Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems

In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods.

A Modified Stability Analysis of Two-Dimensional Linear Time Invariant Discrete Systems within the Unity-Shifted Unit Circle

This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.

Compressive Measurement Identification of Linear Time-Invariant System Application in DC Motor

In traditional system identification (SI), actual values of system parameters are concealed in the input and output data;hence, it is necessary to apply estimation methods to determine the parameters. In signal processing, a signal with N elements must be sampled at least N times. Thus, most SI methods use N or more sample data to identify a model with N parameters;however, this can be improved by a new sampling theory called compressive sensing (CS). Based on CS, an SI method called compressive measurement identification (CMI) is proposed for reducing the data needed for estimation, by measuring the parameters using a series of linear measurements, rather than the measurements in sequence. In addition, the accuracy of the measurement process is guaranteed by a criterion called the restrict isometric principle. Simulations demonstrate the accuracy and robustness of CMI in an underdetermined case. Further, the dynamic process of a DC motor is identified experimentally, establishing that CMI can shorten the identification process and increase the prediction accuracy.

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

A Model-free Approach to Fault Detection of Continuous-time Systems Based on Time Domain Data

In this paper, a model-free approach is presented to design an observer-based fault detection system of linear continuoustime systems based on input and output data in the time domain. The core of the approach is to directly identify parameters of the observer-based residual generator based on a numerically reliable data equation obtained by filtering and sampling the input and output signals.

Mixed sensitivity H_∞ control for LTI systems with varying time delays

Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty（in form of multiplicative uncertainty）. That uncertainty is approximated and then an H∞based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.

Study on Four Disturbance Observers for FO-LTI Systems

This paper addresses the problem of designing disturbance observer for fractional order linear time invariant U+0028 FO-LTI U+0029 systems, where the disturbance includes time series expansion disturbance and sinusoidal disturbance. On one hand, the reduced order extended state observer U+0028 ROESO U+0029 and reduced order cascade extended state observer U+0028 ROCESO U+0029 are proposed for the case that the system state can be measured directly. On the other hand, the extended state observer U+0028 ESO U+0029 and the cascade extended state observer U+0028 CESO U+0029 are presented for another case when the system state cannot be measured directly. It is shown that combination of ROCESO and CESO can achieve a highly effective observation result. In addition, the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper. Finally, numerical simulations are given to illustrate the effectiveness of the proposed methods. © 2014 Chinese Association of Automation.

COMPREHENSIVE DAMPING COEFFICIENT——A NEW DEFINITION TO DAMPING EFFECT OF LINEAR TIME-INVARIANT SYSTEMS

A new concept is presented to express the damping property of linear time-invariant systems, by the Lyapunov theorem in view of quadratic form-defined energy. Two definitions are introduced: damping energy function D(X_0, X)=Ci∫_(x_0, x) x_idx_(i-1)and comprehensive damping coefficient η-min(Ci/a_(n-i)). It is concluded that (ⅰ) of the Hurwitz determinants, △_(x-1) is proportional to the damping effect of oscillating systems, (ⅱ) the comprehensive damping coefficients of linear time-invariant systems are derived as. piecewise rational fractions which can be easily calculated and (ⅲ) the damping torque coefficient obtained for synchronous machines is independent of ω.

CAutoCSD-Evolutionary Search and Optimisation Enabled Computer Automated Control System Design

This paper attempts to set a unified scene for various linear time-invariant (LTI) control system design schemes, by transforming the existing concept of “computer-aided control system design” (CACSD) to novel “computer-automated control system design” (CAutoCSD). The first step towards this goal is to accommodate, under practical constraints, various design objectives that are desirable in both time and frequency domains. Such performance-prioritised unification is aimed at relieving practising engineers from having to select a particular control scheme and from sacrificing certain performance goals resulting from pre-commitment to such schemes. With recent progress in evolutionary computing based extra-numeric, multi-criterion search and optimisation techniques, such unification of LTI control schemes becomes feasible, analytical and practical, and the resultant designs can be creative. The techniques developed are applied to, and illustrated by, three design problems. The unified approach automatically provides an integrator for zero-steady state error in velocity control of a DC motor, and meets multiple objectives in the design of an LTI controller for a non-minimum phase plant and offers a high-performance LTI controller network for a non-linear chemical process.

线性定常系统的输入-输出能量解耦

提出一种介于动态解耦与静态解耦之间的能量解耦方法 ,即从输入_输出的能量关系上实现解耦 ,使得任何一个输入的能量主要控制对应的一个输出的能量 ,对其它输出能量的影响尽可能小 .所给实例表明 。

Gauss-Legendre求积公式在系统仿真中的应用

本文将Gauss-Legendre求积公式应用到线性定常系统的快速仿真中,提出了一种新方法。在以保持A-稳定性为前提使每步仿真计算量为最小的意义下,它是最优的。该方法与现有同阶方法相比,其截断误差系数也较小,并具有L-稳定性,因而特别适合于Stiff系统的仿真。文中还讨论了实时问题。

基于PID参数整定的无模型自适应控制器参数整定方法

本文针对一阶线性时不变(FOLTI)系统,将常用的比例–积分–微分(PID)控制器参数整定方法推广到无模型自适应控制(MFAC)参数整定中,利用PID控制参数整定方法整定直接型MFAC方案的伪梯度初值,以期改变MFAC控制律初始参数的试凑式选取,提升MFAC应用的方便性和可接受性.通过仿真,验证了所提伪梯度初值整定方法的有效性,并对比了FOLTI系统的系统参数和系统结构发生变化后,应用MFAC与PID控制的性能差异.

分数阶线性定常系统的稳定性及其判据

介绍了分数阶微分方程和分数阶系统 ,给出分数阶线性定常系统的传递函数描述和状态空间描述 .给出了分数阶线性定常系统的稳定性条件 ,并结合分数阶状态方程给出定理的证明 .直接从复分析中的辐角原理出发 ,推导出分数阶线性定常系统 2个有效的稳定性判据 :分数阶系统奈奎斯特判据和分数阶系统对数频率判据 .

存在均匀通信时滞的AGC稳定极限计算

广域复杂电力系统的通信时滞导致了系统动力学模型是带有时滞的系统模型,计算时滞系统的时滞极限是研究时滞系统的关键,也是当前亟须解决的问题。文中对带有通信时滞信号的自动发电控制(AGC)系统建立了线性定常均匀时滞系统模型,借助状态空间的分析方法和矩阵分析理论,简捷有效地定量计算出AGC时滞极限。通过对华东电网的仿真验证了该算法的有效性和正确性。

大型连栋温室环境参数的线性时不变系统建模

华北地区大型连栋温室夏季强制通风降温的水、能消耗很大,为了使环境调控既能适宜作物生长又能降低调控消耗,迫切需要精确有效的环境温度和湿度动态模型。该文采用线性时不变系统的ARX模型及系统辨识方法,对华北地区连栋温室夏季强制通风降温动态过程进行室内温度和湿度建模。试验在2003年夏季6-7月进行,以1min的时间间隔连续采集室内温度、湿度、室外温度、湿度、光照强度、风速、风机运行状态和数据采集时刻8个参数,将采集的数据分成辨识集和证实集两组,用辨识集数据采用最小二乘法进行模型系数回归,用证实集数据进行模型验证,验证指标为最大绝对误差(MAE)、最大相对误差(MRE)、均方误差(RMSE)和可解释方差(vaf)。证实结果显示,温度模型的最大预测误差(MAE)为3.57℃,均方误差(RMSE)小于0.198℃;湿度模型的最大预测误差(MAE)为7.3%,均方误差(RMSE)小于0.624%;温度和湿度模型的vaf均大于98.9%。说明尽管模型在个别点的预测误差稍大,但总体的预测精度较高,能够满足一般情况下作物栽培对环境预测的要求。

PID控制的应用与理论依据

PID控制是自动控制中产生最早、应用最广的一种控制方法。从PID控制的结构形式、实际控制工程需求和实现条件分析了PID控制的独特优点 ,同时又介绍了二阶线性定常系统PID控制器的设计方法 ,叙述了高阶线性定常系统的特征建模原理 ,重点分析和推导了基于特征模型的带消除静差的二次型最优控制设计方法 ,证明了高阶线性定常系统和一大批非线性系统能用PID控制器实现位置恒值控制的基本原理 ,为随输出状态不同而选择不同P、I、D参数等各种人工调节方法提供了合理性解释 。

利用变换深度域速度函数制作深度域合成地震记录

在时间域中,谐波经过反射系数“系统”后不改变频率,符合线性时不变系统的条件,因此在时间域中可以用子波与反射系数序列褶积的方法计算时间域合成地震记录。由于在深度域中圆波数是介质速度的函数,深度域子波的波数随介质速度变化,因此地震子波在深度域中传播并不满足线性时不变系统的条件,不能直接用褶积的方法计算深度域合成地震记录。文中利用简单的理论模型,通过对深度域中的速度、深度参数进行适当的变换,使其在“新深度域”中符合线性时不变系统的条件,在保证层间旅行时不变的情况下,定义深度域地震子波的介质速度为标准速度,将其他各层的速度都以标准速度进行调整,并对层间厚度也做相应的调整。通过上述变换,可把时间域中的计算方法引用到深度域中,再通过反变换处理,将“新深度域”中的褶积结果反变换到原深度域中。文中还指出,如果不考虑深度域与时间域之间的重采样误差,常规时间域合成地震记录经时深转换到深度域后的结果应该与本文介绍的深度域合成地震记录结果一致。

广义线性系统的鲁棒稳定性分析与综合

研究广义线性系统的鲁棒稳定性分析与综合问题．基于广义线性系统的Lyapunov方程和Riccati方程，给出了相关的鲁棒稳定性分析与综合方法．

基于运动序列分割的运动捕获数据关键帧提取

采用线性时不变系统把高维运动数据映射到低维状态空间;在低维状态空间中,定义了姿态之间的相似性度量;并采用误差平方和准则对时序的低维数据点集进行运动分割,分割点上的运动姿态被定义为关键帧.实验结果表明:该算法能够较好地提取出运动序列中的关键帧,并且这些关键帧能够很好地概括原始运动序列的内容.

临夏台钻孔系统性质的论证

对中国临夏台2013年至2014年两年的井水位和四分量钻孔应变资料进行了预处理以消除趋势与突跳.根据文献(Means,1982;Young and Budynas,2005),相互正交的两条测线的应变观测值之和等于面应变.文献(刘序俨等,1988)证明近地表的面应变的2/3等于体应变,因此,可由4分量钻孔应变观测值得到钻孔体应变,然后根据体应变与井水位观测资料,从时域和频域对该钻孔系统的性质进行了论证.结果表明,在时域,体应变与井水位高度负相关.钻孔系统的灵敏度为—0.1620mm/10-9.把两年中的某两个月份的两者时间坐标轴和纵轴比例尺放大,发现井水位曲线的峰/谷与体应变观测曲线的谷/峰一一对应,两者的相位滞后非常小.在频域内,本文采用Venedikov调和分析方法分别取得了井水位与体应变9个月的半日波与全日波数个波群的逐月潮汐因子与相位滞后,然后作简单计算,得到了钻孔系统对上述波群的灵敏度与相位滞后.结果表明9个月中大多数波群的灵敏度不但十分相近,且非常接近由时域得到的周年频率分量的灵敏度,但相位滞后误差较大,本文对此进行了分析,认为由反正切得到的相位滞后受计算误差影响较大,应以时域经审视所得的相位滞后接近于零为准.通过时域与频域的分析,表明井水位对体应变的响应基本是线性时不变的,论证了临夏台钻孔系统基本上满足了叠加性、齐次性与时不变性,基本上为一线性时不变系统.