Reduced-order Unknown Input Observer Research Articles

Data-driven reduced-order unknown-input observers

In this paper we propose a data-driven approach to the design of reduced-order unknown-input observers (rUIOs). We first recall the model-based solution, by assuming a problem set-up slightly different from those traditionally adopted in the literature, in order to be able to easily adapt it to the data-driven scenario. Necessary and sufficient conditions for the existence of a reduced-order unknown-input observer, whose matrices can be derived from a sufficiently rich set of collected historical data, are first derived and then proved to be equivalent to the ones obtained in the model-based framework. Finally, a numerical example is presented, to validate the effectiveness of the proposed scheme.

A Comprehensive Fault Detection and Isolation Method for DC Microgrids Using Reduced-Order Unknown Input Observers

Fault diagnosis is of critical importance to the safety of power electronic devices in DC microgrids. To detect and isolate different component faults in DC microgrids, this paper introduces a comprehensive protection scheme using reduced-order unknown input observers (ROUIOs). As opposed to conventional protection strategies, the proposed method provides a centralized fault detection and isolation (FDI) solution for DC microgrids that covers multiple faults occurring in different components in a unified process. Moreover, it reduces the complexity of observer model and relaxes the requirements of measurement signals compared with existing observer-based FDI methods for DC microgrids. To this end, the state-space model of a multi-terminal DC microgrid with different faults is first established. On this basis, a bank of ROUIOs are designed with the aim of classifying different component faults in the system. At last, the performance of the proposed FDI method is verified through numerical simulations with MATLAB/Simulink and hardware tests. Test results show that the proposed method can accurately detect and isolate different component faults in DC microgrids in a short response time of 1 ms.

Asymptotical Consensus of MIMO Linear Multiagent Systems With a Nonautonomous Leader and Directed Switching Topology: A Continuous Approach

In this paper, we investigate the asymptotical consensus tracking problems for multiple-input-multiple-output (MIMO) linear multi-agent systems (MASs) with directed switching topology and a non-autonomous leader subject to nonzero unknown inputs. First, we design a full order unknown input observer (UIO) based on relative outputs to estimate the relative full states. Based on this UIO, we design a continuous consensus controller by introducing a decay function which remains positive into the term that is used to eliminate the effects of leader's nonzero inputs. And by using the multiple Lyapunov functions (MLFs) method, we prove that asymptotical consensus can be achieved if the average dwell time (ADT) is greater than a positive threshold. Second, we design a continuous consensus controller based on a reduced order UIO that can significantly simplify calculations. Finally, we give two examples about multiple unmanned aerial vehicles (UAVs) to verify the theoretical results. Compared with existing works, the continuous controllers here can not only achieve zero error consensus tracking, but also are chattering free.

A distributed reduced-order unknown input observer

This paper presents a method of designing distributed observers for linear systems with unknown inputs. Under the requirement of distributed state estimation, outputs of the system are jointly and severally measured by a group of local observer nodes, for the sensing capability of each one is often limited. Therefore, at a local observer, an accurate full state estimation relies on communications with neighbors if the outputs available for use are restricted. In such distributed scenarios, this paper gives conditions for the unknown input decoupling state estimation, under which the designed distributed observer works and has a lower order. For a linear dynamical system of dimension n, the ith local observer is of dimension n−pi if pi-dimensional outputs are available. Each local observer can produce an n-dimensional state estimation with an exponential rate of convergence, free from unknown inputs and more efficient than its full-order counterparts. And beyond that, the design can be done in a robustly completely distributed way.

State and unknown input set-valued estimation for uncertain linear discrete-time systems

Set-valued algorithms are designed in this work to compute rigorous bounds of the unknown inputs of uncertain discrete-time linear systems. First, based on the classical full-order and reduced-order unknown input observers, non-conservative numerical schemes are proposed to characterize the reachable set of the estimation error. Then, by using these results, set-membership estimators of the unknown inputs are presented. Moreover, the results of these estimators can be merged together via set-intersection operators to obtain more accurate estimates.

Consensus Disturbance Rejection of MIMO Linear Multiagent Systems With Directed Switching Topologies: A Reduced Order Observer Approach

In this brief, consensus disturbance rejection problem is investigated for multiple-input-multiple-output (MIMO) linear multi-agent systems (MASs) subject to non-vanishing disturbances under directed switching topologies. First, we design a reduced order unknown input observer (UIO) based only on the relative outputs to estimate the relative full states. Then a consensus controller together with a disturbance observer (DO) is designed to achieve the cooperative goal. Second, by using the average dwell time (ADT) method, it is proven that consensus can be achieved if the ADT is greater than a positive threshold, meanwhile the non-vanishing disturbances are attenuated by DO. Finally, theoretical result is verified by performing simulation.

Formula omitted] output feedback control for fractional-order T-S fuzzy model with time-delay

This paper addresses H∞ observer-based control issue for fractional-order uncertain Takagi-Sugeno (T-S) fuzzy model with unknown input and time-delay in the case of system order in (0,1). In order to construct the state estimation variables, reduced-order fuzzy observer is devised. By utilizing Lyapunov method of fractional-order derivative, the sufficient conditions are provided to ensure the effectiveness of proposed reduced-order unknown input observer and the stabilization of augmented T-S fuzzy model with an H∞-norm σ. The conditions are shown in terms of linear matrix inequalities (LMIs) and the matrices of unknown input fuzzy observer are computed by relevant LMIs. Furthermore, by solving LMIs, the T-S fuzzy output feedback control is realized. Finally, a numerical example and a single-link robot arm example are simulated to illustrate the validity of the addressed strategy.

Robust fault estimation of a blade pitch and drivetrain system in wind turbine model

In this article, a novel robust fault estimation scheme to ensure efficient and reliable operation of wind turbines has been presented. Wind turbines are complex systems with large flexible structures that work under very turbulent and unpredictable environmental conditions for a variable electrical grid. The proposed observer-based estimation scheme consists of a set of possible faults affecting the dynamics, sensors, and actuators of wind turbines. First, the pitch and drivetrain system faults occur simultaneously with process and sensor disturbances that are called unknown input signals. Second, through a series of coordinate transformations, the faulty subsystem is decoupled from the rest of the system. The first subsystem is affected by unknown inputs, and the second one is affected by faults. A reduced-order unknown input observer is designed to reconstruct states accurately, whereas a reduced-order sliding mode observer is designed for the second subsystem such that it is robust against unknown inputs and faults. Moreover, the reduced-order unknown input observer guarantees the asymptotic stability of the error dynamics using the Lyapunov theory method and completely removes unknown inputs; on the other hand, the reduced-order sliding mode observer is designed to reconstruct faults for the faulty subsystem accurately. Until now, authors only focused on an unknown input signal in the dynamics of the system, especially in nonlinear systems. The estimated fault will be adequate to accommodate the control loop, and sufficient conditions are developed to guarantee the stability of the state estimation error. In the next step, to figure the effectiveness of the proposed approach, a wind turbine benchmark system model is considered with faults and unknown inputs scenarios. The simulation results are used to validate the robustness of the proposed algorithms under noise conditions, and the results show that the algorithm could classify faults robustly.

Observer-Based Consensus Protocol for Directed Switching Networks With a Leader of Nonzero Inputs.

We aim to address the consensus tracking problem for multiple-input-multiple-output (MIMO) linear networked systems under directed switching topologies, where the leader is subject to some nonzero but norm bounded inputs. First, based on the relative outputs, a full-order unknown input observer (UIO) is designed for each agent to track the full states' error among neighboring agents. With the aid of such an observer, a discontinuous feedback protocol is subtly designed. And it is proven that consensus tracking can be achieved in the closed-loop networked system if the average dwell time (ADT) for switching among different interaction graph candidates is larger than a given positive threshold. By using the boundary layer technique, a continuous feedback protocol is skillfully designed and employed. It is shown that the consensus error converges into a bounded set under the designed continuous protocol. Second, as part of the full states' error can be constructed via the agents' outputs, a reduced-order UIO is thus designed based on which discontinuous and continuous feedback protocols are, respectively, proposed. By using the stability theory of the switched systems, it is proven that the consensus error converges asymptotically to 0 under the designed discontinuous protocol, and converges into a bounded set under the designed continuous protocol. Finally, the obtained theoretical results are validated through simulations.

Corrigendum to “Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays”

Corrigendum to “Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays”

Reduced-Order Observer Design for Switched Descriptor Systems With Unknown Inputs

This paper presents a systematical reduced-order observer design method for a class of switched descriptor systems containing unknown inputs (UIs) in both the dynamic and the output equations. Generally speaking, when the output of the system contains UIs, the reduced-order observer design will become much more challenging. In order to overcome the difficulty brought by the UIs in the output, first, by introducing a new UI vector, a new equivalent system is obtained, which does not contain UIs in the corresponding output any more. Then, for the purpose of reduced-order observer design, the observer matching condition (OMC) and the minimal phase condition (MPC) are discussed, and it is shown that the new general system maintains both the OMC and the MPC. Subsequently, based on the discussions on the existence conditions, a reduced-order unknown input observer is developed to asymptotically estimate the state of the original system. Finally, an electronic circuit example is given to show the effectiveness of the proposed method.

Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays

In this work, we consider the design problem of a full-order and also reduced-order unknown input observers for a particular class of time-delay systems. Asymptotic stability and existence conditions for the designed observers are established. The quadruple-tank process is used as a benchmark to prove the efficiency of the proposed algorithms.

Distributed sensor fault diagnosis for a formation system with unknown constant time delays

In this paper, a distributed velocity sensor fault diagnosis scheme is presented for a formation of a second-order multi-agent system with unknown constant communication time delays. An existing distributed proportion-derivation (DPD) formation control law is adopted and a delay-independent condition is proposed to guarantee the asymptotical formation stability of the formation system based on the Nyquist stability criterion. Then a distributed fault diagnosis scheme is developed. In each agent, a distributed fault detection residual generator (DFDRG) and a bank of distributed fault isolation residual generators (DFIRGs) are designed based on the closed-loop model of the whole system. Each DFIRG is built up on the basis of a reduced-order unknown input observer (UIO) which is robust to the fault of one neighboring agent. According to the robust relationship between DFIRGs and faults, distributed fault isolation can be achieved. Conditions are presented to guarantee that each agent is able to diagnose faults of itself and its neighbors despite the disturbance of time delays. Finally, outdoor experimental results illustrate the effectiveness of the proposed schemes.

Full-order and Reduced-order Observer Design for One-sided Lipschitz Nonlinear Fractional Order Systems with Unknown Input

This paper studies the problem of designing the unknown input observers (UIOs) for fractional order one-sided Lipchitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using the matrix generalized inverse approach, sufficient conditions for asymptotic stability of the observer error dynamic systems are presented, which guarantee the existence of the full-order and reduced-order UIOs. All the conditions are obtained in terms of linear matrix inequality (LMI). Furthermore, we show that the obtained results can be applied to a fractional order electrical circuit with the unknown input signal. Two examples are given to demonstrate the applicability of the proposed approach.

Reduced-order switched UIO design for switched discrete-time descriptor systems

In this paper, a reduced-order switched unknown input observer design is investigated for switched discrete-time descriptor systems. By a series of equivalent transformations, the original descriptor system with unknown inputs is transformed into a reduced-order standard system without unknown inputs, and then a switched reduced-order unknown input observer is designed by using standard switched system stability analysis techniques. Besides, the sufficient condition for the existence of the switched observer is also discussed in detail. Moreover, based on the state estimation, a delayed unknown input reconstruction method is also proposed. Finally, two simulation examples are given to show the effectiveness of the proposed methods.

Reduced order unknown input observer based distributed fault detection for multi-agent systems

This paper is devoted to the problem of distributed fault detection for multi-agent systems. A reduced order unknown input observer based fault detection method is proposed. By constructing reduced order unknown input observers in one agent, the fault in its neighbor can be detected. In the observer design process, only the measurement output of the neighbor agents is used. Two cases are considered. For the case that the observer matching condition is satisfied, the influence of unknown input on residual is removed completely; if this condition is not satisfied, the influence of a part of unknown input is removed, and the influence of the other part is attenuated. Compared with the existing results, the overall dimension of all the observers is decreased greatly. At last, two examples are given to show the effectiveness of the fault detection method.

Reduced-Order Observer Design for Discrete-Time Descriptor Systems With Unknown Inputs: An Linear Matrix Inequality Approach

Reduced-order observer design methods for both linear and nonlinear discrete-time descriptor systems based on the linear matrix inequality (LMI) approach are investigated. We conclude that the conditions under which a full-order observer exists can also guarantee the existence of a reduced-order observer. By choosing a special reduced-order observer gain matrix, a reduced-order unknown input observer is proposed for linear system with unknown inputs, and then an unknown input reconstruction is provided for some special cases. We also extend above results to the cases of nonlinear systems. Finally, three numerical comparative simulation examples are given to illustrate the effectiveness and merits of proposed methods.

Unknown input observer design for one-sided Lipschitz nonlinear systems

This paper considers the observer design problem for one-sided Lipschitz nonlinear systems with unknown inputs. The systems under consideration are a larger class of nonlinearities than the well-studied Lipschitz systems and have inherent advantages with respect to conservativeness. For such systems, we first propose a full-order nonlinear unknown input observer (UIO) by using the linear matrix inequality (LMI) approach. Following a similar design procedure and using state transformation, the reduced-order nonlinear UIO is also constructed. Sufficient conditions to guarantee existence of full-order and reduced-order UIOs are established by carefully considering the one-sided Lipschitz condition together with the quadratic inner-bounded condition. Based on the matrix generalized inverse technique, the UIO conditions are formulated in terms of LMIs. Moreover, the proposed observers are applied to a single-link flexible joint robotic system with unknown inputs. Simulation results are finally given to illustrate the effectiveness of the proposed design.

New results on fault reconstruction using a finite-time converging unknown input observer

This study presents a fault reconstruction scheme that converges in a pre-assigned finite time, which is chosen as the parameter of the finite-time converging unknown input observer (FT_UIO). After the convergence time, the actuator faults can be detected and diagnosed promptly and accurately by the simple threshold test on the fault estimates, provided by the fault reconstruction scheme, which are free from the transient observation error because of the initial condition mismatch and the intermittent output disturbance. The fault reconstruction scheme consists of the FT_UIO and the fault reconstruction algorithm. The FT_UIO, designed with two distinct reduced-order unknown input observers that converge asymptotically, provides a disturbance and fault-free state estimate that converges in the pre-assigned finite time. The state estimate obtained from FT_UIO is applied to reconstruct the faults of interest. The proposed scheme is compared with the design previously reported in the simulation.

Modélisation d'observateurs pour la détection de fautes actionneurs et la localisation de fautes de mesure. Détection et localisation de fautes actionneurs

A new design procedure of a reduced order unknown input observer (UIO) is proposed to generate residuals for fault detection isolation. The originality of this work consists in the chosen approach for the procedure implementation. Indeed the kernel of the actuator fault distribution matrix is generated thanks to generalized inverses. Residual sensivity linked to the constant faults can be set up to facilitate the design of the fault decision stage. Residuals generated by a bank of observers allow the detection isolation of every actuator fault on the one hand and the isolation between actuator faults and sensor faults on the other hand.