On zero locations for sampled stochastic systems

Zero locations of stochastic models have significant influence on optimal prediction algorithms as well as on the convergence speed of identification method. The possible zero locations for a sampled stochastic system are examined. In particular, it is shown and numerically illustrated that the sampled zeros can appear only in a restricted set within the unit circle. A complete analysis of second-order systems is given, and all possible zero locations are characterized. It is shown how the zero location in this case depends on the continuous-time model parameters and the sampling interval     

Analytic study on the intrinsic zeros of sampled-data systems

This paper investigates the properties of the mapping from the simple zero γ of a scalar continuous-time system to the corresponding zero Γ(T) of the sampled-data system that results by its discretization using a zero-order hold, where T is the sampling period. It is shown that Γ(T) admits a Taylor expansion with respect to T, and that it coincides with that of exp(γT) at least up to the second-order term, in general, and at least up to the third-order term if the relative degree of the continuous-time system is greater than or equal to two. The result is applied to derive a new stability condition of Γ(T) for sufficiently small sampling periods     

Edge detection in multispectral images

This paper proposes an extension of edge detectors based on second-order differential operators to the case of multiple band (color) images. To this end, we define a local directional measure of multispectral contrast. A definition of edge point is then given, as the location of a directional maximum of the contrast function. Extremal contrast edges are defined, as loci of zero crossing points of the first directional derivative of the contrast function. The qualitative properties of the so defined edges are briefly discussed. An algorithm for edge location with subpixel resolution is proposed, with an example of application to actual RGB imagery.     

Efficient zero location tests for delta-operator-based polynomials

Two different kinds of stability tests, or more generally zero location tests, are proposed when a real polynomial formulated in the delta-operator is given. The method used is a simple linear transformation based on some known discrete-time tests, including the Schur-Cohn test (SCT), and the proposed algorithms are computationally efficient. Furthermore, it is shown that as the sampling interval vanishes, all new algorithms converge to their continuous-time limits, therefore providing smooth transitions from the shift-operator-based discrete-time tests to the continuous-time ones. One of these limits is the classic Routh test (RT), and the other is a new test, closely related to the RT. Examples are given to demonstrate the tests which show clear numerical advantages over the traditional shift-operator-based ones such as the SCT in case of fast sampling. The significance of these new tests lies beyond the fact that they have provided efficient and reliable zero location tests directly in the delta-domain. These tests provide the missing links between the discrete-time shift-operator-based tests and the continuous-time ones. As a consequence, two separate and yet related families of zero location tests are established, which include the well-known RT and the SCT     

基于二阶循环统计量的盲均衡算法

提出一种新的基于循环二阶统计量的盲均衡算法.通过对信道输出信号进行过采样,建立单输入多输出信道模型.由于过采样等效信道矩阵具有特殊结构,使得仅仅根据零延迟时的协方差矩阵所包含的信息就能实现信道估计,根据不同延迟下的协方差矩阵也可求得不同时延的均衡器矩阵,然后用最小均方误差MMSE准则来优化均衡器得到最佳延迟协方差矩阵.仿真结果表明了该算法的有效性.     

熵能量堆煤图像的定位与识别

目的 针对煤矿皮带堆煤传感器受复杂环境干扰导致检测效率较低的问题,提出一种新的基于熵能量(EE)的堆煤图像定位与识别方法。方法 该方法首先在堆煤图像初始化区域内设定采样单元,统计采样单元前景和背景区域的信息熵,计算信息熵分布的极大值所对应的的灰度阶并统计其出现的概率;然后计算采样单元的熵能量和能量频率,归一化频率系数,并利用能量频率的二阶偏导确定堆煤边缘区域,将采样单元移动至堆煤边缘处;最后,根据采样单元的坐标位置计算堆煤高度和半径,进行实时预警。结果 在煤矿井下皮带堆煤视频上进行算法测试,该算法的单帧图像平均处理速度为0.35 s/帧,堆煤事故预警时间间隔最大为0.35 s,平均识别准确率为97.1%,测试结果表明,该方法对堆煤模糊边缘、环境噪音具有抗干扰特点,可以有效克服强噪音、模糊边缘等因素对堆煤识别的影响。结论 该方法对复杂环境中堆煤定位与识别具有很好的实时性和准确性,对提高煤矿安全生产效率具有重要意义。     

Second-order consensus in multi-agent dynamical systems with sampled position data

This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis.     

一种采用变采样周期-变结构的炉温控制系统

本文提出一种采用变采样周期、变结构的电阻炉温度控制系统. 文章从建立纯滞后时间τ的模型出发,在采样过程中使采样周期随纯滞后时间的变化而 变化.而在采样周期缩短到允许的最小值后,模型结构由带纯滞后模型转变为不带纯滞后的 二阶模型. 试验表明该系统的最大超调最小于0.5%.     

Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information

In this paper, the consensus problem for second-order multi-agent systems using impulsive control with sampled hetero-information is investigated. Necessary and sufficient conditions for sampling interval to achieve consensus for the second-order multi-agent systems are obtained. Analysis for the upper bound of sampling interval, convergence performance, and communication cost of the proposed control protocols are also discussed. Some numerical examples are given to demonstrate the effectiveness of the proposed control protocols.     

Stability analysis in a second-order differential equation with delays

A second-order differential equation with finite discrete delays is considered. Local stability of the zero equilibrium is investigated, and we obtain some sufficient conditions for the zero equilibrium is stable or unstable. Moreover, it is found that there exist the local Hopf bifurcations of the system when the delay varies.     

A normalized Schur-Cohn stability test for the delta-operator-basedpolynomials

The author previously (1997) proposed two delta-operator-based stability tests, or more generally zero location tests. Those tests establish two families of such tests, each spanning from the discrete-time to the continuous-time with the delta operator providing smooth transitions between the two domains. In this paper a third family is proposed. Specifically, the normalized Schur-Cohn test in the discrete-time domain is transformed into the delta-operator domain resulting in a new delta-operator test. The limit of this new test as the sampling interval vanishes is shown to be the Pham-Le Breton test (1991) in the continuous-time domain. Its relationships with the well-known Routh test and others are studied. A numerical example shows the advantage of the new test for fast sampling     

Design of generalized terminal sliding mode control for second-order systems

In this paper, a generalized terminal sliding surface is proposed for second-order systems. It is shown that the proposed scheme guarantees that the system state gets to zero in a finite time, and the proposed generalized terminal sliding surface is a superset of the conventional terminal sliding surfaces. The experimental results are given to show the validity of the main result.     

Stationary consensus of heterogeneous multi-agent systems with bounded communication delays

Consensus seeking is investigated for the discrete-time heterogeneous multi-agent systems composed of first-order agents and second-order agents, and two stationary consensus algorithms are constructed for the first-order agents and the second-order agents, respectively. Based on the properties of nonnegative matrices, sufficient consensus criteria are obtained for the agents with bounded communication delays under fixed topology and switching topologies, respectively. With some prerequisites on the coupling weights and the sampling interval, the asymptotic consensus achievement of the dynamic agents is independent of the communication delay, but strictly depends on the connectedness of the interconnection topology. Simulation results illustrate the correctness of the results.     

Asymptotic behaviours and stability of zero dynamics in nonlinear discrete-time systems using Taylor approach and multirate input

It is well known that the existence of unstable sampled zero dynamics is recognised as a major barrier in many control problems. When the usual digital control with zero-order hold (ZOH) or fractional-order hold (FROH) input is used, unstable sampled zero dynamics inevitably appear in the discrete-time model even though the continuous-time system with relative degree more than or equal to three is of minimum phase. In this paper, we show how an approximate sampled-data model can be obtained for nonlinear systems by the use of multirate input and hold such as a generalised sample hold function (GSHF) in order that discrete zero dynamics of the resulting model can be arbitrarily placed. Furthermore, the properties of sampled zero dynamics are studied and the conditions for ensuring the stability of sampling zero dynamics of the desired model are derived. The results presented here generalise well-known notion of sampling zero dynamics from the linear case to nonlinear systems, and GSHF can provide some advantages over ZOH or FROH in terms of stability of discrete system zero dynamics.     

基于离散小波变换的输电线路故障精准定位

为了提高架空线路和地下电缆组合输电线路发生故障时的定位精度,提出了一种基于离散小波变换(DWT)的输电线路故障定位新方法。通过DWT对输电线路单端测得的瞬态信号进行多分辨率分析(MRA),在低故障起始角情况下,利用线模电流和零模电流检测故障,结合小波模量极大值(WMM)求解从故障点到变电站的行波到达时间,从而对输电线路故障进行精准定位。采用半正弦电压响应的方法克服了采样频率有限和故障起始角低的缺点,运用100kHz半正弦信号的发送时间与接收导数信号的时间之差计算故障距离。在考虑谐波畸变和故障电阻、接地电阻、故障位置和起始角变化的情况下对所提方法进行测试,结果表明：对于100km的输电线路,即使在故障靠近总线（<2%）且故障起始角较低的情况下,所提出的方法得到的故障定位误差仅为0.14km。     

Stability of PID-controlled second-order time-delay feedback systems

In the previous papers, the stability of PID-controlled first-order time-delay systems has been investigated by means of several methods, of which the Nyquist criterion, a generalization of the Hermite–Biehler Theorem, and the root location method are well known. Explicit expressions of the boundaries of the stability region, which is the set of controller parameters that give stable closed-loop systems, have been determined. From these studies, one can verify that not all plants can be made stable and then obtain the set of process parameters that allow stable closed-loop systems. With this set, one can implement the stability region of the process parameters. In a recent paper the stability conditions based on Pontryagin’s studies and valid for arbitrary-order plants have been presented. The procedure deduced for the controller parameters is exhaustive, but that deduced for the process parameters requires further mathematical evaluations, whose complexity is proportional to the number of process time constants. In the aforementioned recent paper these evaluations have been performed for a second-order time-delay plant whose transfer function has no zero. The aim of this paper is to execute these calculations for a second-order plant whose transfer function has one zero and to provide the related stability region.     

Super-Convergence in Maximum Norm of the Gradient for the Shortley–Weller Method

We prove in this paper the second-order super-convergence in \(L^{\infty }\)-norm of the gradient for the Shortley–Weller method. Indeed, this method is known to be second-order accurate for the solution itself and for the discrete gradient, although its consistency error near the boundary is only first-order. We present a proof in the finite-difference spirit, using a discrete maximum principle to obtain estimates on the coefficients of the inverse matrix. The proof is based on a discrete Poisson equation for the discrete gradient, with second-order accurate Dirichlet boundary conditions. The advantage of this finite-difference approach is that it can provide pointwise convergence results depending on the local consistency error and the location on the computational domain.     

Analytic design of adaptive sampling control law in sampled-data systems

A unified analytic approach is presented for the design of adaptive sampling control law in sampled-data systems. This is accomplished by introducing an objective function which measures the performance of the sampler over each sampling interval, and then minimize it to obtain the sampling control law. A total of six different control laws, which are functions of the sampled function, are derived from the generalized objective function by selecting different weighting coefficients. More than half of these control laws are identical to existing results. Similar control laws as functions of the system output can be derived as well. Also included are some experimental results on the performances of four representative control laws in a second-order system subject to step disturbance.     

Controllability of discrete-time multi-agent systems with directed topology and input delay

This paper investigates the controllability of first-order and second-order discrete-time multi-agent systems with directed topology and input delay. The problem is studied in the leader–follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents. Sufficient and necessary conditions are derived for the controllability of first-order discrete-time multi-agent systems. With sampling period and feedback gain satisfying certain conditions, it is proved under three different protocols that the controllability of second-order discrete-time multi-agent systems is equivalent to that of a pair of submatrices of Laplacian matrix. In addition, the controllability of both first-order and second-order discrete-time multi-agent systems with input delay is shown, through some transformations, to be equivalent to that of the transformed non-delayed systems. Finally, some simulation examples are given to illustrate the theoretical results.     

基于事件触发的二阶多智能体领导跟随一致性

研究二阶多智能体系统在固定有向拓扑下的领导跟随一致性问题.为了节省网络和计算资源,给出一种基于事件触发控制的一致性算法.针对每个跟随者智能体,设计基于状态误差形式的触发函数,只有当状态误差满足一定条件,即触发函数取值为零时智能体才触发事件,同时更新并传递自身的采样信息,在两个相邻事件触发时刻之间,控制输入只受领导者控制信号的影响.利用模型变换、矩阵理论和Lyapunov稳定性理论给出多智能体系统达到领导跟随一致性的充分条件.仿真结果验证了理论方案的可行性和有效性.