Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems

The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.

The identification algorithm for commensurate order linear time-invariant fractional systems

An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.

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.

Mixed Gl2／GH2 multi-channel multi-objective control synthesis for discrete time systems

This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l2 (Gl2) and generalized H2 (GH2) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl2/GH2 control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

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.

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.

ON FORMABILITY OF LINEAR CONTINUOUS-TIME MULTI-AGENT SYSTEMS

This paper is focused on formability of multi-agent systems （MASs）. The problem is concerned with the existence of a protocol that has the ability to drive the MAS involved to the desired formation, and thus, is of essential importance in designing formation protocols. Formability of an MAS depends on several key factors： agents＇ dynamic structures, connectivity topology, properties of the desired formation and the admissible control set. Agents of the MASs considered here are described by a general continuous linear time-invariant （LTI） model. By using the matrix analysis and algebraic graph theory, some necessary and sufficient conditions on formability of LTI-MASs are obtained. These conditions characterize in some sense the relationship of formability, connectivity topology, formation properties and agent dynamics with respect to some typical and widely used admissible protocol sets.

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.

无时限信号通过LTI系统的间接复频域分析方法

提出了一种无时限信号通过LTI系统的间接复频域分析方法。基于信号分解的概念,将无时限复指数信号分解为反因果信号和因果信号之和,利用LTI因果系统响应的可加性,给出系统零状态响应的间接复频域分析方法,然后将周期信号分解为反因果周期信号和因果周期信号之和,借助等效Jordan引理,利用LTI因果稳定系统响应的可加性,给出系统零状态响应的间接复频域分析方法,有效地解决了无时限信号通过LTI系统时系统零状态响应的复频域求解问题。

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。

高阶时滞多智能体系统一致性控制(英文)

本文讨论了多输入网络化时滞多智能体系统的一致性问题.应用无向或有向图描述网络化系统的拓扑结构.多智能体的一致性收敛问题可以转化为线性时滞系统的稳定性问题.通过双线性矩阵不等式可以得到高阶多智能体系统时滞相依以及时滞独立的一致性准则.最后,举例一个无向拓扑结构的时滞多智能体来说明本文方法的有效性.

基于因果微积分定理讨论时域分析和s域分析

本文从因果微分定理、因果积分定理和拉氏变换出发,推导了拉氏变换中的时域微分性质、时域积分性质、初值定理和终值定理;系统时域分析是对系统微分方程使用因果微分定理得出的,而系统s域分析是对系统微分方程使用拉氏变换中的时域微分性质得出的,两者的原理和方法完全类似,我们对两者进行了全面的比较。这些分析和比较很有利于学生对拉氏变换中的几个重要性质的理解,也有利于学生明确系统时域分析与系统s域分析的区别与联系。

卷积结合律成立的条件

有些函数的卷积积分或卷积和满足卷积的结合律 ,而另一些函数的卷积则不满足此性质。当满足卷积结合律时 ,参与卷积的函数之间有一定的约束关系 。

利用系统性质求解系统响应

研究了系统存在状态跳变的情况下,基于线性时不变性质的运用,对线性常系数微分方程所描述的系统响应进行求解。

一般模式点光源下一维PSD的响应函数

本文从Lucovsky方程入手,根据rc传输线模型和理想脉冲响应函数,提出PSD线性时不变系统(LTI)的模型近似,并基于该模型得出一般模式点光源下的PSD的响应函数。光强随时间变化的点光源可以均匀分割成一系列时域脉冲信号,并近似认为是方波脉冲信号,在线性时不变系统情况下,该光源的电流响应近似等于这些方波脉冲信号的线性叠加。结果表明,PSD的一般响应函数是自身衰减因子和外界响应因子的乘积序列的叠加。此外,基于PSD一般响应函数的交流响应表明,PSD的响应电流对高频交变光信号不敏感,且随光强的变化滞后性震荡。

奇异摄动系统的一致稳定和镇定（英文）

针对一类线性时不变奇异摄动系统,研究其在稳定和镇定性方面关于小参数的一致性问题.当小参数处于有界而非闭区间时,将奇异摄动系统视为参数系统.同时,进一步地讨论该系统对小参数的依赖性.最后,利用线性矩阵不等式方法,给出了系统关于小参数具有一致性的稳定和镇定条件.

LS-Based Parameter Estimation of DARMA Systems with Uniformly Quantized Observations

This paper is concerned with the parameter estimation of deterministic autoregressive moving average(DARMA)systems with quantization data.The estimation algorithms adopted here are the least squares(LS)and the forgetting factor LS,and the signal quantizer is of uniform,that is,with uniform quantization error.The authors analyse the properties of the LS and the forgetting factor LS,and establish the boundedness of the estimation errors and a relationship of the estimation errors with the size of quantization error,which implies that the smaller the quantization error is,the smaller the estimation error is.A numerical example is given to demonstrate theorems.

无时限序列通过LSI系统的间接z域分析方法

提出了一种无时限序列通过LSI系统的间接z域分析方法。基于序列分解的概念,将无时限复指数序列分解为反因果序列和因果序列之和,利用LSI因果系统响应的可加性,给出系统零状态响应的间接z域分析方法,然后将周期序列分解为反因果周期序列和因果周期序列之和,利用LSI因果稳定系统响应的可加性,给出系统零状态响应的间接z分析方法,有效地解决了无时限序列通过LSI系统时系统零状态响应的z域求解问题。

Design of high-speed and low-power finite-word-length PID controllers

ASIC or FPGA implementation of a finite word-length PID controller requires a double expertise： in control system and hardware design. In this paper, we only focus on the hardware side of the problem. We show how to design configurable fixed-point PIDs to satisfy applications requiring minimal power consumption, or high control-rate, or both together. As multiply operation is the engine of PID, we experienced three algorithms： Booth, modified Booth, and a new recursive multi-bit multiplication algorithm. This later enables the construction of finely grained PID structures with bit-level and unit-time precision. Such a feature permits to tailor the PID to the desired performance and power budget. All PIDs are implemented at register-transfer4evel （RTL） level as technology-independent reusable IP-cores. They are reconfigurable according to two compilemtime constants： set-point word-length and latency. To make PID design easily reproducible, all necessary implementation details are provided and discussed.