Fault detection for linear distributed-parameter systems using finite-dimensional functional observers

In this article, finite-dimensional residual generators are directly designed for Riesz-spectral systems with bounded input and output operators to detect faults. This is achieved by using finite-dimensional observers, that can estimate linear functionals of the state without spillover. These observers allow for a decoupling of the unknown disturbances from the estimation error dynamics under mild assumptions. Then, a finite-dimensional residual generator is obtained by approximately decoupling the state from the residual, that is generated by the observer states and the outputs. It is shown that the resulting approximation error can be made small by increasing the observer order. Then, fault detection with the finite-dimensional residual generator can be assured by introducing a time-varying threshold. A faulty Euler–Bernoulli beam with structural damping illustrates the proposed finite-dimensional fault detection approach.     

Finite-dimensional observers for delay systems

A finite-dimensional observer theory is formulated for a class of point delayed systems. The observer is characterized by the fact that it directly generates a finite-dimensional feedback controller for this class of systems. The theory is based on a preliminary approximation theory which allows the delay system to be exponentially approximated by a system of ordinary differential equations.     

A finite-dimensional asymptotic observer for a class of distributed parameter systems

A finite-dimensional asymptotic observer is derived on the basis of a Calcrkin approximation for a class of distributed parameter systems. The systems are described by a partial differential equation of parabolic type. The measured outputs are assumed to be obtained through a finite number of sensors located in the interior. The sensor influence functions are added to the usual basis for the Galerkin approximation and Schmidt's orthogonalization is performed to yield a new basis. The Galerkin approximate solution is sought in terms of this basis. By this procedure the observation spillover problem is overcome. Moreover, in view of the fact that it is generally difficult to obtain the closed-form expressions for the eigenfunctions of the equation, the method is useful for practical substantiation of the observer. The uniform convergence of the Galerkin approximate sequence for the partial differential equation is proved and used to ensure the convergence of the estimated state in a somewhat stronger sense. A numerical example is given which illustrates the power of the method.     

非线性MIMO系统的降维状态观测器

研究一类多输入多输出（ＭＩＭＯ）非线性时变系统的降维状态观测器设计问题,提出了一种非线性降维状态观测器设计方案,并从理论上证明了状态观测误差的指数收敛性,其中设计的降维状态观测器具有收敛速度可调的特性,最后给出了数值算例,仿真结果表明了本文方法的有效性。     

Terminal sliding mode observers for a class of nonlinear systems

This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer.     

Continuity of dynamical systems: The continuous-time case

The purpose of this paper is to study continuity of the parametrization of continuous-time linear time-invariant differential systems having a finite-dimensional state space. We show that convergence of the behavior of such systems corresponds to convergence of the coefficients of a set of associated differential equations. For this to hold, both the behavior and the convergence need to be appropriately defined.     

Active state estimation of nonlinear systems

In this paper, state observers for control systems with nonlinear outputs are studied. For such systems, the observability does not only depend on the initial conditions, but also on the exciting control used. Thus, for such systems, design of active control is an integral part of the design for state observers. Here some sufficient conditions are given for the convergence of an observer. It is also discussed, via a camera example, how to actively excite a system in order to improve the observability.     

基于状态观测器的一类非线性系统的模糊鲁棒控制

利用T－S模型对一类非线性不确定系统进行模糊建模,在此基础上研究模糊鲁棒观测器及模糊状态鲁棒控制器的设计,并证明所设计的模糊鲁棒观测器和模糊状态鲁棒控制器具有全局渐近稳定性质。     

非线性不确定系统的自适应观测器设计

非线性状态观测器可改善过程控制性能和故障诊断,针对一类参数不确定非线性系统提出了自适应观测器设计方法。通过微分同胚变换,将非线性系统转换为仅依赖原系统输入、输出的自适应观测器规范形式。利用自适应调节器估计未知参数,用构造的观测器实现状态的重构。Lyapunov稳定性理论分析了状态观测误差动态方程的稳定性,用来证明所设计的自适应观测器为全局渐近收敛的,既实现了系统状态的渐近重构又确保了在持续激励条件下未知参数估计以指数快速收敛到真值,并通过仿真试验。仿真结果表明提出方法的有效性。     

A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation

We study observer design for sampled-data nonlinear systems using two approaches: (i) the observer is designed via an approximate discrete-time model of the plant; (ii) the observer is designed based on the continuous-time plant model and then discretized for sampled-data implementation (emulation). We investigate under what conditions, and in what sense, these designs achieve convergence for the unknown exact discrete-time model. We present examples which show that designs that violate our conditions may indeed lead to instability when implemented on the exact model.     

Continuous state representations for AR Systems

In this paper we consider in a behavioral setting the subclass of dis-crete-time, linear, finite-dimensional systems, which can be represented by autoregressive (AR) equations. It will be shown that, with respect to the convergence of all coefficients in an AR representation, there exist continuously dependent input-state-output (i/s/o) representations, under the condition that some specified degree remains constant. This continuous i/s/o representation is given by the Fuhrmann realization.     

A parametric approach to finite-dimensional control of linear distributed-parameter systems

This article considers the design of finite-dimensional compensators for distributed-parameter systems using eigenvalue assignment. The proposed compensator consists of an observer estimating additional outputs and a static feedback of the measurable and the estimated outputs. Since the additional outputs can be asymptotically reconstructed, the compensator can be designed using the separation principle, i.e. the closed-loop eigenvalues are given by the observer eigenvalues and the eigenvalues resulting from the static output feedback control. In order to solve the corresponding eigenvalue assignment problem, the parametric approach for the design of static output feedback controllers in finite-dimensions is extended to distributed-parameter systems. By using a parameter optimisation it is possible to assign all closed-loop eigenvalues within specified regions of the complex plane in order to stabilise the system and to assure a desired control performance. A heat conductor is used to demonstrate the proposed design procedure.     

A robust observer for discrete time nonlinear systems

This paper extends the results developed in (Ciccarella et al., 1993) and presents a robust observer for discrete time nonlinear systems. A simple, robust and easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems. Combined parameter and state estimation is made for a numerical example, which compares the robust observer to the observer given in (Ciccarella et al., 1993).     

Eigenspectrum-based extended Luenberger observers for a class of distributed parameter systems

State estimation is an important problem in distributed parameter system especially with nonlinear dynamics in industrial process. An extended Luenberger observer based on the eigen-spectrum of the system operator is developed in this paper to handle this problem. The distributed parameter system is projected into a finite-dimensional subspace where a low-order ordinary differential equation describing the dominant dynamics of the system is derived. A Luenberger observer extended with a nonlinear part is developed based on that dominant dynamics. A sufficient condition is given in this paper for the convergence of the estimated error. Finally, by applying the developed design method to the temperature estimation of a catalytic rod, the achieved simulation results show the effectiveness of the proposed observer.     

Distributed-parameter observer-based control implementation using finite spatial measurements

Distributed-parameter systems have infinite dimensional states and hence, in practical observer and control design applications, the problem of approximate finite-dimensional state reconstruction arises. In this paper a useful approach for implementing such an approximation is presented, which makes use of double Walsh series expansions and is based on finited output measurements at a specified set of spatial points.     

Observability through delayed measurements: a new approach to state observers design

An original approach for the construction of state observers for dynamic systems is presented in this article. New notions of observability (delay-observability and delay-drift-observability), useful for the development of the observer equations and for the convergence proof, are introduced and compared with other standard observability concepts. In particular, it is shown that delay-drift-observability is an extension of the well-known drift-observability property. The construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form, which is a common feature of many other approaches. A numerical example is reported, where a system that is not drift-observable is considered. In this case, the proposed observer is easily constructed and performs well.     

非线性时滞系统的观测器设计

研究了一类满足Lipschitz条件的下三角非线性时滞系统的观测器设计问题.通过构造适当的Lyapunov泛函,用递推法给出了使得误差动态系统渐近趋于零的非线性时滞系统的状态观测器.