Structured genetic algorithm for robust H∞ controlsystems design

A structured genetic algorithm (SGA) approach is developed for robust controller design based on the concept of an H^∞ loop-shaping technique and the method of inequalities. Such an SGA is capable of simultaneously searching the orders and coefficients of the precompensator and postcompensator for the weighted plant. It is, therefore, not necessary to predefine the order of compensators as in usual practice. A multiple objective ranking approach is also incorporated so that the design criteria of extreme plants can be easily achieved. The effectiveness of such a technique is illustrated by a high-purity distillation column design example     

Second-order H∞ optimal LMS and NLMS algorithmsbased on a second-order Markov model

It is shown that two algorithms obtained by simplifying a Kalman filter considered for a second-order Markov model are H^∞ suboptimal. Similar to least mean squares (LMS) and normalised LMS (NLMS) algorithms, these second order algorithms can be thought of as approximate solutions to stochastic or deterministic least squares minimisation. It is proved that second-order LMS and NLMS are exact solutions causing the maximum energy gain from the disturbances to the predicted and filtered errors to be less than one, respectively. These algorithms are implemented in two steps. Operation of the first step is like conventional LMS/NLMS algorithms and the second step consists of the estimation of the weight increment vector and prediction of weights for the next iteration. This step applies simple smoothing on the increment of the estimated weights to estimate the speed of the weights. Also they are cost-effective, robust and attractive for improving the tracking performance of smoothly time-varying models     

On linear H∞ equalization of communicationchannels

As an alternative to existing techniques and algorithms, we investigate the merit of the H^∞ approach to the linear equalization of communication channels. We first give the formulation of all causal H^∞ equalizers using the results of and then look at the finite delay ease. We compare the risk-sensitive H^∞ equalizer with the MMSE equalizer with respect to both the average and the worst-case BER performances and illustrate the improvement due to the use of the H^∞ equalizer     

H∞ control applied to boost power converters

The controller in a pulse-width-modulation (PWM) power converter has to stabilize the system and guarantee an almost constant output voltage in spite of the perturbations in the input voltage and output load over as large a bandwidth as possible. Boost and flyback power converters have a right-half-plane zero (RHPZ) in their transfer function from the duty cycle to the output voltage, which makes it difficult to achieve the aforementioned goals. Here, the authors propose to design a controller using H^∞ control theory, via the solution of two algebraic Riccati equations. The almost optimal H^∞ controller is of the same order as the converter and has a relatively low DC gain. The closed-loop characteristics of a typical low-power boost power converter with four different control schemes were compared by computer simulation. The H^∞ control was found to be superior in a wide frequency range, while being outperformed by the others at extremely low frequencies. Good agreement was found between simulation results and experimental measurements     

Combined LMS/F algorithm

A new adaptive filter algorithm has been developed that combines the benefits of the least mean square (LMS) and least mean fourth (LMF) methods. This algorithm, called LMS/F, outperforms the standard LMS algorithm judging either constant convergence rate or constant misadjustment. While LMF outperforms LMS for certain noise profiles, its stability cannot be guaranteed for known input signals even For very small step sizes. However, both LMS and LMS/F have good stability properties and LMS/F only adds a few more computations per iteration compared to LMS. Simulations of a non-stationary system identification problem demonstrate the performance benefits of the LMS/F algorithm     

N2LMS: enhanced LMS algorithm for speech applications

A modified LMS algorithm, for the echo control of speech signals in a conference environment, has been analysed. Initial results show that the algorithm can provide lower misadjustment and more uniform speech-band cancellation compared with the conventional LMS algorithm at equal convergence rates, with very little additional computation     

Mean-square performance of the filtered-reference/ filtered-error LMS algorithm

This paper describes two properties of the filtered-reference/filtered-error least-mean-square (LMS) algorithm proposed by Sujbert. First, by using the averaging method, the stability condition of the algorithm is investigated, which is affected by the compensating filter being inserted into both the input signal path and the error signal path. Second, the formula to express the mean-square error of the algorithm is theoretically derived by the ordinary differential equation method. Based on the derived formula, the convergence speed of the algorithm is compared to other types of LMS algorithms.     

Newton/LMS algorithm using modified DCT

A Newton/LMS algorithm using a modified DCT is proposed which uses an efficient technique of inverting the input autocorrelation matrix when the periodic pseudorandom sequence is used as the reference signal. The number of operations is greatly reduced and the computational results show fast convergence rate and low misadjustment error. The application of the algorithm to the case of nonperiodic reference signal is also described.<>     

Bursting in the LMS algorithm

The least mean square (LMS) algorithm is known to converge in the mean and in the mean square. However, during short time periods, the error sequence can blow up and cause severe disturbances, especially for non-Gaussian processes. The paper discusses potential short time unstable behavior of the LMS algorithm for spherically invariant random processes (SIRP) like Gaussian, Laplacian, and K₀. The result of this investigation is that the probability for bursting decreases with the step size. However, since a smaller step size also causes a slower convergence rate, one has to choose a tradeoff between convergence speed and the frequence of bursting     

Stability of the quantized LMS algorithm

The least mean square (LMS) algorithm is investigated for stability when implemented with two's complement quantization. The study is restricted to algorithms with periodically varying inputs. Such inputs are common in a variety of applications, and for system identification, they can always be generated as shown with an example. It is shown that the quantized LMS algorithm is just a special case of a quantized periodically shift-varying (PSV) filter. Two different sufficient conditions are obtained for the bounded input bounded output (BIBO) stability of the PSV filter. When the filter is BIBO stable, two different bounds on the filter output are also derived. These conditions and bounds are then applied to the quantized LMS algorithm. The results are illustrated with examples.     

基于压力应变的放大电路实验

基于压力传感器的高阻抗小信号输出,分别通过单个运算放大器差分电路、三个运算放大器构成的仪用放大电路以及集成仪用放大电路来放大,应用零点与增益调整电路来实现重量与电压的一一对称,通过数字万用表的电压值来表示重量。该实验具有趣味性、实用性和不确定性有利于学生发现问题、分析问题、解决问题。     

Robust design of the LMS algorithm

A method to optimize the step size of the LMS algorithm when it is used to identify a time-varying system is proposed. The formulation allows uncertain specifications of the input excitation and the plant variation. The method is robust in that it minimizes the mean square error for the worst-case data of these variables     

Cr3+→Nd3+ energy transfer and Nd3+ laser action studies of La3Ga5SiO14:Cr3+,Nd3+ co-doped crystal

Energy transfer between Cr³⁺ and Nd³⁺ ions has been investigated in the 4.2-300-K temperature range by using steady-state and site-selective time-resolved laser spectroscopy. Radiative and nonradiative energy transfer has been studied from the time-resolved emission spectra and the donor fluorescence decays. The transfer efficiency was calculated as a function of temperature by using the Cr³⁺ lifetimes of the single doped and co-doped samples. Laser experiments were carried out in a diffusive cavity by pumping a co-doped rod 54 mm long and 5 mm in diameter with xenon flashlamps. The laser spectral emission shows a complex structure which varies as a function of pump energy. The temporal evolution of the laser spectrum is discussed in terms of a simple four-level spectral rate-equation laser model which takes into account the existence of two main broad Nd³⁺ site distributions with a large spectral overlap     

Adaptive system identification using robust LMS/F algorithm

Adaptive system identification (ASI) problems have attracted both academic and industrial attentions for a long time. As one of the classical approaches for ASI, performance of least mean square (LMS) is unstable in low signal‐to‐noise ratio (SNR) region. On the contrary, least mean fourth (LMF) algorithm is difficult to implement in practical system because of its high computational complexity in high SNR region, and hence it is usually neglected by researchers. In this paper, we propose an effective approach to identify unknown system adaptively by using combined LMS and LMF algorithms in different SNR regions. Experiment‐based parameter selection is established to optimize the performance as well as to keep the low computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.     

Almost-sure convergence of the continuous-time LMS algorithm

The authors consider the stability properties of the conventional continuous-time least mean square algorithm. The algorithm for the case of stationary ergodic inputs is investigated and a necessary and sufficient condition for exponential almost-sure convergence is presented. This condition is shown to be less restrictive than the well-known persistency of excitation condition. Also, the authors point out and clarify an apparently common error regarding the connections between persistency of excitation and positive definite autocorrelation in stationary ergodic vector waveforms     

Analysis of the frequency-domain block LMS algorithm

We present a new analysis of the frequency-domain block least-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algorithm in the frequency domain. As compared with the previous analysis, the new analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its convergence behavior. In particular, we show how the transformation of input samples to the frequency domain, combined with the effect of the involved windowing matrices, and step-normalization affect the convergence behavior of both constrained and unconstrained versions of the FBLMS algorithm. We also report a procedure for derivation of misadjustment equations of various versions of the FBLMS algorithm     

Effect of electron cyclotron resonance H+,Ne+, Ar+, and Xe+ plasma precleaning ontitanium silicide formation

A vacuum integrated cluster tool process incorporating electron cyclotron resonance plasma cleaning, Ti sputter deposition, and rapid thermal annealing in N₂ is used to form a TiN_x<1/TiSi_y bilayer on (100) Si where the film composition is controlled by the preclean chemistry. Chemical cleaning with nominal 10 eV H⁺ completely removes native Si oxide resulting in a hydrogen terminated surface that promotes silicidation compared to one cleaned with buffered-oxide-etching (BOE). If the native oxide is only partially reduced, viz., SiO_x<2 surface, for example by shortening the H⁺ exposure time, then silicidation is largely inhibited and a thicker nitride layer is formed. Sputter cleaning with 50 to 250 eV Ar⁺ results in a bilayer that is roughly equivalent to that formed with BOE, whereas 50 to 150 eV Xe⁺ bombardment favors nitridation. Precleaning with >150 eV Ne⁺ promotes silicidation, thereby minimizing nitride thickness. The effects of precleaning are significant as the activation energy for TiSi_y formation is reduced from 1.8 eV characteristic of a BOE cleaned surface to 1.2 eV on Si etched with 250 eV Ne⁺. Mechanistically, the silicide kinetics are shown to be inhibited by the presence of a thin amorphous layer that is formed only when cleaning Si with Ar⁺ and Xe⁺ with the effect that both knock-on oxygen atoms and implanted noble gas atoms trapped within the amorphous layer retard the requisite solid-phase epitaxial regrowth kinetics. Recrystallizing the amorphous Si surface prior to metallization appears to restore the near-normal silicide kinetics that is characteristic of Ne⁺ cleaning     

fα noise source streamlines SPICE simulations

The methodology described in this article for creating a PWL noise source is an effective way of generating general f^α noise for time-domain circuit simulations. The benefit of using digitally-interpolated noise waveforms is significant. Using an external computer program to produce digitally-interpolated PWL noise sources removes the burden of spectrally shaping the noise from the circuit simulator, eliminating the need for high-order analog filters. By designing a custom FIR interpolating filter, unique types of spectral shaping are possible without increasing the computational burden     

On the optimality of the gridding reconstruction algorithm

Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction (LSR), on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise. Hence, it is rarely used in practice. Despite their seemingly different approaches, the gridding and LSR methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as the ones which yield the minimum approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This problem is studied and solved in the general form of approximation using linearly structured matrices. This method not only supports more general forms of the gridding algorithm, it can also be used to accelerate the reconstruction techniques from incomplete data. The application of this method to a case of two-dimensional (2-D) spiral magnetic resonance imaging shows a reduction of more than 4 dB in the average reconstruction error.