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

Integrated fault estimation and accommodation design for discrete-time Takagi-Sugeno fuzzy systems with actuator faults

This paper addresses the problem of integrated robust fault estimation (FE) and accommodation for discrete-time Takagi–Sugeno (T–S) fuzzy systems. First, a multiconstrained reduced-order FE observer (RFEO) is proposed to achieve FE for discrete-time T–S fuzzy models with actuator faults. Based on the RFEO, a new fault estimator is constructed. Then, using the information of online FE, a new approach for fault accommodation based on fuzzy-dynamic output feedback is designed to compensate for the effect of faults by stabilizing the closed-loop systems. Moreover, the RFEO and the dynamic output feedback fault-tolerant controller are designed separately, such that their design parameters can be calculated readily. Simulation results are presented to illustrate our contributions

Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults

The goal of this paper is to describe a novel fault tolerant tracking control (FTTC) strategy based on robust fault estimation and compensation of simultaneous actuator and sensor faults. Within the framework of fault tolerant control (FTC) the challenge is to develop an FTTC design strategy for nonlinear systems to tolerate simultaneous actuator and sensor faults that have bounded first time derivatives. The main contribution of this paper is the proposal of a new architecture based on a combination of actuator and sensor Takagi-Sugeno (T-S) proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators together with a T-S dynamic output feedback control (TSDOFC) capable of time-varying reference tracking. Within this architecture the design freedom for each of the T-S estimators and the control system are available separately with an important consequence on robust L₂ norm fault estimation and robust L₂ norm closed-loop tracking performance. The FTTC strategy is illustrated using a nonlinear inverted pendulum example with time-varying tracking of a moving linear position reference. Keyword

Active fault-tolerant control of nonlinear systems with wind turbine application

The thesis concerns the theoretical development of Active Fault-Tolerant Control (AFTC) methods for nonlinear system via T-S multiple-modelling approach. The thesis adopted the estimation and compensation approach to AFTC within a tracking control framework. In this framework, the thesis considers several approaches to robust T-S fuzzy control and T-S fuzzy estimation: T-S fuzzy proportional multiple integral observer (PMIO); T-S fuzzy proportional-proportional integral observer (PPIO); T-S fuzzy virtual sensor (VS) based AFTC; T-S fuzzy Dynamic Output Feedback Control TSDOFC; T-S observer-based feedback control; Sliding Mode Control (SMC). The theoretical concepts have been applied to an offshore wind turbine (OWT) application study. The key developments that present in this thesis are:• The development of three active Fault Tolerant Tracking Control (FTTC) strategies for nonlinear systems described via T-S fuzzy inference modelling. The proposals combine the use of Linear Reference Model Fuzzy Control (LRMFC) with either the estimation and compensation concept or the control reconfiguration concept.• The development of T-S fuzzy observer-based state estimate fuzzy control strategy for nonlinear systems. The developed strategy has the capability to tolerate simultaneous actuator and sensor faults within tracking and regulating control framework. Additionally, a proposal to recover the Separation Principle has also been developed via the use of TSDOFC within the FTTC framework.• The proposals of two FTTC strategies based on the estimation and compensation concept for sustainable OWTs control. The proposals have introduced a significant attribute to the literature of sustainable OWTs control via (1) Obviating the need for Fault Detection and Diagnosis (FDD) unit, (2) Providing useful information to evaluate fault severity via the fault estimation signals.• The development of FTTC architecture for OWTs that combines the use of TSDOFC and a form of cascaded observers (cascaded analytical redundancy). This architecture is proposed in order to ensure the robustness of both the TSDOFC and the EWS estimator against the generator and rotor speed sensor faults.• A sliding mode baseline controller has been proposed within three FTTC strategies for sustainable OWTs control. The proposals utilise the inherent robustness of the SMC to tolerate some matched faults without the need for analytical redundancy. Following this, the combination of SMC and estimation and compensation framework proposed to ensure the close-loop system robustness to various faults.• Within the framework of the developed T-S fuzzy based FTTC strategies, a new perspective to reduce the T-S fuzzy control design conservatism problem has been proposed via the use of different control techniques that demand less design constraints. Moreover, within the SMC based FTTC, an investigation is given to demonstrate the SMC robustness against a wider than usual set of faults is enhanced via designing the sliding surface with minimum dimension of the feedback signals

Robust Fault-Tolerant Control for aircraft systems

The need to design controllers that guarantee both stability and performance upon the occurrence of faults has been an active area of research. To address this problem, in this thesis we present different methodologies to design robust controllers that guarantee both stability and robustness for actuator faults and uncertainties. In the first part of this thesis, we introduce the classical uncertainty formulation using Linear Fractional Transformation (LFT) and describe LFT\u27s special cases-norm bounded and convex polytopic uncertainty descriptions. Practical methods to formulate these uncertainty structures are described. In the same spirit, formulation of faults and their modeling for robust control system design is provided. In the second part of this thesis, we demonstrate the application of a Luenberger observer for fast Fault Diagnosis and Isolation (FDI). We describe the methodology to design a robust optimal control for actuator faults and present controller reconfiguration mechanism based on switching for the design of Fault Tolerant Control (FTC). System with both norm bounded uncertainties and actuator faults is formulated and an analytic method to find a robust stabilizing and guaranteed cost reliable controllers are also mentioned. To the end, we implement designed linear controllers in Boeing 747 (B747) nonlinear system. We also define and evaluate potential problems that arise in switching based FTC and their effect on the closed loop nonlinear system. Robustness of linear controllers in nonlinear B747 was evaluated using excessive Monte Carlo simulation and results are presented

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

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