Missile guidance law design based on free-time convergent error dynamics

To solve the finite-time error-tracking problem in mis-sile guidance,this paper presents a unified design approach through error dynamics and free-time convergence theory.The proposed approach is initiated by establishing a desired model for free-time convergent error dynamics,characterized by its independence from initial conditions and guidance parameters,and adjustable convergence time.This foundation facilitates the derivation of specific guidance laws that integrate constraints such as leading angle,impact angle,and impact time.The theo-retical framework of this study elucidates the nuances and syn-ergies between the proposed guidance laws and existing methodologies.Empirical evaluations through simulation com-parisons underscore the enhanced accuracy and adaptability of the proposed laws.

Optimal trajectory design accounting for the stabilization of linear time-varying error dynamics

This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization.Consequently,the trajectory is designed such that the Linear Time-Varying(LTV)dynamic system,describing the controller’s error dynamics,is stable,while additionally the desired optimality criterion is optimized and all enforced constraints on the trajectory are fulfilled.This is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent,quadratic Lyapunov function candidate.Special care is taken with regard to ensuring the correct definiteness of the ensuing matrices within the Lyapunov stability analysis,specifically considering a numerically stable formulation of these in the numerical optimization.The developed algorithm is applied to a trajectory design problem for which the LTV system is part of the path-following error dynamics,which is required to be stable.The main benefit of the proposed scheme in this context is that the designed trajectory trades-off the required stability and robustness properties of the LTV dynamics with the optimality of the trajectory already at the design phase and thus,does not produce unstable optimal trajectories the system must follow in the real application.

Impact Angle/Time Constraint Guidance Design Based on Fast Terminal Error Dynamics

Considering the problem that the optimal error dynamics can only converge at the terminal time,an impact angle/time constraint missile guidance law with finite-time convergence is designed in this paper,which is based on the pure proportional navigation(PPN)guidance law and the fast terminal error dynamics(FTED)approach.The missile guidance model and FTED equation are given first,and the dynamic equation of impact angle/time error based on PPN is also derived.Then,the guidance law is designed based on FTED,and the guidance error can converge to 0 in a finite time.Furthermore,considering the field of view constraint,the guidance law is improved by using the saturation function mapping method.Finally,a numerical simulation example is given to verify the effectiveness of the guidance law,which shows that the guidance law proposed in this paper can make the missile quickly adjust to the desired states in advance,and effectively relieve the overload saturation pressure of the actuator.

ANALYSIS AND MEASUREMENT FOR THE DYNAMIC ERRORS OF COORDINATE MEASURING MACHINES

The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at the probing position from dynamic rotational errors is presented.It is pointed out that the finite element method might be used for modeling dynamic errors.However,dynamic errors are difficult to be modeled so a combined practical and theoretical approach is needed.In addition,the dynamic errors are measured with inductive position sensors.

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.

Research on identifying the dynamic error model of strapdown gyro on 3-axis turntable

The dynamic errors of gyros are the important error sources of a strapdown inertial navigation system. In order to identify the dynamic error model coefficients accurately, the static error model coefficients which lay a foundation for compensating while identifying the dynamic error model are identified in the gravity acceleration fields by using angular position function of the three-axis turntable. The angular acceleration and angular velocity are excited on the input, output and spin axis of the gyros when the outer axis and the middle axis of a three-axis turntable are in the uniform angular velocity state simultaneously, while the inner axis of the turntable is in different static angular positions. 8 groups of data are sampled when the inner axis is in 8 different angular positions. These data are the function of the middle axis positions and the inner axis positions. For these data, harmonic analysis method is applied two times versus the middle axis positions and inner axis positions respectively so that the dynamic error model coefficients are finally identified through the least square method. In the meantime the optimal angular velocity of the outer axis and the middle axis are selected by computing the determination value of the information matrix.

Pre-Compensation for Continuous-Path Running Trajectory Error in High-Speed Machining of Parts with Varied Curvature Features

Parts with varied curvature features play increasingly critical roles in engineering, and are often machined under high-speed continuous-path running mode to ensure the machining efficiency. However, the continuous-path running trajectory error is significant during high-feed-speed machining, which seriously restricts the machining precision for such parts with varied curvature features. In order to reduce the continuous-path running trajectory error without sacrificing the machining efficiency, a pre-compensation method for the trajectory error is proposed. Based on the formation mechanism of the continuous-path running trajectory error analyzed, this error is estimated in advance by approximating the desired toolpath with spline curves. Then, an iterative error pre-compensation method is presented. By machining with the regenerated toolpath after pre-compensation instead of the uncompensated toolpath, the continuous-path running trajectory error can be effectively decreased without the reduction of the feed speed. To demonstrate the feasibility of the proposed pre-compensation method, a heart curve toolpath that possesses varied curvature features is employed. Experimental results indicate that compared with the uncompensated processing trajectory, the maximum and average machining errors for the pre-compensated processing trajectory are reduced by 67.19% and 82.30%, respectively. An easy to implement solution for high efficiency and high precision machining of the parts with varied curvature features is provided.

Correction of Dynamic Error Result from Measurement System Limitations

The main cause of dynamic errors is due to frequency response limitation of measurement system. One way of solving this problem is designing an effective inverse filter. Since the problem is ill-conditioned, a small uncertainty in the measurement will came large deviation in reconstncted signals. The amplified noise has to be suppressed at the sacrifice of biasing in estimation. The paper presents a kind of designing method of inverse filter in frequency domain based on stabilized solutions of Fredholm integral equations of the fast kind in order to reduce dynamic errors. Compared with previous several work, the method has advantage of generalization. Simulations with different Signal-to-Noise ratio （SNR） are investigated. Flexibility of the method is verified. Application of correcting dynamic error is given.

Excitation Prediction by Dynamic Transmission Error under Sliding Friction in Helical Gear System

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Dynamic error research and application of an angular measuring system belonging to a high precision excursion test turntable

Angular measuring system is the most important component of a servo turntable in inertial test apparatus. Its function and precision determine the turntable＇ s function and precision. It attaches importance to research on inertial test equipment. This paper introduces the principle of the angular measuring system using amplitude discrimination mode. The dynamic errors axe analyzed from the aspects of inductosyn, amplitude and function error of double-phase voltage and wavefonn distortion. Through detailed calculation, theory is provided for practical application; system errors are allocated and the angular measuring system meets the accuracy requirement. As a result, the schedule of the angular measuring system can be used in practice.

Correction of sensor’s dynamic error caused by system limitations

The method based on particle swarm optimization(PSO)integrated with functional link articial neural network(FLANN)for correcting dynamic characteristics of sensor is used to reduce sensor’s dynamic error caused by its system limitations.Combining the advantages of PSO and FLANN,with this method a dynamic compensator can be realized without knowing the dynamic model of the sensor.According to the input and output of the sensor and the reference model,the weights of the network trained were used to initialize one particle station of the whole particle swarm when the training of the FLANN had been finished.Then PSO algorithm was applied,and the global best particle station of the particle swarm was the parameters of the compensator.The feasibility of dynamic compensation method is tested.Simulation results from simulator of sensor show that the results after being compensated have given a good description to input signals.

STUDY OF THE EFFECTS OF REDUCING SYSTEMATIC ERRORS ON MONTHLY REGIONAL CLIMATE DYNAMICAL FORECAST

A nested-model system is constructed by embedding the regional climate model RegCM3 into a general circulation model for monthly-scale regional climate forecast over East China. The systematic errors are formulated for the region on the basis of 10-yr (1991-2000) results of the nested-model system, and of the datasets of the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) and the temperature analysis of the National Meteorological Center (NMC), U.S.A., which are then used for correcting the original forecast by the system for the period 2001-2005. After the assessment of the original and corrected forecasts for monthly precipitation and surface air temperature, it is found that the corrected forecast is apparently better than the original, suggesting that the approach can be applied for improving monthly-scale regional climate dynamical forecast.

ASSESSING THE DYNAMIC ERRORS OF COORDINATE MEASURING MACHINES

The main factors affecting the dynamic errors of coordinate measuring machines are analyzed. It is pointed out that there are two main contributors to the dynamic errors: One is the rotation of the elements around the joints connected with air bearings and the other is the bending of the elements caused by the dynamic inertial forces. A method for obtaining the displacement errors at the probe position from dynamic rotational errors is presented. The dynamic rotational errors are measured with inductive position sensors and a laser interferometer. The theoretical and experimental results both show that during the process of fast probing, due to the dynamic inertial forces, there are not only large rotation of the elements around the joints connected with air bearings but also large bending of the weak elements themselves.

Time Series Analysis and Prediction of COVID-19 Pandemic Using Dynamic Harmonic Regression Models

Rapidly spreading COVID-19 virus and its variants, especially in metropolitan areas around the world, became a major health public concern. The tendency of COVID-19 pandemic and statistical modelling represents an urgent challenge in the United States for which there are few solutions. In this paper, we demonstrate combining Fourier terms for capturing seasonality with ARIMA errors and other dynamics in the data. Therefore, we have analyzed 156 weeks COVID-19 dataset on national level using Dynamic Harmonic Regression model, including simulation analysis and accuracy improvement from 2020 to 2023. Most importantly, we provide new advanced pathways which may serve as targets for developing new solutions and approaches.

Continuous rotation north-finding algorithm based on constrained adaptive Kalman filter

As an orientation measurement system,north-finder has been playing a significant role in both military and civilian fields of orientation and control.In this paper,to deal with drawbacks in the conventional north-finding systems,a dynamic strategy based on continuous rotation modulation to measure the rotational angular velocity of the earth is proposed.By modeling the dynamic error,optimizing the process constraint and estimating dynamic noise,a method combining delay compensation and hardware adjustment,and a constrained adaptive Kalman filter(CAKF)algorithm are designed for the north-finding strategy.According to simulation and experiments,the proposed algorithm can achieve the high-precision north-finding with robust and anti-noise performance.

Quantitative analysis of the performance of vector tracking algorithms

Vector tracking changes the classical structure of receivers. Combining signal tracking and navigation solution,vector tracking can realize powerful processing capabilities by the fusion technique of receiving channel and feedback correction. In this paper,we try to break through the complicated details of numerical analysis,consider the overall influencing factors of the residual in observed data,and use the intrinsic link between a conventional receiver and a vector receiver. A simple method for performance analysis of the vector tracking algorithm is proposed. Kalman filter has the same steady performance with the classic digital lock loop through the analysis of the relation between gain and band width. The theoretical analysis by the least squares model shows that the reduction of range error is the basis for the superior performance realized by vector tracking. Thus,the bounds of its performance enhancement under weak signal and highly dynamic conditions can be deduced. Simulation results verify the effectiveness of the analysis presented here.

INS stochastic error detection during kinematic tests and impacts on INS/GNSS performance

Inertial Navigation System(INS)and Global Navigation Satellite System(GNSS)integration requires accurate modelling of both INS deterministic and stochastic errors.The Allan Variance(AV)analysis on INS static data is one method of determining INS stochastic errors.However,it is known that INS errors can vary depending on a vehicle’s motion and environment,and application of AV results from static data in kinematic operations typically results in an over-confident estimation of stochastic.In order to overcome this limitation,this paper proposes the use of Dynamic Allan Variance(DAV).The paper compares the resulting performance of the INS/GNSS integrated system by varying the stochastic coefficients obtained from the AV and DAV.The results show that the performance improved when utilizing the stochastic coefficients obtained from the DAV,applied on a kinematic dataset compared to the AV,applied on a static laboratory dataset.

Optimal three-dimensional impact time guidance with seeker’s field-of-view constraint

This paper proposes a new three-dimensional optimal guidance law for impact time control with seeker’s Field-of-View(FOV) constraint to intercept a stationary target. The proposed guidance law is devised in conjunction with the concept of biased Proportional Navigation Guidance(PNG). The guidance law developed leverages a nonlinear function to ensure the boundedness of velocity lead angle to cater to the seeker’s FOV limit. It is proven that the impact time error is nullified in a finite-time under the proposed method. Additionally, the optimality of the biased command is theoretically analyzed. Numerical simulations confirm the superiority of the proposed method and validate the analytic findings.

A unified formulation of optimal guidance-to-collision law for accelerating and decelerating targets

This paper provides a unified formulation of optimal guidance-to-collision law for a target with an arbitrary acceleration or deceleration.The collision course for general target acceleration or deceleration is first determined from the engagement geometry in conjunction with the nonlinear engagement kinematics in the proposed approach.The heading error defined in the collision course is then adopted as a variable to be nullified for accomplishing the intercept condition.The proposed guidance law is derived based on the heading error dynamics and the optimal error dynamics to ensure optimality and finite-time convergence.As illustrative examples,the proposed guidance command for a constant target acceleration and a target deceleration in the form of a quadratic function of speed are provided.Additionally,the time-to-go prediction method is suggested for implementing the proposed method.The characteristics of the proposed guidance command are analytically investigated to provide insight into the proposed method.The key benefits of the proposed method lie in not producing unnecessary guidance commands near a target compared to other methods and ensuring optimality in guidance command even in the nonlinear engagement kinematics.Finally,numerical simulations are performed to validate the proposed method and to show our findings.

Evaluation of measurement uncertainty of the high-speed variable-slit system based on the Monte Carlo method

This paper presents a dynamic and static error transfer model and uncertainty evaluation method for a high-speed variable-slit system based on a two- dimensional orthogonal double-layer air-floating guide rail structure. The motion accuracy of the scanning blade is affected by both the moving component it is attached to and the moving component of the following blade during high-speed motion. First, an error transfer model of the high-speed variable-slit system is established, and the influence coefficients are calculated for each source of error associated with the accuracy of the blade motion. Then, the maximum range of each error source is determined by simulation and experiment. Finally, the uncertainty of the blade displacement measurement is evaluated using the Monte Carlo method. The proposed model can evaluate the performance of the complex mechanical system and be used to guide the design.