A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

A general formulation for fault detection in stochastic continuous-time dynamical systems

In this work, a general formulation for fault detection in stochastic continuoustime dynamical systems is presented. This formulation is based on the definition of a pre-Hilbert space so that orthogonal projection techniques, based on the statistics of the involved stochastic processes can be applied. The general setting gathers different existing schemes within a unifying framework

A fault detection scheme for time-delay systems using minimum-order functional observers

This paper presents a method for designing residual generators using minimum-order functional observers to detect actuator and component faults in time-delay systems. Existence conditions of the residual generators and functional observers are first derived, and then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing minimum-order functional observers to detect faults in the system. The advantages of having minimum-order observers are obvious from the economical and practical points of view as cost saving and simplicity can be achieved, particularly when dealing with high-order complex systems. Extensive numerical examples are given to illustrate the proposed fault detection scheme. In all the numerical examples, we design minimum-order residual generators and functional observers to detect faults in the system

Robust model-based fault diagnosis for chemical process systems

Fault detection and diagnosis have gained central importance in the chemical process industries over the past decade. This is due to several reasons, one of them being that copious amount of data is available from a large number of sensors in process plants. Moreover, since industrial processes operate in closed loop with appropriate output feedback to attain certain performance objectives, instrument faults have a direct effect on the overall performance of the automation system. Extracting essential information about the state of the system and processing the measurements for detecting, discriminating, and identifying abnormal readings are important tasks of a fault diagnosis system. The goal of this dissertation is to develop such fault diagnosis systems, which use limited information about the process model to robustly detect, discriminate, and reconstruct instrumentation faults. Broadly, the proposed method consists of a novel nonlinear state and parameter estimator coupled with a fault detection, discrimination, and reconstruction system. The first part of this dissertation focuses on designing fault diagnosis systems that not only perform fault detection and isolation but also estimate the shape and size of the unknown instrument faults. This notion is extended to nonlinear processes whose structure is known but the parameters of the process are a priori uncertain and bounded. Since the uncertainty in the process model and instrument fault detection interact with each other, a novel two-time scale procedure is adopted to render overall fault diagnosis. Further, some techniques to enhance the convergence properties of the proposed state and parameter estimator are presented. The remaining part of the dissertation extends the proposed model-based fault diagnosis methodology to processes for which first principles modeling is either expensive or infeasible. This is achieved by using an empirical model identification technique called subspace identification for state-space characterization of the process. Finally the proposed methodology for fault diagnosis has been applied in numerical simulations to a non-isothermal CSTR (continuous stirred tank reactor), an industrial melter process, and a debutanizer plant

Model-based fault diagnosis for aerospace systems: a survey

http://pig.sagepub.com/content/early/2012/01/06/0954410011421717International audienceThis survey of model-based fault diagnosis focuses on those methods that are applicable to aerospace systems. To highlight the characteristics of aerospace models, generic nonlinear dynamical modeling from flight mechanics is recalled and a unifying representation of sensor and actuator faults is presented. An extensive bibliographical review supports a description of the key points of fault detection methods that rely on analytical redundancy. The approaches that best suit the constraints of the field are emphasized and recommendations for future developments in in-flight fault diagnosis are provided

Robust Diagnosis by Observer Using the Bond Graph Approach

In this chapter, we have proposed a Luenberger observer linear systems diagnostic technique using the bond graph. Indeed, an observer can reconstruct or estimate the current state of a real system using the available measurements, without prior knowledge of the initial conditions. In addition, it allows to estimate the nonmeasurable states of a system. The design of the observer is carried out using graphical methods from the structural properties of the model bond graph becomes simple and practical to build. We presented the bond graph approach for the construction of a full-order observer and proposed a new BG-based observer diagnostic method. Subsequently, we presented the uncertain parameter systems modeled by the bond graph approach, and we also proposed a new method for diagnosing systems with uncertain parameters by Luenberger observer. In the last part of this chapter, we developed and proposed an observer bench diagnosis technique (BG-DOS/BG-GOS) to detect and locate defects

Estimation of Liquid Level in a Harsh Environment Using Chaotic Observer

The increased demand for liquid level measurement has been a key factor in designing accurate and reliable control systems. Here, a study was carried out to calculate the liquid level in a tank using a pressure sensor for changes in inlet liquid parameters like temperature, density and velocity. Prediction of their variables for the long term is essential due to the randomness present in the input and measurement. Hence, observer design for state estimation of a non-linear dynamic system with uncertainties in the measurement and process becomes important. This work provides a feedback observer solution for a system with multiple inputs and single measurable output. A full state observer model is developed to estimate a system’s states with a sensor placed at a definite position from the pipe’s input point through which the liquid flows at different densities and temperatures. Using the observability properties, Luenberger full state observer is designed by various methods, verified using MATLAB and SIMULINK for the system state estimation. To incorporate process noise and measurement noise, the Kalman estimator is integrated with the system. Chaotic systems are susceptible to initial conditions, variations in parameters and are complex dynamic systems. However, providing consistently precise measurements through particular meters necessitates time-consuming computations that can be reduced by employing machine learning approaches that make use of optimizers. The results obtained are compared with the prediction models obtained using Artificial Neural Networks and are validated through the readings obtained from the experimental setup

Observer-based Fault Diagnosis: Applications to Exothermic Continuous Stirred Tank Reactors

For chemical engineering dynamic systems, there is an increasing demand for better process performance, high product quality, absolute reliability & safety, maximum cost efficiency and less environmental impact. Improved individual process components and advanced automatic control techniques have brought significant benefits to the chemical industry. However, fault-free operation of processes cannot be guaranteed. Timely fault diagnosis and proper management can help to avoid or at least minimize the undesirable consequences. There are many techniques for fault diagnosis, and observer-based methods have been widely studied and have proved to be efficient for fault diagnosis. The basic idea of an observer-based approach is to generate a specific residual signal which carries the information of specific faults, as well as the information of process disturbances, model uncertainties, other faults and measurement noises. For fault diagnosis, the residual should be sensitive to faults and insensitive to other unknown inputs. With this feature, faults can be easily detected and may be isolated and identified. This thesis applied an observer-based fault diagnosis method to three exothermic CSTR case studies. In order to improve the operational safety of exothermic CSTRs with risks of runaway reactions and explosion, fault diagnostic observers are built for fault detection, isolation and identification. For this purpose, different types of most common faults have been studied in different reaction systems. For each fault, a specific observer and the corresponding residual is built, which works as an indicator of that fault and is robust to other unknown inputs. For designing linear observers, the original nonlinear system is linearized at steady state, and the observer is designed based on the linearized system. However, in the simulations, the observer is tested on the nonlinear system instead of the linearized system. In addition, an efficient & effective general MATLAB program has been developed for fault diagnosis observer design. Extensive simulation studies have been performed to test the fault diagnostic observer on exothermic CSTRs. The results show that the proposed fault diagnosis scheme can be directly implemented and it works well for diagnosing faults in exothermic chemical reactors