Comparison of vibration mitigation controllers for adaptive optics systems

Vibrations are detrimental to the performance of modern adaptive optics (AO) systems. In this paper, we describe new methods tested to mitigate the vibrations encountered in some of the instruments of the Gemini South telescope. By implementing a spectral analysis of the slope measurements from several wavefront sensors and an imager, we can determine the frequencies and magnitude of these vibrations. We found a persistent vibration at 55 Hz with others occurring occasionally at 14 and 100 Hz. Two types of AO controllers were designed and implemented, Kalman and H∞, in the multiconjugate AO tip-tilt loop. The first results show a similar performance for these advanced controllers and a clear improvement in vibration rejection and overall performance over the classical integrator scheme. It is shown that the reduction in the standard deviation of the residual slopes (as measured by wavefront sensors) is highly dependent on turbulence, wind speed, and vibration conditions, ranging--in terms of slopes RMS value--from an almost negligible reduction for high speed wind to a factor of 5 for a combination of low wind and strong vibrations.     

Fundamental limits on isoplanatic correction with multiconjugate adaptive optics

We investigate the performance of a general multiconjugate adaptive optics (MCAO) system in which signals from multiple reference beacons are used to drive several deformable mirrors in the optical beam train. Taking an analytic approach that yields a detailed view of the effects of low-order aberration modes defined over the metapupil, we show that in the geometrical optics approximation, N deformable mirrors conjugated to different ranges can be driven to correct these modes through order N with unlimited isoplanatic angle, regardless of the distribution of turbulence along the line of sight. We find, however, that the optimal deformable mirror shapes are functions of target range, so the best compensation for starlight is in general not the correction that minimizes the wave-front aberration in a laser guide beacon. This introduces focal anisoplanatism in the wave-front measurements that can be overcome only through the use of beacons at several ranges. We derive expressions for the number of beacons required to sense the aberration to arbitrary order and establish necessary and sufficient conditions on their geometry for both natural and laser guide stars. Finally, we derive an expression for the residual uncompensated error by mode as a function of field angle, target range, and MCAO system geometry.     

Torsional vibrations of circular elastic plates with thickness steps

This paper presents a theoretical study of torsional vibrations in isotropic elastic plates. The exact solutions for torsional vibrations in circular and annular plates are first reviewed. Then, an approximate method is developed to analyze torsional vibrations of circular plates with thickness steps. The method is based on an approximate plate theory for torsional vibrations derived from the variational principle following Mindlin's series expansion method. Approximate solutions for the zeroth- and first-order torsional modes in the circular plate with one thickness step are presented. It is found that, within a narrow frequency range, the first-order torsional modes can be trapped in the inner region where the thickness exceeds that of the outer region. The mode shapes clearly show that both the displacement and the stress amplitudes decay exponentially away from the thickness step. The existence and the number of the trapped first-order torsional modes in a circular mesa on an infinite plate are determined as functions of the normalized geometric parameters, which may serve as a guide for designing distributed torsional-mode resonators for sensing applications. Comparisons between the theoretical predictions and experimental measurements show close agreements in the resonance frequencies of trapped torsional modes.     

A new kind of energy transfer from high frequency mode to low frequency mode in a composite laminated plate

This paper brings to light a new type of nonlinear resonant motion in a fiber-reinforced composite laminated rectangular thin plate, which is not reported in other literature. The investigated system is a simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitation whose frequency is near to the first-order natural frequency of the plate. This new phenomenon demonstrates that the responses of a low-order frequency mode can be excited by those of a high-order frequency mode. The high-order frequency is the first-order natural frequency of the test plate, and the low-order frequency here is lower than the first-order nature frequency. Experimental research works on the nonlinear vibrations of the composite laminated rectangular thin plate have been carried out for the first time. It is found from the experimental results that the nonlinear dynamic responses consist of four modes, whose frequencies include a lower frequency than the first-order natural frequency, 1/3 sub-harmonic, 2/3 sub-harmonic and the first-order natural frequencies. In this case, the amplitude of the mode for lower frequency is larger than those of modes for the aforementioned frequencies. Moreover, the theoretical job goes to analyze this new phenomenon. An analytical mode is given to explain the interactions between the first-order mode and the lower-frequency mode observed in the experiment. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion are formulated for the test plate under parametric excitation. Galerkin’s method is utilized to discretize the partial differential governing equations of motion for the composite laminated rectangular thin plate to a two-degree-of-freedom nonlinear system. The results of numerical simulations qualitatively agree very well with the experimental results. In addition, the multi-pulse chaotic motions are also found in numerical simulations.     

运行列车引起的周围地面振动规律研究

在京广铁路线附近进行了现场试验,测试分析了速度在21km/h―128km/h范围内运行列车引起的地面振动。结果表明:运行列车引起的地面振动的频率集中在10Hz―100Hz,车速对地面水平向振动的频率有一定影响;地面振动随至振源距离的增大呈波动性衰减;货物列车引起的地面加速度振级在各个方向上均明显大于旅客列车,其差值一般在10dB左右;列车引起的地面竖向振动大于两个方向的水平向振动,竖向振级为60dB―110dB;垂直线路的水平向振级为50dB―95dB;平行线路的水平向振级为55dB―80dB;线路附近的地面振动超过了我国关于环境振动规范的规定,说明运行列车引起的环境振动问题应当引起重视。     

低密频太阳能帆板动力学参数在轨辨识和振动控制

太阳能帆板是典型的柔性空间结构,其固有频率低且密集,阻尼很小。为了抑制其振动,建立了基于动力学参数辨识的振动控制方法。该方法利用特征系统实现算法及其扩展算法如ERA/DC或OKID辨识结构的动力学参数,然后利用最优控制理论设计控制器。根据辨识和控制的方法以及适用的情况,提出了三种在轨辨识和控制集成方案,即ERA(ERA/DC)和LQR或LQG,OKID和LQG。对一具有低密频大型柔性空间站结构的数值仿真表明,上述在轨辨识和控制集成方案具有辨识速度快,辨识精度高,控制效果好等优点,适于柔性空间结构的在轨辨识和控制。     

Kalman filtering to suppress spurious signals in adaptive optics control

In many scenarios, an adaptive optics (AO) control system operates in the presence of temporally non-white noise. We use a Kalman filter with a state space formulation that allows suppression of this colored noise, hence improving residual error over the case where the noise is assumed to be white. We demonstrate the effectiveness of this new filter in the case of the estimated Gemini Planet Imager tip-tilt environment, where there are both common-path and non-common-path vibrations. We discuss how this same framework can also be used to suppress spatial aliasing during predictive wavefront control assuming frozen flow in a low-order AO system without a spatially filtered wavefront sensor, and present experimental measurements from Altair that clearly reveal these aliased components.     

城市轨道交通槽型梁结构噪声计算与分析

该文用模态叠加法对城市轨道交通槽型梁进行车-轨-桥耦合动力计算,借助SYSNOISE求出模态声传递向量MATVs,进而用MATVs和梁的模态坐标响应计算桥梁的结构噪声。噪声计算值与实测值在频率分布和幅值上有较高的一致性,证明振动与噪声数值模型的可靠性。槽型梁结构噪声的线性声压级峰值频率为40Hz~80Hz,数值计算表明:动力分析只需考虑轮轨竖向接触即可满足结构噪声计算要求;考虑200Hz以下的声源激励和100Hz以下的结构模态作为边界条件可达到较好的噪声计算精度;调节轨下胶垫的刚度能有效减小结构振动,降低结构噪声2dB~3dB;声压级和车速有强线性关系。     

Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots

The design of the laser-guide-star-based adaptive optics (AO) systems for the Extremely Large Telescopes requires careful study of the issue of elongated spots produced on Shack-Hartmann wavefront sensors. The importance of a correct modeling of the nonuniformity and correlations of the noise induced by this elongation has already been demonstrated for wavefront reconstruction. We report here on the first (to our knowledge) end-to-end simulations of closed-loop ground-layer AO with laser guide stars with such an improved noise model. The results are compared with the level of performance predicted by a classical noise model for the reconstruction. The performance is studied in terms of ensquared energy and confirms that, thanks to the improved noise model, central or side launching of the lasers does not affect the performance with respect to the laser guide stars' flux. These two launching schemes also perform similarly whatever the atmospheric turbulence strength.     

Energy Scavenging From Low-Frequency Vibrations by Using Frequency Up-Conversion for Wireless Sensor Applications

This paper presents an electromagnetic (EM) vibration-to-electrical power generator for wireless sensors, which can scavenge energy from low-frequency external vibrations. For most wireless applications, the ambient vibration is generally at very low frequencies (1-100 Hz), and traditional scavenging techniques cannot generate enough energy for proper operation. The reported generator up-converts low-frequency environmental vibrations to a higher frequency through a mechanical frequency up-converter using a magnet, and hence provides more efficient energy conversion at low frequencies. Power is generated by means of EM induction using a magnet and coils on top of resonating cantilever beams. The proposed approach has been demonstrated using a macroscale version, which provides 170 nW maximum power and 6 mV maximum voltage. For the microelectromechanical systems (MEMS) version, the expected maximum power and maximum voltage from a single cantilever is 3.97 muW and 76 mV, respectively, in vacuum. Power level can be increased further by using series-connected cantilevers without increasing the overall generator area, which is 4 mm². This system provides more than an order of magnitude better energy conversion for 10-100 Hz ambient vibration range, compared to a conventional large mass/coil system.     

高速列车车体结构振动和车内声学特性分析

为了研究高速载客列车车体结构振动及车内声学特性，建立高速列车有限元模型，对全车体进行模态分析和轨道谱响应分析，并基于声与结构耦合对车体内腔进行声学模态分析。车体前200阶固有模态频率跨度为0.62～100.27 Hz，前6阶0.62～1.51 Hz为车身整体相对于转向架的低频振动，其余各阶为车身结构的弹性振动。当施加我国200 km/h等级提速线路通用轨道谱激励时，体振动在0～2.00 Hz的低频有较大响应。车体内腔前200阶声学模态频率跨度为0～126.66 Hz，在20～100 Hz之间模态比较密集。     

Vibration spectrum of a pulse-tube cryostat from 1 Hz to 20 kHz

The vibrations of the cold finger of a low-vibration helium pulse-tube cryostat are measured from 1 Hz to 20 kHz using an optical interferometer specially designed to measure small amplitude vibrations at high frequencies in the presence of large vibrations at lower frequencies. While the vibrational amplitude is dominated by the contribution at the fundamental compressor frequency of 1.4 Hz, the pulse tube contributes mechanical noise at frequencies up to 15 kHz, where the spectral density is measured to be 4 × 10⁻¹² m/Hz^1/2. Root-mean-squared vibration amplitudes of 5.2 μm and 3 μm are measured along perpendicular axes in the horizontal plane, and 1.0 μm in the vertical direction. The effect of a suspended sample holder for the purpose of attenuating high-frequency vibrations is evaluated. Finally, the cryostat is shown to be considerably noisier than typical laboratory floors.     

Multirate asynchronous sampling of sparse multiband signals

Because optical systems have a huge bandwidth and are capable of generating low-noise short pulses, they are ideal for undersampling multiband signals that are located within a very broad frequency range. We propose a new scheme for reconstructing multiband signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels. The scheme, which we call multirate sampling (MRS), entails gathering samples at several different rates whose sum is significantly lower than the Nyquist sampling rate. The number of channels does not depend on any characteristics of a signal. In order to be implemented with simplified hardware, the reconstruction method does not rely on the synchronization between different sampling channels. Also, because the method does not solve a system of linear equations, it avoids one source of lack of robustness of previously published undersampling schemes. Our simulations indicate that our MRS scheme is robust both to different signal types and to relatively high noise levels. The scheme can be implemented easily with optical sampling systems.     

弹性车体垂向运行平稳性一系最优控制研究

采用基于轨道谱及包括轮轴间时延预瞄的最优控制算法,在一系悬挂中加入主动控制,设计其主动控制规律,从降低轨道至车体振动的传递入手,对铁道车辆弹性车体垂向动力学模型进行仿真分析。结果表明,该最优控制算法对车辆系统的振动有较好的抑制作用;可以改善轨道至弹性车体中部的振动加速度传递率,在控制车体刚体振动的同时,也能抑制整车的弹性振动;最优控制算法对车辆系统的1Hz左右的低频振动、以及包含人体垂向振动敏感频域(4Hz-8Hz)的4Hz~10Hz频率内的振动衰减明显,但对车体高频振动作用不大。并与二系主动悬挂系统比较,发现一系主动悬挂能更有效的控制车体的弹性振动,且抑制的频率范围较宽,车辆运行平稳性更佳,为今后弹性车体减振措施选择提供依据。     

Fourier transform infrared and inelastic neutron scattering study of HY zeolites

A combination ofFTi.r. and INS spectroscopy is used in a vibrational study of the bending and stretching vibrations of the acidic hydroxyl groups of Y zeolites. The influence of the number of acidic Bro¨nsted sites and theSi/Al ratio is discussed. Out-of-plane hydroxyl bending modes are assigned to vibrations centered around 419 cm⁻¹ and in-plane hydroxyl bending modes are assigned to vibrations centered around 1089 cm⁻¹. Upon dealumination, these bands are shifted by approximately 30 cm⁻¹ to lower values. The less intense bands at 319,470,565,765, and 1130 cm⁻¹ are assigned to proton-coupled framework vibrations. Upon dealumination, the mode at 319 cm⁻¹ is shifted to lower frequencies and the modes at 565 and 1130 cm⁻¹ are shifted to higher frequencies.     

Fast computation of an optimal controller for large-scale adaptive optics

The linear quadratic Gaussian regulator provides the minimum-variance control solution for a linear time-invariant system. For adaptive optics (AO) applications, under the hypothesis of a deformable mirror with instantaneous response, such a controller boils down to a minimum-variance phase estimator (a Kalman filter) and a projection onto the mirror space. The Kalman filter gain can be computed by solving an algebraic Riccati matrix equation, whose computational complexity grows very quickly with the size of the telescope aperture. This "curse of dimensionality" makes the standard solvers for Riccati equations very slow in the case of extremely large telescopes. In this article, we propose a way of computing the Kalman gain for AO systems by means of an approximation that considers the turbulence phase screen as the cropped version of an infinite-size screen. We demonstrate the advantages of the methods for both off- and on-line computational time, and we evaluate its performance for classical AO as well as for wide-field tomographic AO with multiple natural guide stars. Simulation results are reported.     

Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes

We present sample Monte Carlo simulation results to illustrate the trends in multiconjugate adaptive optics (MCAO) performance as the telescope aperture diameter increases from 8 to 32 m with all other first-order system parameters held constant. The MCAO system considered includes three deformable mirrors, a 1-arc min square field of view, and five wave-front-sensing references consisting of either natural guide stars or laser guide stars at a range of either 30 or 90 km. The rms residual wave-front error decreases slowly with increasing aperture diameter with natural guide stars, whereas performance degrades significantly with increasing aperture diameter for laser guide stars at 30 km if the number of guide stars is held fixed. Performance with laser guide stars at 90 km is a weak function of telescope aperture diameter in the range from 8 to 32 m, with rms wave-front errors no more than 20% greater than the corresponding natural guide-star case for the same level of wave-front sensor's measurement noise.     

Generalization of the continuous and discrete structural approaches to the solution of problems of the dynamics of laminated composite plates and structures with stratification. Part 2. Analytic decomposition of unknown functions. Results and comparisons

A three-dimensional solution of the problem of determination of the frequencies and modes of natural vibrations of multilayer plates is obtained on the basis of the method of analytic separation of variables. We compare the models with analytic separation of variables and polynomial approximation of unknown functions over the thickness of the structure. Within the framework of the continuous structural approach, the applied model enables one to determine the frequencies and modes of natural vibrations for a broad range of problems with sufficiently high accuracy. If it is necessary to improve the accuracy of results, then one can pass to the discrete structural version of the model. Ukrainian Transport University, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 93–99, November–December, 1999.     

工程爆破对周围环境振动影响的测试与分析

基于基坑三向振动速度现场测试,通过数据处理与1/3倍频分析,研究了不同距离测点的爆破振动频率特性,段药量和不同起爆网路对爆破振动频率的影响,各向振动加速度振级随距离的变化规律。结果表明,爆破地震的频率主要集中在15Hz⁸0Hz范围内;段药量越小,主振频率越高,主频域处于较高的频率范围,高频所占的能量比例较大;地表延时分区起爆与V型起爆相比,其质点振动加速度峰值较小,主频有明显提高,并且出现多峰;爆破引起的地面垂直方向振级大于两个水平方向振级,Z向振级为50dB80Hz范围内;段药量越小,主振频率越高,主频域处于较高的频率范围,高频所占的能量比例较大;地表延时分区起爆与V型起爆相比,其质点振动加速度峰值较小,主频有明显提高,并且出现多峰;爆破引起的地面垂直方向振级大于两个水平方向振级,Z向振级为50dB¹15dB,X向振级为45dB115dB,X向振级为45dB¹10dB,Y向振级为40dB110dB,Y向振级为40dB¹05dB,随着测点至爆源距离的增大,不同方向的振级均呈现衰减趋势,同时又表现出一定的波动性,50m以内时,振级衰减较快,50m以外,振级衰减较慢。     

Signal-to-noise ratio of phase sensing telescope interferometers

The paper described is the third part of a trilogy dealing with the principles, performance, and limitations of what the author named "telescope-interferometers" (TIs). The basic idea consists in transforming one telescope into a wavefront error (WFE) sensing device. This can be achieved in two different ways, namely, off-axis and phase-shifting TIs. In both cases the point-spread function measured in the focal plane of the telescope carries information about the transmitted WFE, which is retrieved by fast and simple algorithms suitable to an adaptive optics (AO) regime. The uncertainties of both types of TIs are evaluated in terms of noise and systematic errors. Numerical models are developed to establish the dependence of driving parameters such as useful spectral range, angular size of the observed star, or detector noise on the total WFE measurement error. The latter is found particularly sensitive to photon noise, which rapidly governs the achieved accuracy for telescope diameters higher than 10 m. A few practical examples are studied, showing that the TI method is applicable to AO systems for telescope diameters ranging from 10 to 50 m, depending on seeing conditions and magnitude of the observed stars. Also discussed is the case of a space-borne coronagraph, where the TI technique provides high sampling of the input WFE map.