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.

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.

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.

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.

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.

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.

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.

Convergence analysis of self-tuning Riccati equation for systems with correlation noises

For linear discrete time-invariant stochastic system with correlated noises,and with unknown state transition matrix and unknown noise statistics,substituting the online consistent estimators of the state transition matrix and noise statistics into steady-state optimal Riccati equation,a new self-tuning Riccati equation is presented.A dynamic variance error system analysis(DVESA)method is presented,which transforms the convergence problem of self-tuning Riccati equation into the stability problem of a time-varying Lyapunov equation.Two decision criterions of the stability for the Lyapunov equation are presented.Using the DVESA method and Kalman filtering stability theory,it proves that with probability 1,the solution of self-tuning Riccati equation converges to the solution of the steady-state optimal Riccati equation or time-varying optimal Riccati equation.The proposed method can be applied to design a new selftuning information fusion Kalman filter and will provide the theoretical basis for solving the convergence problem of self-tuning filters.A numerical simulation example shows the effectiveness of the proposed method.