Reduced-order Functional Observers Research Articles

Parametric design of reduced-order functional observers for linear time-varying delay systems

This paper investigates the design of reduced-order functional observer for linear time-invariant systems (LTI) with time-varying delay. Firstly, the sufficient condition for the existence of reduced-order delay-free functional observers is obtained. Secondly, by solving generalized Sylvester matrix equations (GSEs), completely parameterized formulas of the coefficient matrices of reduced-order function observer are established. The free parameter matrices in the formulas provide the design degrees of the freedom and improve the convergence rate of the error system. Finally, two numerical and a practical examples are provided to illustrate the effectiveness of the proposed approach.

A Modal Transformation Approach to Design Reduced Order Functional Observer-Based WADC for Low-Frequency Oscillations

Low-frequency oscillations (LFOs) are one of the major concerns in modern power system; hence, these should be appropriately treated in order to achieve reliable operation. In this regard, we propose a novel wide-area damping controller (WADC) to dampen LFO modes effectively. The proposed WADC utilized thyristor controlled series compensator (TCSC) based flexible ac transmission system (FACTS) device through which supplementary input is provided. The selection of modal feedback signals for WADC design is carried out using coordinated modal transformation and linear quadratic regulator (LQR) approach. However, these signals are not accessible directly through the phasor measurement devices (PMDs). Hence, this paper utilizes a reduced-order functional observer to estimate the feedback signals using PMD data. The estimated feedback signals are further modulated by simple gains to improve the damping of critical LFO modes. The proposed methodology is validated on benchmark 4-machine 11-bus system and a more practical 25-machine, 105-bus system representing the complex Eastern Regional Grid (ERG) of India. The results obtained on these nonlinear systems show a significant improvement in damping of the critical LFOs leaving the other modes almost unaffected.

Parametric design to reduced-order functional observer for linear time-varying systems

This article studies the parametric design of reduced-order functional observer (ROFO) for linear time-varying (LTV) systems. Firstly, existence conditions of the ROFO are deduced based on the differentiable nonsingular transformation. Then, depending on the solution of the generalized Sylvester equation (GSE), a series of fully parameterized expressions of observer coefficient matrices are established, and a parametric design flow is given. Using this method, the observer can be constructed under the expected convergence speed of the observation error. Finally, two numerical examples are given to verify the correctness and effectiveness of this method and also the aircraft control problem.

A new method for designing distributed reduced-order functional observers of interconnected time-delay systems

This paper reports a new method for designing distributed reduced-order functional observers of a class of interconnected systems with time delays. The systems under consideration belong to a class of large-scale systems where each system is formed by a number of interconnected subsystems. Moreover, the interconnections and the states of the local subsystems are subject to heterogeneous time delays. The novel contribution of this paper lies in the development of new coordinate state transformations, which are used to transform the interconnected subsystems into decoupled subsystems. Most significantly, each decoupled subsystem does not contain any time delay in the state vector. Moreover, each decoupled subsystem is expressed in an observable canonical form, with time delays only appearing in the inputs and outputs of the system. Due to this novel structure, a reduced-order functional observer for each decoupled subsystem can be easily designed to estimate the unmeasurable local state vector. The designed observers for the local subsystems do not need to exchange the state estimates amongst themselves, and therefore, each observer for each local subsystem can be designed independently. Because of the state transformations, the designed observers have a more general structure than any of the existing distributed functional observers available in the literature. Numerical examples are given to illustrate the effectiveness and advantages of our results.

Distributed Functional Observer Based Fault Detection for Interconnected Time-Delay Systems

This paper presents a novel distributed functional observer based fault detection (FD) scheme for interconnected time-delay systems with unknown inputs. The scheme employs a set of stand-alone residual generators, one at each subsystem, to detect actuator faults in the system. At each subsystem, depending on the strength of the interactions amongst the subsystems, a residual generator is designed by utilizing either a reduced-order distributed or decentralized functional observer. Our FD scheme offers several advantages in terms of simplicity due to the deployment of stand-alone reduced-order functional observers, and reliability owing to the independence of the operation of each residual generator. Two numerical examples are given to illustrate the effectiveness of our proposed FD scheme.

Reduced-order functional observers with application to partial state estimation of linear systems with input-delays

Reduced-order multi-functional observer design for multi-input multi-output linear time-invariant (LTI) systems with constant delayed-inputs is studied. This research is useful in the input estimation of LTI systems with actuator delay, as well as system monitoring and fault detection of these systems. Two approaches for designing an asymptotically stable functional observer for the system are proposed: delay-dependent and delay-free. The delay-dependent observer is infinite-dimensional, while the delay-free structure is finite-dimensional. Moreover, since the delay-free observer does not require any information on the time delay, it is more practical in real applications. However, the delay-dependent observer contains less restrictive assumptions and covers more variety of systems. The proposed observer design schemes are novel, simple to implement, and have improved numerical features compared to some of the other available approaches to design (unknown-input) functional observers. In addition, the proposed observers usually possess lower order than ordinary Luenberger observers, and the design schemes do not need the observability or detectability requirements of the system. The necessary and sufficient conditions of the existence of an asymptotic observer in each scenario are explored. The extensions of the proposed observers to systems with multiple delayed-inputs are also discussed. Several numerical examples and simulation results are employed to support our theories.

Decentralised state feedback control of multiagent systems using reduced-order functional observers

This paper presents a solution to the global state feedback control problem for multiagent systems under a complete decentralised information structure. The proposed solution is based on the design of reduced-order functional observers to estimate asymptotically the global control signals by using only the corresponding local output information subject to the condition of no information cross flows. New existence conditions for the reduced-order decentralised observers are derived and design procedures are presented. A numerical example is included for illustration.