Mehrdad Saif

A novel approach to the design of unknown input observers

A novel state estimator design scheme for linear dynamical systems driven by partially unknown inputs is presented. It is assumed that there is no information available about the unknown inputs, and thus no prior assumption is made about the nature of these inputs. A simple approach for designing a reduced-order unknown input observer (UIO) with pole-placement capability is proposed. By carefully examining the dynamic system involved and simple algebraic manipulations, it is possible to rewrite equations eliminating the unknown inputs from part of the system and to put them into a form where it could be partitioned into two interconnected subsystems, one of which is directly driven by known inputs only. This makes it possible to use a conventional Luenberger observer with a slight modification for the purpose of estimating the state of the system. As a result, it is also possible to state similar necessary and sufficient conditions to those of a conventional observer for the existence of a stable estimator and also arbitrary placement of the eigenvalues of the observer. The design and computational complexities involved in designing UIOs are greatly reduced in the proposed approach. >

Sliding mode observer for nonlinear uncertain systems

A new sliding mode observer for a class of nonlinear uncertain systems is proposed in this article. The proposed sliding mode observer works under much less conservative conditions than previous nonlinear unknown input observers. Also, a functional version of the observer is proposed in certain cases where it may not be possible to design an observer capable of estimating the entire state of the system.

Brief Unknown disturbance inputs estimation based on a state functional observer design

We consider the problem of function of state plus unknown input estimation of a linear time-invariant system using only the measured outputs. Two reduced-order input estimators built upon a state functional observer are proposed. The first is an extension of a state/input estimator, while the second is based on adaptive observer design technique. The proposed estimator can be designed under less restrictive conditions than those of the previous work, and unlike some of the past studies the proposed observer can be designed for certain nonminimum phase systems.

A new approach to robust fault detection and identification

A methodology for instrument fault detection and identification (FDI) in linear dynamical systems subject to plant parameter variations or uncertainties is presented. At the heart of this approach is a robust estimator for which the necessary and sufficient conditions to its existence are outlined. The robust estimator can simultaneously estimate the unmeasurable state variables of the system for the purpose of control and provide necessary information for FDI purposes. A novel feature of this approach is that it can actually identify the shape and magnitude of the failures. The scheme allows for fast and accurate FDI, and can account for structural uncertainties and variations in the parameters of the dynamical model of the system. The overall fault tolerant control system strategy proposed is verified through simulation studies performed on the control of a vertical takeoff and landing (VTOL) aircraft in the vertical plane. >

Unknown input observer design for a class of nonlinear systems: an LMI approach

A full order nonlinear unknown input observer (NUIO) for a class of Lipschitz nonlinear systems with unknown inputs is designed. A sufficient NUIO existence condition which requires solving a nonlinear matrix inequality is derived. To avoid solving the nonlinear matrix inequality directly, the existence condition is then reformulated as a new sufficient existence condition in terms of an LMI. An important advantage of this LMI based condition is that it enables us to design the proposed full order NUIO using Matlab LMI toolbox and thus makes the difficult NUIO design problem an easy task for the considered class of nonlinear systems. The new sufficient condition, when applied to linear systems, is also necessary. An example is given to show how to use the LMI approach to design the proposed NUIO, and simulation results are presented

Fault detection and isolation based on novel unknown input observer design

With an emphasis on fault isolation and by treating fault detection as a byproduct of fault isolation, both actuator and sensor fault detection and isolation (FDI) problems for a class of uncertain Lipschitz nonlinear systems are studied using an unknown input observer (UIO) design technique. To solve the actuator fault detection and isolation problem, we develop a particular system structure by regrouping the system inputs, which is suitable for UIO design. By filtering the regrouped outputs properly, the same system structure can be developed for sensor fault detection and isolation problem, which allows us to treat the sensor fault detection and isolation problem as an actuator fault detection and isolation problem. To accomplish FDI efficiently, a novel full order nonlinear UIO is designed with a special property suitable for fault isolation purposes and a necessary and sufficient condition for its existence are presented. The LMI based sufficient condition enables the designers to use Matlab LMI toolbox and makes the computationally difficult UIO design much easier. For UIO based FDI, the following three problems are investigated: 1) under what conditions is it possible to isolate single and/or multiple faults? 2) What is the maximum number of faults that can be isolated simultaneously? 3) How to design fault isolation schemes to achieve multiple fault isolation (that is, to make decisions on how many faults have occurred and the location of each fault)? Conditions for problem 1) are derived and the maximum number of faults that can be isolated is determined for problem 2) to solve problem 3) an FDI scheme is designed using a bank of nonlinear UIOs and its design procedure is presented in a step by step fashion. An example is given to show how to use the proposed FDI scheme and simulations results illustrate that the proposed technique works well for FDI in uncertain Lipschitz nonlinear systems

Observer-Based Fault Diagnosis of Satellite Systems Subject to Time-Varying Thruster Faults

This paper presents a novel fault diagnosis approach in satellite systems for identifying time-varying thruster faults. To overcome the difficulty in identifying time-varying thruster faults by adaptive observers, an iterative learning observer (ILO) is designed to achieve estimation of time-varying faults. The proposed ILO-based fault-identification strategy uses a learning mechanism to perform fault estimation instead of using integrators that are commonly used in classical adaptive observers. The stability of estimation-error dynamics is established and proved. An illustrative example clearly shows that time-varying thruster faults can be accurately identified.

Brief paper: Observer design and fault diagnosis for state-retarded dynamical systems

In this paper, we propose a reduced-order observer, for state estimation in a class of state-delayed dynamical systems driven by known as well as unknown inputs. Conditions for existence of the proposed observer, plus the stability and convergence proof for the observer based on the Razumikhin theorem are given. Additionally, the proposed observer is utilized in an analytical-redundancy-based approach for sensor and actuator failure detection problem in the same class of time delay dynamical systems. Finally, the applicability and effectiveness of the proposed FDI scheme is illustrated through numerical examples.

Adaptive actuator fault detection, isolation and accommodation in uncertain systems

Adaptive actuator fault detection, isolation, and accommodation problems for linear multi-input single-output (MISO) systems with unknown system parameters are investigated. To solve the detection problem, we construct an adaptive estimate of the output signal. By comparing it with the output of the system, any type of actuator faults can be detected. However, the fault isolation problem is much more complicated. In order to solve it using an adaptive approach, the article considers constant actuator faults, which arise when the actuator output (such as a valve) is stuck at some fixed value. A novel idea which entails controller design for fault isolation is proposed. Thus, the controller in this case is not only designed to meet the control objective, but also to help with fault isolation, in case of an actuator failure. To accomplish this, assuming that there are m inputs, a group of additive functions, called fault isolation design functions in m − 1 inputs, solely used for fault isolation, are introduced. Assuming that less than m − 1 faults can occur, adaptive estimates of the output need to be defined to isolate the faults. Isolation is accomplished by comparing these estimates with the output of the actual system. If there exists only one estimate that matches the output of the system, it is concluded that the combination corresponding to the estimate is the faulty combination. This determines the number of actuator faults and isolates the faulty actuators. Once the faults are detected and isolated, the adaptive fault accommodation problem is accomplished by simply turning off the faulty actuators and using the remaining normal actuators. Finally, an illustrative example with simulation results is provided to support the theoretical results.

State observation, failure detection and isolation (FDI) in bilinear systems

This paper explores the design of a reduced order observer with unknown inputs for the purpose of fault detection and isolation (FDI) in a class of bilinear systems. An approach for sensor and actuator failure detection and isolation (FDI), based on the proposed observer is presented. Finally, the applicability and effectiveness of the proposed FDI scheme is illustrated on an electrohydraulic system.