Error Control Strategies for Numerical Integrations in Fast Collocation Methods

We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.

A New Class of Nonlinear Error Control Codes Based on Neural Networks

By mcans of stable attractors of discret Hopfield neural network (DHNN) , anew class of nonlinear error control codes is sugsested and some relativetheorems are presented. A kind of single error control codes is also given forillustrating this new approach.

Based on Adaptive Backstepping Error Control for Permanent Magnet Synchronous Motor

Permanent Magnet Synchronous Motor (PMSM) displays chaotic phenomenon when PMSM in power on or power off. At present, there are many methods to control chaos in PMSM. However, there appears oscillation in course of control chaos in PMSM, which has an effect on practical application. This paper proposes error control based on adaptive backstepping to control chaos in PMSM;an error control item is added in each step virtual control design which has control effect of unknown dynamical error on system. This scheme can eliminate oscillation in course of control chaos. Finally, the simulation results show the effectiveness of theoretical analysis.

Beacon-driven Leader Based Protocol over a GE Channel for MAC Layer Multicast Error Control

In wireless networks current standard MAC layer protocols don’t provide any error correction scheme for broadcast/multicast. In this paper, we enhance a Leader Based Protocol (LBP) and propose a Beacon-driven Leader Based Protocol (BLBP) for the MAC layer multicast error control. To guarantee a very low Packet Loss Ratio (PLR) under strict delay constraints for video multicast over a Gilbert-Elliott (GE) channel, we analyze BLBP and compare it with LBP and different application layer multicast error control schemes via simulation experiments. Both the theoretical analysis and simulation results show that BLBP can correct nearly all the errors for all receivers in the MAC layer and is more efficient than LBP. BLBP is also more efficient than the application layer Automatic Repeat request (ARQ) scheme and the total multicast delay is much shorter. BLBP is very good for real-time multicast applications with strict delay constraints.

Error Control Strategy in Ultrasonic Body Area Networks

Recently,ultrasonic waves had been introduced as the transmission medium in Body Area Networks(BANs) to reduce the incalculable damage caused by radio waves. However,the communications based on ultrasonic waves suffer from poor propagation of signals in air and consume too much energy. To address these limitations,firstly,we make the theoretical analysis to ensure ultrasonic waves could be used in BANs(UBANs). Then,we propose an error control strategy in UBANs to dynamically adjust the error control scheme and the Max-Retries based on the current channel state,which is called UECS. The UECS is based on IEEE 802.15.6 standards and considering the characteristics of ultrasonic waves in BANs. Simulation results show that UECS achieves better performance in terms of packet delivery ratio and energy consumption compared with the traditional strategies.

Zero phase error control based on neural compensation for flight simulator servo system

Using the future desired input value, zero phase error controller enables the overall system＇s frequency response exhibit zero phase shift for all frequencies and a small gain error at low frequency range, and based on this, a new algorithm is presented to design the feedforward controller. However, zero phase error controller is only suitable for certain linear system. To reduce the tracking error and improve robustness, the design of the proposed feedforward controller uses a neural compensation based on diagonal recurrent neural network. Simulation and real-time control results for flight simulator servo system show the effectiveness of the proposed approach.

A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem

In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H1 and L2 norms. Finally, some numerical experiments are carried out to support the theoretical results.

Machining Error Control by Integrating Multivariate Statistical Process Control and Stream of Variations Methodology

For aircraft manufacturing industries, the analyses and prediction of part machining error during machining process are very important to control and improve part machining quality. In order to effectively control machining error, the method of integrating multivariate statistical process control （MSPC） and stream of variations （SoV） is proposed. Firstly, machining error is modeled by multi-operation approaches for part machining process. SoV is adopted to establish the mathematic model of the relationship between the error of upstream operations and the error of downstream operations. Here error sources not only include the influence of upstream operations but also include many of other error sources. The standard model and the predicted model about SoV are built respectively by whether the operation is done or not to satisfy different requests during part machining process. Secondly, the method of one-step ahead forecast error （OSFE） is used to eliminate autocorrelativity of the sample data from the SoV model, and the T2 control chart in MSPC is built to realize machining error detection according to the data characteristics of the above error model, which can judge whether the operation is out of control or not. If it is, then feedback is sent to the operations. The error model is modified by adjusting the operation out of control, and continually it is used to monitor operations. Finally, a machining instance containing two operations demonstrates the effectiveness of the machining error control method presented in this paper.

Quantitative feedback theory and zero phase error tracking control combined robust control for radar truck leveling simulator

Radar leveling system is the key equipment for improving the radar mobility and survival capability. A combined quantitative feedback theory (QFT) controller is designed for the radar truck leveling simulator in this paper, which suffers from strong nonlinearities and system parameter uncertainties. QFT can reduce the plant uncertainties and stabilize the system, but it fails to obtain high-precision tracking. This drawback can be solved by a robust QFT control scheme based on zero phase error tracking control (ZPETC) compensation. The combined controller not only possesses high robustness, but greatly improves the system performance. To verify the effiectiveness and the potential of the proposed controller, a series of experiments have been carried out. Experimental results have demonstrated its robustness against a large range of parameters variation and high tracking precision performance, as well as its capability of restraining the load coupling among channels. The combined QFT controller can drive the radar truck leveling platform accurately, quickly and stably.

Use of Total Precipitable Water Classification of A Priori Error and Quality Control in Atmospheric Temperature and Water Vapor Sounding Retrieval

This study investigates the use of dynamic a priori error information according to atmospheric moistness and the use of quality controls in temperature and water vapor profile retrievals from hyperspectral infrared （IR） sounders. Temperature and water vapor profiles are retrieved from Atmospheric InfraRed Sounder （AIRS） radiance measurements by applying a physical iterative method using regression retrieval as the first guess. Based on the dependency of first-guess errors on the degree of atmospheric moistness, the a priori first-guess errors classified by total precipitable water （TPW） are applied in the AIRS physical retrieval procedure. Compared to the retrieval results from a fixed a priori error, boundary layer moisture retrievals appear to be improved via TPW classification of a priori first-guess errors. Six quality control （QC） tests, which check non-converged or bad retrievals, large residuals, high terrain and desert areas, and large temperature and moisture deviations from the first guess regression retrieval, are also applied in the AIRS physical retrievals. Significantly large errors are found for the retrievals rejected by these six QCs, and the retrieval errors are substantially reduced via QC over land, which suggest the usefulness and high impact of the QCs, especially over land. In conclusion, the use of dynamic a priori error information according to atmospheric moistness, and the use of appropriate QCs dealing with the geographical information and the deviation from the first-guess as well as the conventional inverse performance are suggested to improve temperature and moisture retrievals and their applications.

Bayesian networks modeling for thermal error of numerical control machine tools

The interaction between the heat source location, its intensity, thermal expansion coefficient, the machine system configuration and the running environment creates complex thermal behavior of a machine tool, and also makes thermal error prediction difficult. To address this issue, a novel prediction method for machine tool thermal error based on Bayesian networks (BNs) was presented. The method described causal relationships of factors inducing thermal deformation by graph theory and estimated the thermal error by Bayesian statistical techniques. Due to the effective combination of domain knowledge and sampled data, the BN method could adapt to the change of running state of machine, and obtain satisfactory prediction accuracy. Ex- periments on spindle thermal deformation were conducted to evaluate the modeling performance. Experimental results indicate that the BN method performs far better than the least squares (LS) analysis in terms of modeling estimation accuracy.

Adaptive Zero Phase Error Feedforward Method for Robotic Force Control

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RESEARCH ON PREVIEW CONTROL TECHNIQUE BASED ON EXTENDED ERROR SYSTEM WITH DELAY

A valid preview control technique is presented for processing servo systemswith input delay based on extended error systems with input delay. The technique usesthe concept of error systems, establishes extended error systems with input delay and de-rives preview control laws based on minimization of evaluation function. Finally, simula-tion is done on linear direct current motor without brush. The results reveal that the tech-nique proposed herein is valid for improving performance of servo systems.

DESIGNING OF TWO NEW FUZZY CONTROLLERS WITH ERROR INTEGRAL AND THEIR APPLICATIONS IN FOLLOWING CONTROL OF WARSHIP-GUNS

Two new fuzzy controllers are designed, one's control rules are adjusted byerror integral, another are with feedforward of error integral. If only the control rules andparameters are selected felicitously, the static errors of the system will be eliminated. The testresults show that the controllers can assuredly improve static performances of the controlledsystem.

Study of a New Method of Tracking Control with Zero Steady-State Error on Very-Low Frequency

A servo control system is prone to low speed and unsteadiness during very-low-frequency follow-up. A design method of feedforward control based on intelligent controller is put foward. Simulation and test results show that the method has excellent control characteristics and strong robustness, which meets the servo control needs with very-low frequency.

Adaptive control of machining process based on extended entropy square error and wavelet neural network

Combining information entropy and wavelet analysis with neural network,an adaptive control system and an adaptive control algorithm are presented for machining process based on extended entropy square error(EESE)and wavelet neural network(WNN).Extended entropy square error function is defined and its availability is proved theoretically.Replacing the mean square error criterion of BP algorithm with the EESE criterion,the proposed system is then applied to the on-line control of the cutting force with variable cutting parameters by searching adaptively wavelet base function and self adjusting scaling parameter,translating parameter of the wavelet and neural network weights.Simulation results show that the designed system is of fast response,non-overshoot and it is more effective than the conventional adaptive control of machining process based on the neural network.The suggested algorithm can adaptively adjust the feed rate on-line till achieving a constant cutting force approaching the reference force in varied cutting conditions,thus improving the machining efficiency and protecting the tool.

CYLINDRICITY ERROR COMPENSATION IN DIAMOND TURNING VIA P－INTEGRATOR REPETITIVE CONTROL

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Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.

Robust Iterative Learning Controller for the Non-zero Initial Error Problem on Robot Manipulator

Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, have been used to control this kind of system, but there are some deficiencie s in those methods: some need accurate and some need complicated operation and e tc. In recent years, in need of controlling the industrial robots, aiming at com pletely tracking the ideal input for the controlled subject with repetitive character, a new research area, ILC (iterative learning control), has been devel oped in the control technology and theory. The iterative learning control method can make the controlled subject operate as desired in a definite time span, merely making use of the prior control experie nce of the system and searching for the desired control signal according to the practical and desired output signal. The process of searching is equal to that o f learning, during which we only need to measure the output signal to amend the control signal, not like the adaptive control strategy, which on line assesses t he complex parameters of the system. Besides, since the iterative learning contr ol relies little on the prior message of the subject, it has been well used in a lot of areas, especially the dynamic systems with strong non-linear coupling a nd high repetitive position precision and the control system with batch producti on. Since robot manipulator has the above-mentioned character, ILC can be very well used in robot manipulator. In the ILC, since the operation always begins with a certain initial state, init ial condition has been required in almost all convergence verification. Therefor e, in designing the controller, the initial state has to be restricted with some condition to guarantee the convergence of the algorithm. The settle of initial condition problem has long been pursued in the ILC. There are commonly two kinds of initial condition problems: one is zero initial error problem, another is non-zero initial error problem. In practice, the repe titive operation will invariably produce excursion of the iterative initial stat e from the desired initial state. As a result, the research on the second in itial problem has more practical meaning. In this paper, for the non-zero initial error problem, one novel robust ILC alg orithms, respectively combining PD type iterative learning control algorithm wit h the robust feedback control algorithm, has been presented. This novel robust ILC algorithm contain two parts: feedforward ILC algorithm and robust feedback algorithm, which can be used to restrain disturbance from param eter variation, mechanical nonlinearities and unmodeled dynamics and to achieve good performance as well. The feedforward ILC algorithm can be used to improve the tracking error and perf ormance of the system through iteratively learning from the previous operation, thus performing the tracking task very fast. The robust feedback algorithm could mainly be applied to make the real output of the system not deviate too much fr om the desired tracking trajectory, and guarantee the system’s robustness w hen there are exterior noises and variations of the system parameter. In this paper, in order to analyze the convergence of the algorithm, Lyapunov st ability theory has been used through properly selecting the Lyapunov function. T he result of the verification shows the feasibility of the novel robust iterativ e learning control in theory. Finally, aiming at the two-freedom rate robot, simulation has been made with th e MATLAB software. Furthermore, two groups of parameters are selected to validat e the robustness of the algorithm.