A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

Anti‐Sway Crane Control Considering Wind Disturbance and Container Mass

A method for estimating the sway angle using an observer has already been proposed. The state observer estimates the sway angle accurately and must use the detected sway angle value. However, the estimated sway angle has an error owing to rope length error, friction force, and wind. Moreover, the container mass cannot be determined, and therefore the observer parameter is not suitable. We already proposed robust antisway control for overcoming rope length error without adding a new sensor. Further, we designed a friction disturbance observer to cancel out the influence of the friction force. In this paper, we first propose a container mass estimation method when a crane system performs rolling up control. The observer parameter can be selected using the estimated mass value. Second, in crane parallel shift control, we propose a robust antisway control even when there is a wind disturbance. We design a wind disturbance observer and propose a wind disturbance estimator to separate the friction observer output from the wind disturbance observer output. We confirm through experiments that the proposed method can reduce vibration.     

M-estimator based Chinese Remainder Theorem with few remainders using a Kroenecker product based mapping vector

The Chinese Remainder Theorem (CRT) explains how to estimate an integer-valued number from the knowledge of the remainders obtained by dividing such unknown integer by co-prime integers. As an algebraic theorem, CRT is the basis for several techniques concerning data processing. For instance, considering a single-tone signal whose frequency value is above the sampling rate, the respective peak in the DFT informs the impinging frequency value modulo the sampling rate. CRT is nevertheless sensitive to errors in the remainders, and many efforts have been developed in order to improve its robustness. In this paper, we propose a technique to estimate real-valued numbers by means of CRT, employing for this goal a Kroenecker based M-Estimation (ME), specially suitable for CRT systems with low number of remainders. Since ME schemes are in general computationally expensive, we propose a mapping vector obtained via Kroenecker products which considerably reduces the computational complexity. Furthermore, our proposed technique enhances the probability of estimating an unknown number accurately even when the errors in the remainders surpass 1/4 of the greatest common divisor of all moduli. We also provide a version of the mapping vectors based on tensorial n-mode products, delivering in the end the same information of the original method. Our approach outperforms the state-of-the-art CRT methods not only in terms of percentage of successful estimations but also in terms of smaller average error.     

水提法提取—电感耦合等离子体质谱法测定婴幼儿配方奶粉中的碘

用水提取婴幼儿奶粉中的碘,亚铁氰化钾和乙酸锌盐析法沉淀蛋白,过滤后可以得到澄清处理液。用电感耦合等离子体质谱对提取样液进行测定,130Te作为内标物进行定量分析。该方法简便快捷,检出限为0.10 mg/kg加标回收率为90.8%~109%,相关系数0.999,精密度试验RSD2%。     

卫星激光通信粗跟踪系统复合控制策略

针对卫星激光通信粗跟踪系统的跟踪稳定精度指标要求高的特点,建立了基于永磁同步电机直接驱动的粗跟踪系统模型并进行了跟踪稳定误差分析。在采用传统PID控制策略存在跟踪误差较大、动态性能较差等不足的基础上,提出了一种基于粗跟踪系统的改进型前馈复合控制策略。从理论上分析了前馈复合控制策略提高了粗跟踪系统的动态性能,为降低跟踪稳定误差提供了改善方案。地面实验验证结果表明,与传统控制策略相比,改进型复合控制策略极大地降低了系统的动态跟踪误差,动态跟踪误差由606μrad降低至13μrad(1δ)。进一步的在轨实验也验证了改进型复合控制策略的合理性和先进性,总体指标满足了卫星激光通信终端的极高精度要求。本文所提出的控制策略对其他高性能跟踪伺服系统设计也具有较大的借鉴意义。     

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

In reliability analysis, the stress-strength model is often used to describe the life of a component which has a random strength (X) and is subjected to a random stress (Y). In this paper, we considered the problem of estimating the reliability R=P [Y<X] when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution. The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample, ranked set sampling and median ranked set sampling methods. Four different reliability estimators under median ranked set sampling are derived. Two estimators are obtained when both strength and stress have an odd or an even set size. The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa. The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study. The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample. In general, the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.     

基于一种改进逐点比较插补法的激光打标机控制加工算法

在激光打标系统中,逐点比较插补法是一种普遍使用的算法。这种算法在控制激光运动轨迹和对图像轨迹的拟合过程中,起到极其重要的作用。由于逐点比较插补法具有运算直观,脉冲输出均匀,调节方便等特点,所以是一种较为适合打标机系统应用的插补算法。但是传统的逐点比较插补算法存在精度低和速度慢等问题。为了改善该算法的性能,对传统逐点比较插补算法进行了改进,并进行了计算和模拟仿真。结果表明改进比较插补算法在精度和速度上都有明显提高。     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

制导炸弹半实物仿真系统误差对仿真结果的影响

在制导炸弹半实物仿真试验中经常发现,同一发制导炸弹多次仿真的俯仰角差别较大,同一批次制导炸弹投弹试验的遥测俯仰角与仿真俯仰角差别也较大,但是俯仰角的收敛趋势均一致,实测脱靶量与仿真脱靶量都合格,且具有一致性。为了分析出现上述现象的原因,基于协方差分析描述函数法(CADFT),建立了制导炸弹半实物仿真系统的误差传播理论,计算了仿真姿态角和姿态角速度的误差。分析了仿真姿态角和姿态角速度的误差对仿真结果的影响。结果表明,在仿真系统各种误差中,气动力和气动力矩误差是主要误差,是引起仿真俯仰角差别的重要原因; 姿态角的动态验模方法不适用于制导炸弹仿真模型,而脱靶量的静态验模方法适用于制导炸弹仿真模型。     

平面结构冗余并联机构的误差敏感度分析

针对一种含闭环支链的平面结构冗余并联机构进行误差敏感度分析。分析了该机构的逆运动学和正运动学。基于矩阵法建立了机构的误差模型，并通过反解、正解结合的方法对该误差模型进行了验证。基于误差模型，得到了评价机构误差敏感度的指标，绘制了各指标在工作空间内的等值线图。基于误差敏感度指标，定义了低误差敏感性工作空间，绘制了低误差敏感性工作空间在工作空间中的分布图。与平面3-RRR并联机构进行了误差敏感度对比分析。结果表明，该机构的低误差敏感性工作空间占比较大，同时可以通过调节其冗余支链不断扩大低误差敏感性工作空间，使机构在大范围空间中保持低误差敏感性。