状态估计与未知输入和可测噪声同时重构方法

针对一类不确定线性系统,讨论了状态估计及未知输入和可测噪声重构方法。首先,对仅具有未知输入的线性系统,讨论了观测器匹配条件不满足前提下的状态估计和未知输入重构问题;通过设计降维观测器和高阶滑模观测器,提出一种未知输入代数重构方法;然后,将以上结论上升到具有未知输入和可测噪声的线性系统,以此提出了状态估计及未知输入和可测噪声同时重构的方法;最后,通过对飞行器模型进行仿真,验证了所提出方法的有效性。     

基于高阶滑模观测器的状态和未知输入同时估计方法

对一类含有未知输入的仿射非线性系统,讨论了一种能同时估计系统状态和末知输入的未知输入观测器设计方法.首先利用李导数对仿射非线性系统进行线性化,将其转化为可控标准型.其次,针对变化后的等价系统,提出了一种高阶、高增益滑模观测器,由此不仅能得到系统状态的估计,同时还得到状态微分的估计.再次,基于状态及其微分的估计,对未知输入提出了一种重构方法.该方法能对强时变未知输入重构,而且重构中没有用到系统微分的信息.最后,通过对两个实际模型的仿真,表明了方法的可行性.     

自适应广义滑模观测器之状态估计和故障重构

针对一类同时具有执行机构故障和输出扰动的不确定性系统,提出了一种自适应广义滑模观测器,实现系统状态的估计和执行机构故障的重构.首先,进行系统变换及状态增广构成一类奇异系统,使得执行机构故障和输出扰动解耦,且输出扰动成为增广系统的状态之一;随后,受未知输入观测器和滑模观测器的启发,设计了一种广义滑模观测器,放宽了传统方法对输出维数的严格约束,并通过融入自适应技术放宽了对故障和不确定性上界已知的要求;最后,利用等效误差注入的思想实现故障重构.针对可重复使用运载器再入段进行的仿真实例,验证了所提方法的有效性.     

不确定线性系统有限时间状态估计与故障重构

针对具有外部干扰和执行器故障的不确定线性系统,给出了一种有限时间内估计系统状态及重构执行器故障的方法．首先,通过状态和输出等价变换,得到不受执行器故障和建模不确定信息干扰的降维解耦系统．在此基础上设计有限时间状态估计器,并设置任意小的时延参数,实现对降维系统状态的有限时间估计,从而达到对原系统状态有限时间估计的目的;其次,考虑高增益滑模微分器对系统输出微分进行有限时间估计;之后,在原系统状态和系统输出微分有限时间估计的基础上,提出一种对系统不确定信息和执行器故障同时估计的方法;最后,通过对具有执行器故障的F-16飞行器纵向系统模型进行仿真,验证所提方法的有效性．     

离散Lipschitz非线性系统状态和未知输入估计

针对含有未知输入和可测噪声的离散Lipschitz非线性系统,研究了状态估计、未知输入以及可测噪声同时估计的问题.首先,对含有未知输入的系统,设计了比例积分观测器,达到同时估计系统状态和未知输入之目的.分析了残差系统的观测性和稳定性,利用H_∞实现该观测器对时变未知输入的有效估计;其次,将观测器增益矩阵的求解转化为求解线性矩阵不等式的形式;进一步地,基于系统状态扩展方法,将所提方法推广至同时含有未知输入和可测噪声的系统;最后,通过两个仿真算例说明了所提方法的正确性和有效性.     

基于辅助输出的线性系统状态和未知输入同时估计方法

在未知输入观测器匹配条件不满足的情况下, 针对一类线性时不变系统, 研究了同时估计系统 状态和未知输入的问题. 首先, 基于可测输出对未知输入的相关度的概念, 给出了辅助输出 的构造方法, 使得匹配条件得以满足. 为了处理辅助输出中的未知信息, 提出了一种高增益 观测器设计方法, 它不仅能估计辅助输出, 而且还能估计辅助输出的导数. 然后, 基于辅助 输出的估计值, 提出了一种降维观测器设计方法, 可以在不受未知输入影响的情况下估计系统 的状态; 接下来, 基于状态和辅助输出及其导数的估计值, 给出了未知输入估计. 最后, 对一个五 阶系统进行了数字仿真, 仿真结果表明所提出的方法是有效的.     

不确定切换线性系统状态和未知输入估计方法

针对具有未知输入的不确定切换线性系统, 在平均驻留时间切换下, 讨论其状态和未知输入估计方法. 通过等价变换解耦切换系统的未知输入, 以构造降维切换系统. 进而, 设计切换观测器实现对原系统的状态估计, 并求解具有线性矩阵不等式限制的最优化问题, 得到观测器存在的充分条件. 在基于函数微分数值解方法求得系统输出微分的基础上, 提出一种切换系统未知输入的估计方法. 最后通过一个数值实例验证了所提出方法的有效性.

     

多故障并发非线性系统一体化跟踪主动容错控制器设计

针对一类执行器及传感器同时发生故障的非线性系统,综合鲁棒滑模重构观测器及自适应滑模容错控制器设计技术,提出一体化跟踪主动容错控制方案.首先,将系统增维变换为广义系统,运用广义约束逆引入辅助矩阵,采用线性矩阵不等式设计观测器系数矩阵,综合自适应律给出广义鲁棒滑模观测器设计程式;在此基础之上,通过设计鲁棒滑模微分器估计输出向量微分,结合广义鲁棒滑模观测器状态估计结论,实现执行器及传感器故障同时重构.其次,基于故障重构及状态估计结论,提出自适应滑模的跟踪主动容错控制律设计程式.最后,通过开展飞行模拟转台伺服系统数值仿真,检验一体化跟踪主动容错控制器设计方法的有效性.     

匹配条件不满足时线性系统未知输入观测器设计

针对一类不满足观测器匹配条件的线性系统,讨论了未知输入观测器设计方法.首先,为了突破观测器匹配条件的限制,提出了一种与未知输入相对阶无关的辅助输出构造方法.然后,把未知输入看作系统状态的一部分,将原系统转化为一个不含未知输入的增维线性描述系统.针对这样的系统转化,对一系列等价前提条件进行了详细的讨论.之后,针对该增维线性描述系统,构造Luenberger观测器来估计原系统的状态和未知输入.同时,借助于高阶滑模微分器,来估计辅助输出中的未知信号.最后,对一个单连杆柔性机械手模型进行了数值仿真,仿真结果表明了方法的有效性.     

不确定动态系统的执行器故障检测与重构

讨论不确定动态系统的执行器故障检测与重构问题.以滑模观测器为基础,利用状态和输出变换方法与奇异值分解方法相结合对系统进行降阶,提出一种鲁棒故障重构观测器.给出了优化滑模策略,并作了严格论证,保证对系统不确定性具有鲁棒性和跟踪系统状态的收敛性.应用等价输出控制的概念和设计的鲁棒故障重构观测器,获取故障信息并实现执行器故障的检测与重构.最后通过数值仿真验证了该方法的有效性和可靠性.     

Sliding-mode observers for nonlinear systems with unknown inputs and measurement noise

This paper deals with the design of observers for Lipschitz nonlinear systems with not only unknown inputs but also measurement noise when the observer matching condition is not satisfied. First, an augmented vector is introduced to construct an augmented system, and an auxiliary output vector is constructed such that the observer matching condition is satisfied and then a high-gain sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time. Second, for nonlinear system with both unknown inputs and measurement noise, an adaptive robust sliding mode observer is developed to asymptotically estimate the system’s states, and then an unknown input and measurement noise reconstruction method is proposed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.     

Unknown Input Reconstruction via Interval Observer and State and Unknown Input Compensation Feedback Controller Designs

In this paper, we investigate the state estimation, unknown input and measurement noise reconstruction problems and the feedback controller design issues for a linear discrete-time system with both unknown inputs and measurement noises. First, an augmented system is constructed and the state vector of the augmented system consists of the original system state and the measurement noise, and the preconditions between the original system and the augmented system is discussed in detail. Second, for the augmented system, a reduced-order observer is designed so that the original system state estimates and the measurement noise reconstruction can be obtained. Third, in order to get the asymptotical unknown input reconstruction, an interval observer for part of the measurable output is proposed and an unknown input reconstruction method based on the interval observer is developed. Finally, an observer-based state feedback and unknown input controller is designed and the closed-loop system stability is analyzed. We point out that the closed-loop system satisfies the so-called separation property. At last, two simulation examples are given to verify the effectiveness of the proposed methods.

     

基于广义未知输入观测器的鲁棒故障估计方法

当干扰存在时,有效地估计故障且放松故障的限制条件需要进一步的研究,为此针对含未知干扰的非线性连续系统的鲁棒故障估计问题提出一种广义未知输入观测器方法。首先,将执行器故障向量和传感器故障向量与原系统状态向量组成广义系统,放松对故障类型的限制,对此广义系统设计未知输入观测器解耦干扰,保证鲁棒性的同时估计出状态变量、执行器故障及其一阶微分和传感器故障。然后通过解线性矩阵不等式（LMI）给出估计误差渐近收敛的条件。最后,在MATLAB 的simulink平台上用三叶片水平轴风力模型仿真验证本文观测器的故障估计有效性鲁棒性。     

State estimation and unknown input reconstruction via both reduced-order and high-order sliding mode observers

This paper considers the problems of the simultaneous estimation of the system states and the unknown inputs for linear systems when the so-called observer matching condition is not satisfied. An auxiliary output vector is introduced so that the observer matching condition is satisfied with respect to it. A high-order sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time based on the system measured outputs. After this, a reduced-order observer is constructed by using the estimated auxiliary outputs as the new system outputs. The reduced-order observer is able to asymptotically estimate the system states without suffering the influence of the unknown inputs. A kind of unknown input reconstruction method based on both the state and the auxiliary output derivative estimates is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.     

Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs

The paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.     

Robust output tracking for uncertain/nonlinear systems subject to almost constant disturbances

In this paper, we consider uncertain/nonlinear systems subject to unknown constant disturbance inputs. We wish to design state feedback controllers which ensure that the system output asymptotically tracks a specified constant reference signal and all states are bounded. The controllers we consider are PI in the sense that they consist of a piece which depends linearly on the state and another piece which depends on the integral of the output tracking error. Our main result reduces the original problem to a stabilization problem for an associated augmented system which we call the derivative augmented system. We obtain controller design procedures for specific classes of uncertain/nonlinear systems. Then we extend these results to the situation in which the reference signal and the disturbance are not necessarily constant but asymptotically approach a constant.