A numerical filtering method for linear state-space models with Markov switching

A class of discrete-time random processes arising in engineering and econometrics applications consists of a linear state-space model whose parameters are modulated by the state of a finite-state Markov chain. Typical filtering approaches are collapsing methods, which approximate filtered distributions by mixtures of Gaussians, each Gaussian corresponding to one possibility of the recent history of the Markov chain, and particle methods. This article presents an alternative approach to filtering these processes based on keeping track of the values of the underlying filtered density and its characteristic function on grids. We prove that it has favorable convergence properties under certain assumptions. On the other hand, as a grid method, it suffers from the curse of dimensionality, and so is only suitable for low-dimensional systems. We compare our method to collapsing filters and a particle filter with examples, and find that it can outperform them on 1- and 2-dimensional problems, but loses its speed advantage on 3-dimensional systems. Meanwhile, our method has a proven theoretical convergence rate that is probably not achieved by collapsing and particle methods.     

Process noise covariance estimation via stochastic approximation

Kalman filtering for linear systems is known to provide the minimum variance estimation error, under the assumption that the model dynamics is known. While many system identification tools are available for computing the system matrices from experimental data, estimating the statistics of the output and process noises is still an open problem. Correlation-based approaches are very fast and sufficiently accurate, but there are typically restrictions on the number of noise covariance elements that can be estimated. On the other hand, maximum likelihood methods estimate all elements with high accuracy, but they are computationally expensive, and they require the use of external optimization solvers. In this paper, we propose an alternative solution, tailored for process noise covariance estimation and based on stochastic approximation and gradient-free optimization, that provides a good trade-off in terms of performance and computational load, and is also easy to implement. The effectiveness of the method as compared to the state of the art is shown on a number of recently proposed benchmark examples.     

三相四开关逆变器供电的IPMSM直接转矩控制系统建模与分析

为获得较高的转矩响应速度和较低的转矩脉动,将基于比例-积分控制器和空间矢量调制的直接转矩控制(PI-SVM DTC)引入到由三相四开关逆变器供电的凸极式永磁同步电机(IPMSM)驱动系统中。鉴于电机的强耦合性,同时为便于分析其定子磁链环,建立了IPMSM在静止坐标系下以定子磁链为状态变量的状态空间模型。为改善系统的稳态性能,构建无差拍全阶状态观测器,实现对定子磁链的闭环观测。揭示了传统定子磁链环极点放置位置存在的问题,并利用一种简单的方法对定子磁链环极点位置进行优化。对PI-SVM DTC的转矩环进行建模分析,为PI控制器的设计提供依据。另外,为抑制三相四开关逆变器直流母线中性点电压偏移,根据其偏移量生成合适的补偿量,并将其添加到定子磁链控制环中。实验结果验证了该模型的有效性。     

感应电能传输系统分段供电的双自由度鲁棒控制

感应电能传输(IPT)系统在采用分段供电模式时,由于跨区段处励磁磁场强度分布不均,总会引起负载端拾取功率波动,影响系统稳定性及性能。针对IPT系统跨区段供电的输出稳定问题,以LCL谐振电路并联的IPT系统为研究对象,设计一种基于双自由度鲁棒控制的恒压输出策略。借助广义状态空间平均建模方法,结合跨区段处的互感扰动规律,建立参数不确定性模型;基于广义混合灵敏度指标,通过改变输出加权函数增益,得到快速抑制互感扰动影响的H∞鲁棒控制器;在此基础上,推导并设计出用于修正参考输入的前置滤波器;实验结果表明,双自由度鲁棒控制不仅对跨区段互感扰动影响具有较好抑制作用,且能明显改善对参考输入的跟踪响应性能。     

State-space ARIMA for supply-chain forecasting

ARIMA is seldom used in supply chains in practice. There are several reasons, not the least of which is the small sample size of available data, which restricts the usage of the model. Keeping in mind this restriction, we discuss in this paper a state-space ARIMA model with a single source of error and show how it can be efficiently used in the supply-chain context, especially in cases when only two seasonal cycles of data are available. We propose a new order selection algorithm for the model and compare its performance with the conventional ARIMA on real data. We show that the proposed model performs well in terms of both accuracy and computational time in comparison with other ARIMA implementations, which makes it efficient in the supply-chain context.     

Controller Design Using Ant Colony Algorithm for a Non-inverting Buck–Boost Chopper Based on a Detailed Average Model

In this article, the non-inverting buck–boost converter and its operation modes are scrutinized. The closed-loop stability of the converter in buck and boost modes is analyzed, and the necessity of using an appropriated controller is demonstrated. Then the application of an adapted ant colony optimization to design a feedback controller is proposed, and a controller based on its existing model is tuned. Simulation and experimental results obtained from the ant colony optimization designed controller are then compared with a controller designed with the classic method. Although the simulation and experimental results prove the efficiency of the proposed control approach, a significant difference between controller behavior in practice and simulation is obvious. Finding these differences, more detailed models, including all parasitic elements, in the buck and boost modes are derived. Applying the proposed model in controller design illustrates that the desired performance of the converter can be guaranteed with a simple proportional-integral (PI) controller. The suggested ant colony-based controller is again tuned based on the more detailed model, which improves the performance of the converter system even more. Furthermore, good agreement between analytical and experimental outputs validates the accuracy of the modeling and simulation.     

基于状态空间的大功率转子斩波调速系统

针对大功率(兆瓦级)转子斩波串级调速系统的斩波回路建模问题,提出一种基于状态空间平均法的斩波回路模型,该模型包含了回路中的绝缘栅双极型晶体管(IGBT)与续流二极管(FWD)非线性元件,解决了在大功率下串级调速系统控制系统设计难的问题。实验表明,设计的双闭环调速系统有良好的可靠性,稳定性,静、动态特性及较高的功率因数。现该系统已运行于工业现场,节能效果良好。     

考虑调整误差的多变量设置调整问题

针对存在初始设置偏差的离散多变量生产制造过程,研究了调整误差服从自回归模型的情况下,考虑调整花费成本为二次型函数时的设置调整问题,在建立过程状态空间方程的基础上,利用卡尔曼滤波方法在线估计过程的状态变量,根据随机二次型最优控制理论得到了使过程质量损失最小的最优调整策略.通过算例解释了最优调整策略的实现方法,并进行了仿真验证,结果表明,得到的调整策略与调整误差为白噪声时的调整策略相比,能更好地减少过程总体质量损失.     

A Spatial-Domain Technique for the Design of 3-D Separable-Denominator State-Space Digital Filters

In this paper,a technique for designing 3-D separable-denominator state-spacedigital filters is developed. The design process is divided intotwo phases. First, the coefficient matrices related to stabilityare constructed for the filter to be stable by using alternatingvariable method. Next, the other matrices are obtained by solvinglinear equations. These phases are repeated until there is nosignificant change in the squared error function.     

把离散系统模型转换成连续系统模型的递推算法及其稳定性

在Newton-Raphson法的基础上,本文提出收敛较快、数值稳定的递推算法把离散系统模 型转换成等价的连续系统模型,分析了算法的稳定性并举例说明所提出的算法的效果.