phase dynamic and signal strength. Based on error characteristic curves, the optimal loop gain control method has been achieved to minimize tracking error. Finally, the completely adaptive loop gain control algorithm was designed. Comparable test results and analysis using the new method, conventional PLL, FLL-assisted PLL, and FAB-LL demonstrate that the AGCF-PLL has stronger adaptability to high target movement dynamic.

Design a Fuzzy PID Controller for Trajectory Tracking of Mobile Robot

In this paper, a trajectory tracking control for a non-holonomic differential wheeled mobile robot (WMR) system is presented. A big number of investigations have been used the kinematic model of mobile robot which is a nonlinear model in nature, thus a hard task to control it. This work focuses on the design of fuzzy PID controller tuned with a firefly optimization algorithm for the kinematic model of mobile robot. The firefly optimization algorithm has been used to find the best values of controller's parameters. The aim of this controller is trying to force the mobile robot tracking a pre-defined continuous path with the least possible value of error. Matlab Simulation results show that a good performance and robustness of the controller. This is confirmed by the value of minimized tracking error and the smooth velocity especially concerning presence of external disturbance or change in initial position of mobile robot.

Optimal design and control of an electromechanical transfemoral prosthesis with energy regeneration.

In this paper, we present the design of an electromechanical above-knee active prosthesis with energy storage and regeneration. The system consists of geared knee and ankle motors, parallel springs for each motor, an ultracapacitor, and controllable four-quadrant power converters. The goal is to maximize the performance of the system by finding optimal controls and design parameters. A model of the system dynamics was developed, and used to solve a combined trajectory and design optimization problem. The objectives of the optimization were to minimize tracking error relative to human joint motions, as well as energy use. The optimization problem was solved by the method of direct collocation, based on joint torque and joint angle data from ten subjects walking at three speeds. After optimization of controls and design parameters, the simulated system could operate at zero energy cost while still closely emulating able-bodied gait. This was achieved by controlled energy transfer between knee and ankle, and by controlled storage and release of energy throughout the gait cycle. Optimal gear ratios and spring parameters were similar across subjects and walking speeds.

Identification of workpiece location on rotary tables to minimize tracking errors in five-axis machining

Abstract Five-axis CNC machine tools are widely used in machining parts with free form surfaces. This paper presents optimal placement of parts on the five-axis machine tool tables to minimize the tracking errors of the rotary servo drives. The cutting forces along the tool path are first simulated at the workpiece coordinate system in Computer-Aided-Manufacture (CAM) environment. The cutting torques transmitted to the rotary and translational drives are predicted using the location of the part on the table and kinematic configuration of the machine tool. The optimal location of the part on the table is identified by minimizing the forces transmitted to the rotary drives as torque disturbances. The proposed model has been experimentally validated on a five-axis machine with tilt-table configuration. It has been shown that the tracking and contouring errors can be significantly reduced with the proposed strategy, which can be used by process planners in digital simulation environment.

A limited-preview filtered B-spline approach to tracking control – With application to vibration-induced error compensation of a 3D printer

A limited-preview filtered B-spline (FBS) approach for minimizing errors in tracking a desired trajectory is presented. In the full-preview FBS approach, the feedforward control input to a stable linear system, with or without non-minimum phase zeros, is decomposed into B-spline basis functions with unknown coefficients; the basis functions are forward filtered using the (modeled) dynamics of the system, and their coefficients selected to minimize tracking errors of the entire trajectory in one batch. Instead, this paper proposes the use of a receding horizon to recursively compute unknown coefficients that minimize tracking errors for small batches (subsets) of the trajectory at a time, by exploiting the local property of B-splines. This allows optimal control signals to be determined at much lower computational cost compared to full-preview FBS, thus enabling online implementation on real-time controllers. The adverse effects of limited preview on tracking accuracy, relative to full preview, are analyzed, and limited-preview FBS is shown in numerical examples to preserve the versatility of full-preview FBS in tracking systems irrespective of their zero locations. The practicality and effectiveness of the limited-preview FBS approach are demonstrated by employing it for online feedforward compensation of tracking errors caused by structural vibrations of a stepper-motor-driven 3D printer. Alleviation of vibration-induced surface waviness and layer-to-layer registration errors, without sacrificing print speed, are demonstrated.

IMPLEMENTATION OF ROBUST COMPOSITE NONLINEAR FEEDBACK FOR ACTIVE FRONT STEERING BASED VEHICLE YAW STABILITY

In this paper, Robust Composite Nonlinear Feedback (CNF) was implemented on Active Front Steering (AFS) vehicle system for yaw stability control. In this control system, the main objective is to get excellent transient response of vehicle yaw rate and at the same time resist to side wind disturbance. To cater unknown constant disturbance, non-integral function for Robust CNF version is used. Meanwhile for vehicle model, 7 degree of freedom vehicle body with Pacejka Tire formula model for typical passenger car is used to simulate controlled vehicle. The computer simulation by Matlab software is performed to evaluate the system performance in J-Turn and Single sine steer with magnitude from 1 to 3.1 degree with additional 400 Nm external side wind disturbance. By using typical Proportional Integration and Derivative (PID) control auto-tuned by Matlab as comparison, the new designed controller demonstrates higher capability to track reference signal faster and having minimal tracking error during disturbance occur where having less than 0.01 degree compared 0.22 degree by PID. The Robust CNF based designed control system is able to compensate disturbance effect efficiently and also has super-fast tracking as classical CNF.

Optimal Mixed Tracking/Impedance Control With Application to Transfemoral Prostheses With Energy Regeneration.

We design an optimal passivity-based tracking/impedance control system for a robotic manipulator with energy regenerative electronics, where the manipulator has both actively and semi-actively controlled joints. The semi-active joints are driven by a regenerative actuator that includes an energy-storing element. External forces can have a large influence on energy regeneration characteristics. Impedance control is used to impose a desired relationship between external forces and deviation from reference trajectories. Multi-objective optimization (MOO) is used to obtain optimal impedance parameters and control gains to compromise between the two conflicting objectives of trajectory tracking and energy regeneration. We solve the MOO problem under two different scenarios: 1) constant impedance; and 2) time-varying impedance. The methods are applied to a transfemoral prosthesis simulation with a semi-active knee joint. Normalized hypervolume and relative coverage are used to compare Pareto fronts, and these two metrics show that time-varying impedance provides better performance than constant impedance. The solution with time-varying impedance with minimum tracking error (0.0008 rad) fails to regenerate energy (loses 9.53 J), while a solution with degradation in tracking (0.0452 rad) regenerates energy (gains 270.3 J). A tradeoff solution results in fair tracking (0.0178 rad) and fair energy regeneration (131.2 J). Our experimental results support the possibility of net energy regeneration at the semi-active knee joint with human-like tracking performance. The results indicate that advanced control and optimization of ultracapacitor-based systems can significantly reduce power requirements in transfemoral prostheses.