Applying constrained nonlinear generalized PI strategy to PDF tracking control through square root B-spline models

For stochastic systems with non-Gaussian variables, the classical control approaches where only expectation and variance are concerned cannot cover the control requirement of the closed loop in some practical processes. In this paper, the tracking control problem for output probability density functions (PDFs) is studied using square root B-spline expansions and non-linear weight dynamical models. After the measurable output PDFs are approximated by the B-spline expansions, a non-linear dynamical model can be established between the control input and the weights related to the PDFs. The tracking control problem for the output PDFs can be reduced to a constrained tracking problem for the non-linear weight dynamics. For this non-linear weight model, a generalized proportional-integral (PI) control strategy is proposed in discrete time context. The objective of the control is to make sure that the output PDFs of the system can follow a given target function, and the closed-loop system is exponentially stable and satisfies the constraint imposed on the state vector. The LMI-based convex optimization approach is adopted to design the parameters of the proposed PI controllers. This result also generalizes some previous works for classical constrained PI tracking control of non-linear discrete-time systems. Simulations are given to demonstrate the efficiency of the proposed approach.     

Entropy Optimization Filtering for Fault Isolation of Nonlinear Non-Gaussian Stochastic Systems

In this paper, the fault isolation (FI) problem is investigated for nonlinear non-Gaussian systems with multiple faults(or abrupt changes of system parameters) in the presence of noises. By constructing a filter to estimate the states, the FI problem can be reduced to an entropy optimization problem subjected to the non-Gaussian estimation error systems. The design objective for the FI purpose is that the entropy of the estimation error is maximized in the presence of diagnosed fault and is minimized in the presence of the nuisance faults or noises. It is shown that the error dynamics is represented by a nonlinear non-Gaussian stochastic system, for which new relationships are applied to formulate the probability density functions (PDFs) of the stochastic error in terms of the PDFs of the noises and the faults. The Renyi's entropy has been used to simplify the computations in the filtering for the recursive design algorithms. It is noted that the output can be supposed to be immeasurable (but with known stochastic distributions), which is different from the existing results where the output is always measurable for feedback. Finally, simulations are given to demonstrate the effectiveness of the proposed data-driven FI filtering algorithms.     

Robust fault detection filter design for a class of time-delay systems via equivalent transformation

This paper is concerned with the robust fault detection filter (RFDF) design for a class of linear timeinvariant systems (LTISs) with output state time delays. Although existing results in literatures study the RFDF for timedelay systems, few is concerned with the output state time-delay systems. The basic idea of our study is to eliminate the time delays of system and transform it to a delay-free system (i.e., a linear time-invariant system without time delays) by the bicausal change of coordinates approach. Then, we design the RFDF for the delay-free LTIS, which is equivalent to the original system with time delays. We first introduce a class of systems with output state time delays, whose fault can be detected by using the RFDF design approach for delay-free systems. Then, since the RFDF design problem can be formulated as a standard H-infinity-model matching problem, it is solved by using H-infinity-optimization LMI techniques. In the last, the adaptive threshold of fault detection is chosen and an illustrative design example is used to demonstrate the validity of the design approach.     

基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制

随机分布系统指的是输入为常规向量而输出为系统输出的概率密度函数所描述的一类随机系统．该类系统控制算法的目标是选择一个控制输入使得系统的实际输出概率密度函数尽可能跟踪一个事先给定的概率密度函数．本文对采用有理平方根B样条逼近其输出概率密度函数的非高斯动态随机分布系统,提出了一种基于非线性自适应观测器的故障诊断方法．该方法可快速有效地诊断出非高斯随机分布系统故障．通过对故障系统的重组,使故障后系统的输出概率密度函数仍能跟踪给定的分布,实现了该随机系统的容错控制,提高了随机系统的可靠性．     

Detecting and diagnosing faults in dynamic stochastic distributions using a rational B-splines approximation to output PDFs

This paper presents a novel approach to detect and diagnose faults in the dynamic part of a class of stochastic systems . the Such a group of systems are subjected to a set of crisp inputs but the outputs considered are the measurable probability density functions (PDFs) of the system output, rather than the system output alone. A new approximation model is developed for the output probability density functions so that the dynamic part of the system is decoupled from the output probability density functions. A nonlinear adaptive observer is constructed to detect and diagnose the fault in the dynamic part of the system. Conver-gency analysis is performed for the error dynamics raised from the fault detection and diagnosis phase and an applicability study on the detection and diagnosis of the unexpected changes in the 2D grammage distributions in a paper forming process is included.     

Stabilization of linear systems with simultaneous state,actuation, and measurement delays

This paper considers the problem of stabilizing continuous-time linear systems with time delays. Specifically, a fixedorder (i.e. full- and reduced-order) dynamic compensation problem is addressed for systems with simultaneous state, input, and output delays. The principal result involves sufficient conditions for characterizing fixed-order dynamic controllers for delay systems via a system of modified coupled Riccati equations. The controllers obtained are delay independent and hence apply to systems with arbitrary unknown delay.     

一类带有传染器故障的混合系统的容错控制

A model-based fault tolerant control approach for hybrid linear dynamic systems is proposed in this paper. The proposed method, taking advantage of reliable control, can maintain the performance of the faulty system during the time delay of fault detection and diagnosis (FDD) and fault accommodation (FA), which can be regarded as the first line of defence against sensor faults.Simulation results of a three-tank system with sensor fault are given to show the efficiency of the method.     

Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model

The task of robust fault detection and diagnosis of stochastic distribution control （SDC） systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Conver- gency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demon- strate the effectiveness of the proposed algorithm.     

一类带有传感器故障的混合系统的容错控制

A model-based fault tolerant control approach for hybrid linear dynamic systems is proposed in this paper. The proposed method, taking advantage of reliable control, can maintain the performance of the faulty system during the time delay of fault detection and diagnosis (FDD) and fault accommodation (FA), which can be regarded as the first line of defence against sensor faults. Simulation results of a three-tank system with sensor fault are given to show the efficiency of the method.     

Double-model adaptive fault detection and diagnosis applied to real flight data

The existing multiple model-based estimation algorithms for Fault Detection and Diagnosis (FDD) require the design of a model set, which contains a number of models matching different fault scenarios. To cope with partial faults or simultaneous faults, the model set can be even larger. A large model set makes the computational load intensive and can lead to performance deterioration of the algorithms. In this paper, a novel Double-Model Adaptive Estimation (DMAE) approach for output FDD is proposed, which reduces the number of models to only two, even for the FDD of partial and simultaneous output faults. Two Selective-Reinitialization (SR) algorithms are proposed which can both guarantee the FDD performance of the DMAE. The performance is tested using a simulated aircraft model with the objective of Air Data Sensors (ADS) FDD. Another contribution is that the ADS FDD using real flight data is addressed. Issues related to the FDD using real flight test data are identified. The proposed approaches are validated using real flight data of the Cessna Citation II aircraft, which verified their effectiveness in practice.     

Development and application of sliding mode LPV fault reconstruction schemes for the ADDSAFE Benchmark

This paper describes the development and the evaluation of a robust sliding mode observer fault detection scheme applied to an aircraft benchmark problem as part of the ADDSAFE project. The ADDSAFE benchmark problem which is considered in this paper is the yaw rate sensor fault scenario. A robust sliding mode sensor fault reconstruction scheme based on an LPV model is presented, where the fault reconstruction signal is obtained from the so-called equivalent output error injection signal associated with the observer. The development process includes implementing the design using AIRBUS׳s the so-called SAO library which allows the automatic generation of flight certifiable code which can be implemented on the actual flight control computer. The proposed scheme has been subjected to various tests and evaluations on the Functional Engineering Simulator conducted by the industrial partners associated with the ADDSAFE project. These were designed to cover a wide range of the flight envelope, specific challenging manoeuvres and realistic fault types. The detection and isolation logic together with a statistical assessment of the FDD schemes are also presented. Simulation results from various levels of FDD developments (from tuning, testing and industrial evaluation) show consistently good results and fast detection times.     

Fault reconstruction for delay systems via least squares and time‐shifted sliding mode observers

In this article, we address the problem of fault reconstruction in delayed systems by introducing a time‐shifted sliding mode observer (SMO). While time‐varying delays of arbitrary duration are considered in the measured output signal, the actuator fault is parametrized as a weighted sum of known regressor functions with unknown coefficients. The prediction scheme utilizes the variation of constants formula to obtain the present time estimate of the unmeasured state. The fault is also identified at present time by means of the continuous‐time Least Squares approaches. Ideal sliding mode can be guaranteed in theory, even in the presence of such adverse delays, since there is no chattering in the output estimation error of the SMO. An application to petroleum engineering with numerical simulations is presented to show the effectiveness of the proposed method.     

复杂动态系统中不同层次故障检诊模块的综合设计

为解决复杂动态系统中不同层次故障检诊模块的协调管理和高效运行问题,研究了其综合设计方法。该方法对复杂动态系统层次建模,提出检诊进程概念以描述系统不同层次的故障检诊,同时建立了检诊进程通用模型,使大部分现存检诊算法可方便地纳入其中,实现了不同层次检诊进程的信息交换与综合设计。数字仿真表明,综合设计不但能提高各模块检诊能力,而且可以总体上提高其应付常规方法难以处理的复杂故障情况。     

变采样周期网络化系统鲁棒容错控制

针对网络控制系统中存在的时变采样周期与时延,通过矩阵Jordan 变换与分解, 将采样周期和时延的不确定性转变为系统结构参数的不确定性,建立了离散时间凸多面体不 确定系统模型。在此基础上,首先设计观测器,保证系统状态和故障估计收敛于实际值。接 着,根据估计的故障,设计了主动动态输出反馈鲁棒容错控制器,给出了执行器发生故障时, 系统能保持渐近稳定的充分条件。将控制器设计问题转化为以线性矩阵不等式形式为约束条 件的凸优化问题,进而得出了最优H∞鲁棒容错控制器参数的具体表达式。数值仿真验证了提 出的设计方法的有效性。     

Observer‐based fault diagnosis and self‐restore control for systems with measurement delays

The problems of fault diagnosis and fault‐tolerant control are considered for systems with measurement delays. In contrast to the present fault diagnosis and fault‐tolerant control approaches, which consider only the input delay and/or state delay, the main contribution of this paper consists of proposing a new observer‐based reduced‐order fault diagnoser construction approach and a design approach to dynamic self‐restore fault‐tolerant control law for systems with measurement delays. First, the time‐delay system is transformed into a delay‐free system in form by a special functional‐based delay‐free transformation approach for measurement delays. Then, the fault diagnosis is realized online via the proposed reduced‐order fault diagnoser. Using the results of fault diagnosis, two dynamic self‐restore control laws are designed to make the system isolated from faults. A numerical example demonstrates the feasibility and validity of the proposed scheme. © 2012 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks.

In this paper, dynamic output feedback control problem is investigated for a class of nonlinear interconnected systems with time delays. Decentralized observer independent of the time delays is first designed. Then, we employ the bounds information of uncertain interconnections to construct the decentralized output feedback controller via backstepping design method. Based on Lyapunov stability theory, we show that the designed controller can render the closed-loop system asymptotically stable with the help of the changing supplying function idea. Furthermore, the corresponding decentralized control problem is considered under the case that the bounds of uncertain interconnections are not precisely known. By employing the neural network approximation theory, we construct the neural network output feedback controller with corresponding adaptive law. The resulting closed-loop system is stable in the sense of semiglobal boundedness. The observers and controllers constructed in this paper are independent of the time delays. Finally, simulations are done to verify the effectiveness of the theoretic results obtained.     

Second order sliding mode observers for the ADDSAFE actuator benchmark problem

This paper presents the evaluation process and results associated with two different fault detection and diagnosis (FDD) schemes applied to two different aircraft actuator fault benchmark problems. Although the schemes are different and bespoke for the problem being addressed, both are based on the concept of a second order sliding mode. Furthermore both designs are considered as ‘local’ in the sense that a localized actuator model is used together with local sensor measurements. The schemes do not involve the global aircraft equations of motion, and therefore have low order. The first FDD scheme is associated with the detection of oscillatory failure cases (OFC), while the second scheme is aimed at the detection of actuator jams/runaways. For the OFC benchmark problem, the idea is to estimate the OFC using a mathematical model of the actuator in which the rod speed is estimated using an adaptive second order exact differentiator. For the jam/runaway actuator benchmark problem, a more classical sliding mode observer based FDD scheme is considered in which the fault reconstruction is obtained from the equivalent output error injection signals associated with a second order sliding mode structure. The results presented in this paper summarize the design process from tuning, testing and finally industrial evaluation as part of the ADDSAFE project.     

时变时滞不确定系统的鲁棒输出反馈控制

研究了时变时滞不确定系统基于状态观测器的动态输出反馈实现鲁棒镇定的分 析和综合问题.所研究的系统不仅同时包含时变状态时滞和时变控制时滞,而且包含时变未 知且有界不确定参数.提出了确保该系统可通过输出反馈鲁棒镇定的充分条件,并将该充分 条件转化为线性矩阵不等式(LMI)问题,最终通过求解两个LMI来构造输出反馈控制律.     

A review on fault detection and diagnosis techniques: basics and beyond

Safety and reliability are absolutely important for modern sophisticated systems and technologies. Therefore, malfunction monitoring capabilities are instilled in the system for detection of the incipient faults and anticipation of their impact on the future behavior of the system using fault diagnosis techniques. In particular, state-of-the-art applications rely on the quick and efficient treatment of malfunctions within the equipment/system, resulting in increased production and reduced downtimes. This paper presents developments within Fault Detection and Diagnosis (FDD) methods and reviews of research work in this area. The review presents both traditional model-based and relatively new signal processing-based FDD approaches, with a special consideration paid to artificial intelligence-based FDD methods. Typical steps involved in the design and development of automatic FDD system, including system knowledge representation, data-acquisition and signal processing, fault classification, and maintenance related decision actions, are systematically presented to outline the present status of FDD. Future research trends, challenges and prospective solutions are also highlighted.