A new method of analysis for PWM switching power converters

A new method of analysis for pulse-width modulation (PWM) switching power converters is presented. It allows one to find an approximate periodic solution for the converter vector state variable. The converter is modelled by a differential equation with periodic coefficients. This equation is substituted by an equivalent system of linear differential equations with constant coefficients. Only the forced (steady-state) solutions should be found for each equation of this system. The equations are solved in sequence. The final steady-state solution of the PWM differential equation is obtained as the sum of these forced solutions. The method allows one to find the converter dc transfer function and efficiency, to evaluate their frequency dependences, and to find the critical frequency and ripple. The first three equations of the equivalent system are usually adequate for practical purposes, and these equations are obtained by an easy formal procedure. One can also obtain the dynamic equation of the state variable dc component, and calculate the converter line to output and duty cycle to output transfer functions. A boost converter is used as an example to confirm the analytical results by numerical simulation.     

Accurate computation of wide-band response of electromagneticsystems utilizing narrow-band information

Cauchy's technique for interpolating a rational function from samples of frequency responses and/or their derivatives is investigated. This technique can be used to speed up the numerical computations of parameters, including input impedance and RCS of any linear time-invariant electromagnetic system. This technique is utilized to find the far field of a slit conducting cylinder (TM incidence) over a bandwidth utilizing the information about the current and its derivatives at a few sample points. The numerical results are presented are in good agreement with exact computational data. This technique is a true interpolation/extrapolation technique as it provides the same defective result as the original electric field integral equation at a frequency which corresponds to the internal resonance of the closed structure     

Green's function for the steady state of a periodically excited circuit

The problem of finding the steady-state solution x(t) of the equation P^{^}x(t) = Q^{^}f(t) is studied, where f(t) is a periodical excitation, and P^{^}and Q^{^}are ordinary linear differential operators with constant coefficients For this purpose, a Green's function is constructed, which is the solution of the problem when the excitation f(t) consists of periodically applied pulses. This Green's function is then used in a convolution integral to find the steady-state solution for any periodical f(t).     

Differential Pulse Code Modulation of Stationary Gaussian Inputs

This paper is concerned with an exact analysis of DPCM systems with stationary Gaussian inputs. We consider a class of digital communication systems in which DPCM is included as a member. An integral equation for the joint probability of the input and the state of the system is derived first. Solution of the equation is sought in the form of a power series in the elements of the covariance matrix of the input that involves generalized Hermite functions. Then the integral equation is reduced to a set of algebraic equations for the coefficients in the series that are solved recursively. The steady-state distribution of the input and the state is thus found. We are interested particularly in the mean-squared error of the system as a function of step size, the sampling interval and the number of quantization levels. Numerical results are shown for the GaussMarkov input; the MSE is calculated in terms of system parameters and performance of DPCM and PCM is compared with reference to the theoretical bound.     

The uncorrelated output components of a nonlinearity

Using his characteristic-function approach, Rice (1945) obtained a double series for the autocorrelation function of a sinusoidal signal and Gaussian noise after passage through a memoryless nonlinearity. It is shown here that the output of the nonlinearity can be expressed as the sum of uncorrelated terms whose auto-correlation functions are the terms of Rice's double series. Such a decomposition of the output is shown to be generally possible if and only if the bivariate probability density functions of the input signal and the input noise can both be expressed in the diagonal form studied by Barrett and Lampard (1955), though not necessarily involving polynomials, as they can in the sinusoidal and Gaussian cases. In addition, a more direct and meaningful equation is found for the coefficients in Rice's double series.     

mBBM方程和Vakhneoko方程的显式精确解

应用试探函数方法求解了mBBM方程和Vakhneoko方程．通过引入试探函数,把难于求解的非线性偏微分方程化为易于求解的代数方程,然后用待定系数法确定相应的常数,从而简洁地求得了方程的精确解。     

具有高斯过程输入的一类非线性系统的输出相关函数

本文研究了在数学期望为零的高斯过程输入情况下,h(lx)具有h(k+p)(lx)=lph(k)(lx)(其中:h(k)(lx)=(k)h(lx)/xk,l为某个实数)性质的输出相关函数。 文中利用上述性质,由Price定理导出一常微分方程。将求非线性系统输出相关函数的问题,变成解常微分方程的问题。 所得结果表明:这类非线性系统的输出相关函数具有相同的形式。不同的h(lx)仅影响其系数。 在此基础上,文中将一般非线性系统的特性f(x)用具有上述性质的函数族来表示,然后直接引用文中前面所得的结果,非常简便地得出了一般非线性系统的输出相关函数的计算公式。     

Application of on-surface MEI method on wire antennas

The formulas of the on-surface measured equation of invariance (OSMEI) for wire antennas are derived. The unknowns of each node on the antenna surface are expressed by the vector potential function and surface current density. The unknowns in the vicinity of each node are coupled in a linear equation and the coefficients of the linear equation are determined by the measured equation of invariance (MEI) method. The final impedance matrix obtained by the OSMEI is a highly sparse matrix. It demonstrates that the currents on thin wire antennas may also be solved by a differential equation-based formulation in addition to the conventional integral equations     

Steady-state solution of linear time-invariant systems

The steady-state solution of the vector differential equation x=Ax+Bw(t) is determined in a compact form by using the solution for an input of a train of impulses.     

Energy-saving trajectory planning for a toggle mechanism driven by a PMSM

In this paper, energy-saving trajectories are planned for a toggle mechanism driven by a permanent magnet synchronous motor (PMSM). The point-to-point (PTP) trajectory is described by a high-degree polynomial, which satisfies the end conditions of displacement, velocity, acceleration and jerk at the initial and final times. The real-coded genetic algorithm (RGA) method is employed to obtain the mechatronic system’s parameters, and to determine the coefficients of the polynomial, and its fitness function is the inverse of various input energies. The numerical simulations and experiments are compared among several degrees’ polynomials during the whole operation motion. Finally, it is found that the input absolute electrical energy (IAEE) occurs when the highest-degree polynomial is chosen. From the percentage of relative error with respect to the absolute input energy of a 7-degree polynomial, it is found that the percentage of relative error achieves 32% as the degree is 24 with enough for minimum input energy degree. The proposed methodology described in this research has the contribution. It can be applied to any mechatronic system which is required to design a minimum-energy point to point trajectory.     

一种基于子空间分解的IIR信道盲辩识算法

本文证明了对IIR信道输出进行过采样 (采样率是输入码率的整数倍 )可以转化成单输入多输出的多信道模型 ,并且不同的信道有相同的AR系数 .基于这一特性本文提出一种基于子空间分解的信道参数盲辩识方法 ,即不同信道的MA系数可以由输出信号的噪声子空间唯一确定 ,而AR系数则可以通过求解YW方程得到     

Statistical dynamics of the phase-locked loop under the action of harmonic interference and noise

The statistical characteristics of a phase-locked loop are determined under the action of input harmonic interference and noise. The stochastic differential equation (SDE) with fixed coefficients has been derived by its averaging over the pulsation period. The derivation of the Fokker-Planck-Kolmogorov (FPK) equation has been implemented. The probability density of an error signal, the mean time between cycle skips, the mean frequency mismatch, and the cycle skip probability are calculated by solving the FPK equation. Two approaches making it possible to obtain statistical characteristics have been compared.     

Identification of double-valued nonlinearities from their harmonic response

A method is presented for determining an equation for a double-valued nonlinearity from a measurement of its response to a sinusoidal input. It is shown that the nonlinearity can be represented as a series in Cheby?shev polynomials of the first and second kind with argument dependent on the input magnitude. The coefficients of the Cheby?shev-polynomial terms in the series are the measured in-phase and quadrature output-harmonic magnitudes.     

Analytical design method for optimal equiripple comb FIR filters

A novel analytical design method for highly selective digital optimal equiripple comb finite-impulse response (FIR) filters is presented. The equiripple comb FIR filters are optimal in the Chebyshev sense. The number of notch bands, the width of the notch bands and the attenuation in the passbands can be independently specified. The degree formula and the differential equation for the generating polynomial of the filter is presented. Based on the differential equation, a fast simple algebraic recursive procedure for the evaluation of the impulse response of the filter is described. Its arithmetic robustness outperforms, by far, the known analytical design method. Highly selective equiripple comb FIR filters with thousands of coefficients can be designed. One example demonstrates the efficiency of the filter design.     

Pulse propagation in a nonlinear dielectric slab waveguide

The evolution of an optical pulse in a single-mode, step index dielectric slab waveguide which is characterized by an intensity dependent dielectric function in the core and cladding regions is treated by means of differential equation techniques. A cubic order non-linearity is considered. The electromagnetic field distribution in the slab waveguide region satisfies a non-linear wave equation. This field can be represented in terms of even TE guided modes with a slowly varying envelope amplitude function. Then using the well known approximation, based on the slowly varying character of the amplitude function, a non linear partial differential equation is obtained for the amplitude function. As the coefficients of this equation depend on the distance across the transverse direction X, an averaging technique over x is applied to reduce the nonlinear partial differential equation into a form that is easily transformed to the so-called non-linear Scroedinger differential equation. This equation is then attacked by means of the well known Inverse Scattering method in the case of reflection less potentials. The single and double soliton solutions are obtained explicitly for a single-mode slab waveguide. Finally numerical results are presented in the time domain.     

Obtaining transfer functions with zero steady-state error from impulse responses

A technique is presented for obtaining approximations to the transfer function of a plant (by modelling the plant's impulse response by a linear combination of orthonormal functions) so that the steady-state responses of the plant and its approximation are the same for constant input. An example is given.     

Parameter sensitivity of indirect universal field-orientedcontrollers

The universal field-oriented (UFO) controller was developed to decouple flux and torque in an arbitrary synchronous flux reference frame, realizing a high degree of generality, which makes the UFO controller compatible with all existing field-oriented controllers, including indirect and direct field orientation. This compatibility is useful to realize drives over a wide speed range using both direct UFO (DUFO) control and indirect UFO (IUFO). In this paper, generalized steady-state torque and flux expressions are derived analytically for detuned operation of the IUFO controller in an arbitrary reference frame. For a given machine (determined by its leakage factor), the expressions can be graphically represented (using only three parameters) as a function of the input command ratios. With these graphs, the steady-state performance of all indirect field-oriented controllers (controlling rotor flux, airgap flux, or stator flux) can be readily evaluated     

Noise Study of an Asynchronous Delta Sigma Modulator

The steady-state probability density function of the error of an asynchronous delta sigma modulator in the presence of a dc input and additive Gaussian noise withRCpower spectrum is obtained by solving the Fokker-Planck equation. The error pdf plots are presented for different system parameters.     

Frequency domain computations for nonlinear steady-state solutions

Steady-state analysis and Fourier analysis play a major role in linear signal processing. In response to a bounded input, a steady-state solution exists if all the poles of the discrete-time linear system are inside the unit circle. Despite the fact that there is no principle of superposition for nonlinear systems, under appropriate sufficient conditions (including all poles inside the unit circle for the linear part of the nonlinear system), there is a bounded solution for all time in response to a bounded input for all time for a time-varying nonlinear difference equation. All solutions that start sufficiently close to this unique solution converge to it as time goes to infinity. This steady-state solution can be computed by applying Fourier and inverse Fourier transforms to each step in a Picard process. In this paper, we develop an algorithm to compute (approximate) steady-state solutions for discrete-time, nonlinear difference equations by employing fast Fourier transforms and inverse fast Fourier transforms at each step of the iterative process. Simulations are provided to illustrate our algorithm