Calaulation of Time-Optimal Control Law for Double Integrator System with Complex Constraints: Endpoint Backward Method

An endpoint backward method is proposed to calculate the time-optimal control law of double integrator system. First, the time intervals between the switch points and the endpoints are calculated. Then, the positions of switch points are decided according to the motion equation, and the switch line is formed. Theoretical analysis shows that this method can be used to solve the double integrator system with functional constraint target set and deal with the second order oscillation system.

Experimental study on the effect of wind on pointing accuracy of antenna structures

Wind loads have instantaneity and turbulence characteristics that will lead to pointing errors in antenna structures,and these errors cannot be ignored in high-frequency observations.Using the Tianma 65 m radio telescope(TMRT)as an example object,the pointing errors caused by wind loads are investigated using an accelerometer system.First,the resonant frequency range of the antenna structure is used for reference to acquire useful signals through the bandpass filtering method.Then,the direct current(DC)component of these signals is filtered out using the fast discrete Fourier transform method,and the baseline of the acceleration is corrected using the least-squares method.Finally,the acceleration integral is solved approximately using the discrete trapezoidal area method,and the structural vibration displacement of the antenna is determined using a double integral of acceleration.The pointing errors are then obtained based on the displacement relationship between the primary and subreflector surfaces.When the wind speed is 3.2 m/s,the antenna pitch angle is 61.7°and the wind direction angle is 80°,the generated pitch pointing error is 3.05'',and the azimuth pointing error is 1.14''.These results are consistent with those obtained via inclinometer measurements,thus validating the signal processing method and the pointing error calculation method proposed in this paper.The research methods and data analysis results reported here provide a basis for further wind-induced pointing error correction studies.

Double Integrable Couplings and Their Constructing Method

To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of the elements of a new loop algebra which is obtained by using perturbation method. Therefore, the approach given in the paper has extensive applicable values, that is, it applies to investigate a lot of double integrable couplings of the known integrable hierarchies of evolution equations. As for explicit applications of the method proposed in the paper, the double integrable couplings of the AKNS hierarchy and the KN hierarchy are worked out, respectively.

On Fatou Type Convergence of Convolution Type Double Singular Integral Operators

In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].

New Double Integrals Weighted Cebysev Type Inequalities

In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.

Enhancement of Solar PV Panel Efficiency Using Double Integral Sliding Mode MPPT Control

The extraction of maximum power from the solar panels,using the sliding mode control scheme,becomes popular for partial weather atmospheric conditions due to its effective dynamic duty cycle ratio.However,the sliding mode control scheme was sophisticated with single integral and double integral sliding mode control scheme,which offer enhanced maximum power extraction and support enhanced solar panel efficiency in partial weather conditions.The operation of the sliding mode control scheme depends on the selection of a sliding surface selection based on the atmospheric weather condition,which enables the effective sliding duty cycle ratio operation for the DC/DC boost converter.The duty cycle ratio of the sliding mode control resembles the usual dynamic behavior to achieve enhanced efficiency compared to the various maximum power point tracking(MPPT)schemes.The major limitation of the sliding mode control scheme is to achieve the steady state voltage error of the solar panel in minimum settling time duration.The single integral sliding mode control scheme achieves the expected steady state voltage error limit but fails to achieve minimum settling time duration.Hence,the single integral sliding mode control is extended to a double integral sliding mode control scheme to achieve both steady state voltage error limits within the minimum settling time duration.This double integral sliding mode control scheme allows us to obtain the higher sliding surface duty cycle ratio which acts as the input signal to the boost converter.This activates the enhanced stable and reliable system operation,and nullifies the lacuna of maximum solar panel efficiency under partial weather conditions.Hence,this paper aims to present the design and performance operation of the double integral sliding mode(DISM)MPPT control scheme.To validate the performance analysis of the proposed DISM MPPT control scheme,the MATLAB/Simulink model is designed and verified.Also,the performance analysis of the proposed DISM MPPT control scheme is compared with the sliding mode controller(SMC)scheme and single integral sliding mode controller(SiSMC)scheme.The performance analysis of the proposed double integral sliding mode controller(DISMC)scheme attains 99.10%of efficiency and a very less setting time of 0.035s when compared to other existingmethods.

Excess Loss of the Coupling System to Double-Function Optical Circulators Utilizing Lens Twice and Two-Fiber Tips

A new type of double function optical circulator for double fibers is proposed in this paper. Two fiber tips and lens twice are employed in this kind of device as the coupling system for what is believed to be the first time. Because two fiber tips and lens twice are used, the function of optical circulator is duplicated in comparison with conventional optical circulator with single fiber tip. Thus the optical circulator has a low cost and a small volume comparatively. Excess loss of the coupling system and the misalignment of the lens twice in angular error and the position error to the developed circulator are analyzed and discussed by using Gauss wave and double integral in theory. The analysis results show that the excess loss is zero when each distance is equal to f between every adjacent： fraction and without misalignment error in the coupling system. In addition, the excess loss is increasing with increment of the distance error and the angular error. The errors of the angular of the optical axis to lens and the distance between the SL to lens are the main source of the excess loss. The higher the errors are, the higher the excess loss is. It＇s very important for reducing the misalignment errors in the coupling system with high ratio of coupling to achieve low excess loss. Details of design and excess loss in the coupling system of this circulator are presented.

Random Double Tensors Integrals

In this work,we try to build a theory for random double tensor integrals(DTI).We begin with the definition of DTI and discuss how randomness structure is built upon DTI.Then,the tail bound of the unitarily invariant norm for the random DTI is established and this bound can help us to derive tail bounds of the unitarily invariant norm for various types of two tensors means,e.g.,arithmetic mean,geometric mean,harmonic mean,and general mean.By associating DTI with perturbation formula,i.e.,a formula to relate the tensor-valued function difference with respect the difference of the function input tensors,the tail bounds of the unitarily invariant norm for the Lipschitz estimate of tensor-valued function with random tensors as arguments are derived for vanilla case and quasi-commutator case,respectively.We also establish the continuity property for random DTI in the sense of convergence in the random tensor mean,and we apply this continuity property to obtain the tail bound of the unitarily invariant norm for the derivative of the tensor-valued function.

A Numerical Method for Area and Volume Calculation

The Calculation of area and volume of B-rep solid is discussed, and a numerical method is presented. The method is based on the integrand simplification of the double integral by quadratic triangular Bezier interpolation.

Crosstalk-free integral imaging display based on double plano-convex micro-lens array

A crosstalk-free integral imaging display consisting of a display panel and double piano-convex micro-lens array is proposed. The double piano-convex micro-lens array includes two micro-lens arrays, A and B. Micro-lens array A is used to eliminate crosstalk by completely reflecting crosstalk lights. Micro-lens array B, located near microqens array A, is used to display three-dimensional images. Computer simulations based on ray-tracing are conducted. Crosstalk-free reconstruction images may be clearly observed from the simulation results.

Some New Inverse-type Hilbert-Pachpatte Integral Inequalities

In this paper, some new generalizations of inverse type Hilbert-Pachpatte integral inequalities are proved. The results of this paper reduce to those of Pachpatte (1998, J. Math. Anal. Appl. 226, 166–179) and Zhao and Debnath (2001, J. Math. Anal. Appl. 262, 411–418).