Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Filter for detecting and isolating faults for a nonlinear system

In the paper the problem of detecting and isolating multiple faults for nonlinear systems is considered. A strategy of state filtering is derived in order to detect and isolate multiple faults which appear simultaneously or sequentially in a discrete time nonlinear systems with unknown inputs. For the considered system for which a fault isolation condition is fulfilled the proposed method can isolate p simultaneous faults with at least p+q output measurements, where q is the number of unknown inputs or disturbances. A reduced output residual vector of dimension p+q is generated and the elements of this vector are decoupled in a way that each element of the vector is associated with only one fault or unmeasured input

Controllers, observers, and applications thereof

Controller scaling and parameterization are described. Techniques that can be improved by employing the scaling and parameterization include, but are not limited to, controller design, tuning and optimization. The scaling and parameterization methods described here apply to transfer function based controllers, including PID controllers. The parameterization methods also apply to state feedback and state observer based controllers, as well as linear active disturbance rejection (ADRC) controllers. Parameterization simplifies the use of ADRC. A discrete extended state observer (DESO) and a generalized extended state observer (GESO) are described. They improve the performance of the ESO and therefore ADRC. A tracking control algorithm is also described that improves the performance of the ADRC controller. A general algorithm is described for applying ADRC to multi-input multi-output systems. Several specific applications of the control systems and processes are disclosed

Set-membership identification and fault detection using a Bayesian framework

This paper deals with the problem of set-membership identification and fault detection using a Bayesian framework. The paper presents how the set-membership model estimation problem can be reformulated from the Bayesian viewpoint in order to, first, determine the feasible parameter set in the identification stage and, second, check the consistency between the measurement data and the model in the fault-detection stage. The paper shows that, assuming uniform distributed measurement noise and uniform model prior probability distributions, the Bayesian approach leads to the same feasible parameter set than the well-known set-membership technique based on approximating the feasible parameter set using sets. Additionally, it can deal with models that are nonlinear in the parameters. The single-output and multiple-output cases are addressed as well. The procedure and results are illustrated by means of the application to a quadruple-tank process.Peer ReviewedPostprint (author's final draft

A failure diagnosis system based on a neural network classifier for the space shuttle main engine

A conceptual design of a model based failure detection and diagnosis system is developed for the space shuttle main engine. This design relies on the accurate and reliable identification of the parameters of the highly nonlinear and very complex engine. The design approach is presented in some detail and results for a failed valve are presented. These preliminary results verify that the developed parameter identification technique together with a neural network classifier can be used for this purpose

Fault detection and isolation for linear dynamic systems

As modern control systems and engineering processes become increasingly more complex and integrated, the consequences of system failures and faults can be disastrous environmentally and economically. This thesis considers the fault detection and isolation (FDI) problem for linear time-invariant (LTI) systems subject to faults, disturbances and model uncertainties. Firstly, a novel on-line approach to the robust FDI problem for linear discrete-time systems is proposed by using input/output measurement analysis over a finite estimation horizon. Upper and lower bounds on the fault signal are computed at each sampling instant so that a fault is detected and isolated when its upper bound is smaller than zero or its lower bound is larger than zero. Moreover, a subsequent-state-estimation technique, together with an estimation horizon update procedure are given to allow the on-line FDI process to be repeated in a moving horizon scheme. Secondly, an optimal solution to theH−/H∞ fault detection (FD) problem is given for linear time-invariant systems subject to faults, disturbances and model uncertainties by using an observer-based approach. A new performance index is developed to capture both fault detection and disturbance rejection requirements which is particularly suitable for handling model uncertainties. A class of optimal solutions to the problem is then given in the form of simple linear matrix inequalities (LMI) with two degrees of freedom. By appropriately choosing these degrees of freedom, fault isolation can also be achieved. Thirdly, in order to improve the FD performance and remove restrictive rank assumptions, routinely made in the literature, observer-based FD problems are investigated at a single frequency and over a finite frequency range, respectively. An optimal solution is derived such that, at a given frequency, the static observer generates a residual signal which minimizes the sensitivity of the residual to disturbances while maintaining a minimum level of sensitivity to faults. Then, an initial investigation is carried out for the FD problem over a finite frequency range. A solution is derived in the form of an LMI optimization by using the generalized KYP lemma followed by a linearization procedure. Conditions under which this solution is optimal are also derived. Fully worked out numerical examples, mostly from the literature, are given to illustrate the effectiveness of all the proposed schemes