Model based fault diagnosis and prognosis of class of linear and nonlinear distributed parameter systems modeled by partial differential equations

With the rapid development of modern control systems, a significant number of industrial systems may suffer from component failures. An accurate yet faster fault prognosis and resilience can improve system availability and reduce unscheduled downtime. Therefore, in this dissertation, model-based prognosis and resilience control schemes have been developed for online prediction and accommodation of faults for distributed parameter systems (DPS). First, a novel fault detection, estimation and prediction framework is introduced utilizing a novel observer for a class of linear DPS with bounded disturbance by modeling the DPS as a set of partial differential equations. To relax the state measurability in DPS, filters are introduced to redesign the detection observer. Upon detecting a fault, an adaptive term is activated to estimate the multiplicative fault and a tuning law is derived to tune the fault parameter magnitude. Then based on this estimated fault parameter together with its failure limit, time-to-failure (TTF) is derived for prognosis. A novel fault accommodation scheme is developed to handle actuator and sensor faults with boundary measurements. Next, a fault isolation scheme is presented to differentiate actuator, sensor and state faults with a limited number of measurements for a class of linear and nonlinear DPS. Subsequently, actuator and sensor fault detection and prediction for a class of nonlinear DPS are considered with bounded disturbance by using a Luenberger observer. Finally, a novel resilient control scheme is proposed for nonlinear DPS once an actuator fault is detected by using an additional boundary measurement. In all the above methods, Lyapunov analysis is utilized to show the boundedness of the closed-loop signals during fault detection, prediction and resilience under mild assumptions --Abstract, page iv

Delay-Adaptive Control of First-order Hyperbolic PIDEs

We develop a delay-adaptive controller for a class of first-order hyperbolic partial integro-differential equations (PIDEs) with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is transformed into a transport partial differential equation (PDE) with unknown propagation speed cascaded with a PIDE. A parameter update law is designed using a Lyapunov argument and the infinite-dimensional backstepping technique to establish global stability results. Furthermore, the well-posedness of the closed-loop system is analyzed. Finally, the effectiveness of the proposed method was validated through numerical simulation

Model based fault diagnosis and prognosis of nonlinear systems

Rapid technological advances have led to more and more complex industrial systems with significantly higher risk of failures. Therefore, in this dissertation, a model-based fault diagnosis and prognosis framework has been developed for fast and reliable detection of faults and prediction of failures in nonlinear systems. In the first paper, a unified model-based fault diagnosis scheme capable of detecting both additive system faults and multiplicative actuator faults, as well as approximating the fault dynamics, performing fault type determination and time-to-failure determination, is designed. Stability of the observer and online approximator is guaranteed via an adaptive update law. Since outliers can degrade the performance of fault diagnostics, the second paper introduces an online neural network (NN) based outlier identification and removal scheme which is then combined with a fault detection scheme to enhance its performance. Outliers are detected based on the estimation error and a novel tuning law prevents the NN weights from being affected by outliers. In the third paper, in contrast to papers I and II, fault diagnosis of large-scale interconnected systems is investigated. A decentralized fault prognosis scheme is developed for such systems by using a network of local fault detectors (LFD) where each LFD only requires the local measurements. The online approximators in each LFD learn the unknown interconnection functions and the fault dynamics. Derivation of robust detection thresholds and detectability conditions are also included. The fourth paper extends the decentralized fault detection from paper III and develops an accommodation scheme for nonlinear continuous-time systems. By using both detection and accommodation online approximators, the control inputs are adjusted in order to minimize the fault effects. Finally in the fifth paper, the model-based fault diagnosis of distributed parameter systems (DPS) with parabolic PDE representation in continuous-time is discussed where a PDE-based observer is designed to perform fault detection as well as estimating the unavailable system states. An adaptive online approximator is incorporated in the observer to identify unknown fault parameters. Adaptive update law guarantees the convergence of estimations and allows determination of remaining useful life --Abstract, page iv

Decentralized sliding mode control and estimation for large-scale systems

This thesis concerns the development of an approach of decentralised robust control and estimation for large scale systems (LSSs) using robust sliding mode control (SMC) and sliding mode observers (SMO) theory based on a linear matrix inequality (LMI) approach. A complete theory of decentralized first order sliding mode theory is developed. The main developments proposed in this thesis are: The novel development of an LMI approach to decentralized state feedback SMC. The proposed strategy has good ability in combination with other robust methods to fulfill specific performance and robustness requirements. The development of output based SMC for large scale systems (LSSs). Three types of novel decentralized output feedback SMC methods have been developed using LMI design tools. In contrast to more conventional approaches to SMC design the use of some complicated transformations have been obviated. A decentralized approach to SMO theory has been developed focused on the Walcott-Żak SMO combined with LMI tools. A derivation for bounds applicable to the estimation error for decentralized systems has been given that involves unknown subsystem interactions and modeling uncertainty. Strategies for both actuator and sensor fault estimation using decentralized SMO are discussed.The thesis also provides a case study of the SMC and SMO concepts applied to a non-linear annealing furnace system modelderived from a distributed parameter (partial differential equation) thermal system. The study commences with a lumped system decentralised representation of the furnace derived from the partial differential equations. The SMO and SMC methods derived in the thesis are applied to this lumped parameter furnace model. Results are given demonstrating the validity of the methods proposed and showing a good potential for a valuable practical implementation of fault tolerant control based on furnace temperature sensor faults

Polynomial Fuzzy Observer-Based Feedback Control for Nonlinear Hyperbolic PDEs Systems

This article explores the observer-based feedback control problem for a nonlinear hyperbolic partial differential equations (PDEs) system. Initially, the polynomial fuzzy hyperbolic PDEs (PFHPDEs) model is established through the utilization of the fuzzy identification approach, derived from the nonlinear hyperbolic PDEs model. Various types of state estimation and controller design problems for the polynomial fuzzy PDEs system are discussed concerning the state estimation problem. To investigate the relaxed stability problem, Euler’s homogeneous theorem, Lyapunov–Krasovskii functional with polynomial matrices (LKFPM), and the sum-of-squares (SOSs) approach are adopted. The exponential stabilization condition is formulated in terms of the spatial-derivative-SOSs (SD-SOSs). Additionally, a segmental algorithm is developed to find the feasible solution for the SD-SOS condition. Finally, a hyperbolic PDEs system and several numerical examples are provided to illustrate the validity and effectiveness of the proposed results

Observation and control of PDE with disturbances

In this Thesis, the problem of controlling and Observing some classes of distributed parameter systems is addressed. The particularity of this work is to consider partial differential equations (PDE) under the effect of external unknown disturbances. We consider generalized forms of two popular parabolic and hyperbolic infinite dimensional dynamics, the heat and wave equations. Sliding-mode control is used to achieve the control goals, exploiting the robustness properties of this robust control technique against persistent disturbances and parameter uncertainties

Geometric Fault Detection and Isolation of Infinite Dimensional Systems

A broad class of dynamical systems from chemical processes to flexible mechanical structures, heat transfer and compression processes in gas turbine engines are represented by a set of partial differential equations (PDE). These systems are known as infinite dimensional (Inf-D) systems. Most of Inf-D systems, including PDEs and time-delayed systems can be represented by a differential equation in an appropriate Hilbert space. These Hilbert spaces are essentially Inf-D vector spaces, and therefore, they are utilized to represent Inf-D dynamical systems. Inf-D systems have been investigated by invoking two schemes, namely approximate and exact methods. Both approaches extend the control theory of ordinary differential equation (ODE) systems to Inf-D systems, however by utilizing two different methodologies. In the former approach, one needs to first approximate the original Inf-D system by an ODE system (e.g. by using finite element or finite difference methods) and then apply the established control theory of ODEs to the approximated model. On the other hand, in the exact approach, one investigates the Inf-D system without using any approximation. In other words, one first represents the system as an Inf-D system and then investigates it in the corresponding Inf-D Hilbert space by extending and generalizing the available results of finite-dimensional (Fin-D) control theory. It is well-known that one of the challenging issues in control theory is development of algorithms such that the controlled system can maintain the required performance even in presence of faults. In the literature, this property is known as fault tolerant control. The fault detection and isolation (FDI) analysis is the first step in order to achieve this goal. For Inf-D systems, the currently available results on the FDI problem are quite limited and restricted. This thesis is mainly concerned with the FDI problem of the linear Inf-D systems by using both approximate and exact approaches based on the geometric control theory of Fin-D and Inf-D systems. This thesis addresses this problem by developing a geometric FDI framework for Inf-D systems. Moreover, we implement and demonstrate a methodology for applying our results to mathematical models of a heat transfer and a two-component reaction-diffusion processes. In this thesis, we first investigate the development of an FDI scheme for discrete-time multi-dimensional (nD) systems that represent approximate models for Inf-D systems. The basic invariant subspaces including unobservable and unobservability subspaces of one-dimensional (1D) systems are extended to nD models. Sufficient conditions for solvability of the FDI problem are provided, where an LMI-based approach is also derived for the observer design. The capability of our proposed FDI methodology is demonstrated through numerical simulation results to an approximation of a hyperbolic partial differential equation system of a heat exchanger that is represented as a two-dimensional (2D) system. In the second part, an FDI methodology for the Riesz spectral (RS) system is investigated. RS systems represent a large class of parabolic and hyperbolic PDE in Inf-D systems framework. This part is mainly concerned with the equivalence of different types of invariant subspaces as defined for RS systems. Necessary and sufficient conditions for solvability of the FDI problem are developed. Moreover, for a subclass of RS systems, we first provide algorithms (for computing the invariant subspaces) that converge in a finite and known number of steps and then derive the necessary and sufficient conditions for solvability of the FDI problem. Finally, by generalizing the results that are developed for RS systems necessary and sufficient conditions for solvability of the FDI problem in a general Inf-D system are derived. Particularly, we first address invariant subspaces of Fin-D systems from a new point of view by invoking resolvent operators. This approach enables one to extend the previous Fin-D results to Inf-D systems. Particularly, necessary and sufficient conditions for equivalence of various types of conditioned and controlled invariant subspaces of Inf-D systems are obtained. Duality properties of Inf-D systems are then investigated. By introducing unobservability subspaces for Inf-D systems the FDI problem is formally formulated, and necessary and sufficient conditions for solvability of the FDI problem are provided