滞后线性定常广义不确定系统的变结构控制设计*

本文首次引入了滞后广义系统的受限等价分解形式，利用滞后正常系统的理论和无滞后广义系统的理论，研究了滞后线性定常广义系统的变结构设计问题，所提供的的研究方法为进一步研究滞后文义系统的其它问题（例如调节，跟踪）开创了一条新的途径。     

Optimal digital controller and observer design for multiple time-delay transfer function matrices with multiple input–output time delays

In this article, we address the optimal digital design methodology for multiple time-delay transfer function matrices with multiple input–output time delays. In our approach, the multiple time-delay analogue transfer function matrix with multiple input–output time delays is minimally realised using a continuous-time state-space model. For deriving an explicit form of the optimal digital controller, the realised continuous-time multiple input–output time-delay system is discretised, and an extended high-order discrete-time state-space model is constructed for discrete-time LQR design. To derive a low-order optimal digital observer for the multiple input–output time-delay system, the multiple time-delay state obtained from the multiple time-delay outputs is discretised. Then, the well-known duality concept is employed to design an optimal digital observer using the low-order discretised multiple input time-delay system together with the newly discretised multiple time-delay state. The proposed approach is restricted to multiple time-delay systems where multiple time delays arise only in the input and output, and not in the state.     

Subspace-based identification of discrete time-delay system

We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant (LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search (ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.     

离散时滞系统最优跟踪控制及应用

本文研究线性时滞离散时间系统的最优跟踪控制问题,首先针对具有控制时滞,且输入输 出之间具有前向直接通道的系统讨论,进而考虑一般多重时滞系统.本文利用线性二次型加 积分(LQI)的最优状态反馈控制理论实现负荷变化时的最优跟踪控制.文中研究了闭环系 统的稳定性及输出完全跟踪,并针对某针厂一无纺针热处理淬火炉,进行了温度跟踪控制的 仿真研究.仿真结果表明,本文提出的控制方案在温度给定值变化条件下能达到快速、小偏差 的跟踪效果.     

Optimal tracking control of a flexible hub–beam system with time delay

In this paper, a new technique of time-delay compensation is proposed for active control of a flexible hub–beam system. The first-order approximation coupling (FOAC) model proposed recently for dynamics of hub–beam systems is used to verify the applicability of this technique. The FOAC model is first linearized to obtain a linearized equation. The linearized equation with time delay is then transformed into a standard form with no time delay by a particular integral transformation. The time-delay controller is designed based on this standard equation using the classical optimal tracking control theory. Since the controller is a function of modal coordinates, a modal filter is presented to estimate the modal coordinates from physical sensor measurements. The effectiveness of the proposed technique for time delay is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in instability of the control system if it is not compensated in control design. The proposed time-delay controller is effective in controlling the system even when the maximum time delay for stability without time-delay compensation is greatly exceeded. Moreover, for the system without time delay, the proposed time-delay controller may possibly obtain much better control effectiveness than the controller without time delay.     

基于Maclaurin展开的时间绝对误差积分次优时滞系统设计

根据经典时间绝对误差积分（ITAE）最优系统标准型,给出了ITAE最优时滞系统的期望模型;利用Maclaurin展开技术,讨论了ITAE次优时滞系统的设计方法,并就ITAE次优和最优的三阶系统进行了频域和时域比较.论文最后给出了基于ITAE次优时滞系统的PID和超前滞后补偿器设计实例.阶跃响应、负载扰动以及参数鲁棒性方面的比较研究表明,本文方法能够获得十分满意的性能指标.     

有色量测噪声下的改进求容积卡尔曼滤波器

为解决标准求容积卡尔曼滤波器在有色量测噪声条件下滤波精度退化的问题,提出改进求容积卡尔曼滤波器及其平方根形式.首先利用一阶马尔科夫模型白化非线性离散随机系统中有色量测噪声,将有色量测噪声下非线性离散随机系统转化为白噪声下非线性时滞系统.然后根据所得非线性时滞系统推导其高斯域的贝叶斯滤波框架,最后基于3度Spherical-Radial规则将该滤波框架近似为改进的求容积卡尔曼滤波器和其平方根形式.机动目标跟踪仿真试验结果表明两种改进求容积卡尔曼滤波算法在标准白噪声条件下与标准求容积卡尔曼滤波算法的估计精度相同,而在有色量测噪声背景下滤波精度和鲁棒性更优.     

结构振动的时滞输出反馈控制器设计

研究结构振动的时滞输出反馈控制,通过部分可测输出量实现整个系统的主动振动控制．首先将系统的运动微分方程改写成状态空间模型,其控制输入中存在时滞．再利用一个线性项加积分项的变换将原时滞输入系统转化成无时滞的形式．在此基础上,应用输出反馈原理和合理的性能指标设计出系统的控制律．最后以一个三层建筑结构为例,研究系统在地震载荷下的动态响应．在数值计算中,时滞量取为采样周期的整数倍,积分步长取为采样周期．仿真结果表明,本文提出的时滞输出反馈控制律是有效且实用的．     

一类非线性时滞系统的解耦控制

利用微分几何方法研究了一类非线性多输入多输出时滞系统的解耦问题．讨论了此类系统可解耦的充分条件，并给出了此类系统实现输入/输出间精确线性化的条件以及其标准形．文中给出了非线性时滞系统得以解耦的非线性状态反馈控制律；此状态控制律不但可以实现输出与时滞状态变量的解耦，还可以实现输出与输入间的精确线性化．而其闭环标准形的给出为此类系统实现各种控制目标带来了方便．     

时滞累积TDAGM($1,N,t)$模型及其在粮食生产中的应用

考虑到社会经济系统中广泛存在时滞因果关系,通过分析驱动因素对系统主行为的时滞累积作用效果以及系统行为线性发展趋势,构建了含时间趋势项的时滞累积型多变量灰色TDAGM($1,N,t$)模型,论证了GM(1, 1)、GM(1,N)、OGM(1,N)、时滞GM(1,N)、TDDGM(1,N)模型均是该模型在不同参数取值下的特殊形式;为避免模型求解过程中微分形式与差分形式转换而产生误差,通过定义TDAGM($1,N,t$)模型的派生形式,给出了TDAGM($1,N,t$)模型时间响应式的直接求解方法;针对模型时滞效应参数的识别和优化问题,基于粒子群优化算法,给出了TDAGM($1,N,t$)模型参数估计的算法框架.时滞系统的数值实验结果表明,TDAGM($1,N,t$)模型能够较好地解决含时滞特征的多变量系统预测问题.将该模型应用于河南省粮食产量预测的实例中,拟合精度较高且预测结果符合河南省粮食生产发展趋势,验证了模型的有效性.     

线性区间离散时滞系统的区域镇定

针对线性离散时滞系统的区域镇定问题, 基于非奇异状态变换技术提出了区间不确定性系统区域可镇定的充分条件, 保证闭环系统的所有极点均位于给定的圆盘区域内. 所给条件可简化为LMI描述形式, 利用LMI工具求解非常方便. 所给实例表明了该方法用于判断线性区间离散时滞系统的区域可镇定性与设计区域镇定控制器的可行性.     

双容纯时滞系统两次优化控制的背驰定律

本文给出双容纯时滞两次优化控制的背弛定律，利用这个定律，可以设计出强鲁棒性的双容纯时滞优化控制系统．文中给出一个具有四阶分时模型的双容纯时滞两次优化控制设计算例，结果表明：利用背驰定律设计双容系统，可以提高它的鲁棒性．     

Adaptive observers for time-delay nonlinear systems in triangular form

A simple nonlinear observer with a dynamic gain is proposed for a class of bounded-state nonlinear systems subject to state delay. By saturating the states of the observer nonlinearities with either symmetric or non-symmetric saturation functions, we show that the observer exists, whatever the delay is. Furthermore, it will be highlighted that the observer design is free from any preliminary analysis of the time-delay system such as estimating the Lipschitz constants of nonlinearities. The proposed design encompasses a wide class of nonlinear and time-delay systems written in triangular form and generalizes previous results on delayless nonlinear systems.     

时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.     

具有持续扰动的时滞系统前馈2反馈最优控制

针对外部持续扰动下的线性时滞系统，提出一种前馈-反馈最优控制的逐次逼近算法．利用逐次逼近算法，将既含有时滞项又含有超前项的两点边值问题转化为不合时滞项和超前项的线性两点边值问题族，并证明了线性两点边值问题族的解序列一致收敛于原系统最优控制律．得到的最优控制律由解析的无时滞前馈-反馈控制部分和伴随向量序列极限形式的时滞补偿控制部分组成．通过截取时滞补偿序列的有限项，得到系统的前馈-反馈次优控制律．仿真示例表明，该方法对外部持续扰动具有良好的鲁棒性．     

Stabilization of delayed fractional-order T-S fuzzy systems with input saturations and system uncertainties

By adopting the Takagi–Sugeno (T-S) fuzzy theory, this paper focuses on the adaptive control of fractional-order time-delay systems involving unknown parameters and input saturations. T-S fuzzy systems with “IF-THEN” rules are employed to describe fractional-order nonlinear systems. The influence of input saturation is handled by designing an auxiliary system. By using a norm conversion, the system's time-delay term is converted into a non-delayed form. Adaptive updating rules are devised to evaluate uncertainties of the system, and a new control approach is proposed. The devised controller can not only guarantee the boundedness of variables involved but also make state variables converge into a sufficiently small neighborhood of the origin, even in the presence of uncertainties, saturation functions, and system parameters. Finally, numerical studies are given to verify the correctness of the designed scheme.     

线性时滞不确定系统的鲁棒性研究

本文研究了具有一般摄动表达形式的时滞不确定系统,将不确定项分解为“秩1”形式和相乘形式,利用Lyapunov方法和二次镇定的概念,求得了较为完善的充分条件,并举例验证。     

基于互联网的远程控制系统时延补偿的仿真研究

本文介绍了由西门子S7—226PLC与MM440变频器组成的电气控制系统在光缆护套机速度控制中的应用，并对该系统的控制原理作了详细的阐述。     

时滞离散系统正弦扰动的最优抑制

研究状态和控制都含时滞的线性离散系统在正弦扰动下的减振控制问题.首先提出一种变量代换,并利用此代换将原系统转换为不含控制时滞的系统.然后利用逐次逼近法将最优控制问题转化为求解一族无时滞的线性两点边值序列问题.得到的最优控制律由解析的状态反馈,前馈和具有记忆的控制项以及时滞补偿序列的极限组成.通过截取时滞补偿序列的有限项,可以得到系统的次优减振控制律.仿真结果表明,该方法容易实现,设计的控制器对正弦扰动有较强的抑制能力.