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

H∞ fuzzy control for systems with repeated scalar nonlinearities and random packet losses

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the H∞ fuzzy control problem for a class of systems with repeated scalar nonlinearities and random packet losses. A modified Takagi-Sugeno (T-S) fuzzy model is proposed in which the consequent parts are composed of a set of discrete-time state equations containing a repeated scalar nonlinearity. Such a model can describe some well-known nonlinear systems such as recurrent neural networks. The measurement transmission between the plant and controller is assumed to be imperfect and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to represent the phenomenon of random packet losses. Attention is focused on the analysis and design of H∞ fuzzy controllers with the same repeated scalar nonlinearities such that the closed-loop T-S fuzzy control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities, which can be readily solved by using standard numerical software. Two examples are given to illustrate the effectiveness of the proposed design method

Actuator and sensor fault estimation based on a proportional-integral quasi-LPV observer with inexact scheduling parameters

© 2019. ElsevierThis paper presents a method for actuator and sensor fault estimation based on a proportional-integral observer (PIO) for a class of nonlinear system described by a polytopic quasi-linear parameter varying (qLPV) mathematical model. Contrarily to the traditional approach, which considers measurable or unmeasurable scheduling parameters, this work proposes a methodology that considers inexact scheduling parameters. This condition is present in many physical systems where the scheduling parameters can be affected by noise, offsets, calibration errors, and other factors that have a negative impact on the measurements. A H8 performance criterion is considered in the design in order to guarantee robustness against sensor noise, disturbance, and inexact scheduling parameters. Then, a set of linear matrix inequalities (LMIs) is derived by the use of a quadratic Lyapunov function. The solution of the LMI guarantees asymptotic stability of the PIO. Finally, the performance and applicability of the proposed method are illustrated through a numerical experiment in a nonlinear system.Peer ReviewedPostprint (author's final draft

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

Robust unknown input observer for state and fault estimation in discrete-time Takagi-Sugeno systems

In this paper, a robust unknown input observer (UIO) for the joint state and fault estimation in discrete-time Takagi-Sugeno (TS) systems is presented. The proposed robust UIO, by applying the H-infinity framework, leads to a less restrictive design procedure with respect to recent results found in the literature. The resulting design procedure aims at achieving a prescribed attenuation level with respect to the exogenous disturbances, while obtaining at the same time the convergence of the observer with a desired bound on the decay rate. An extension to the case of unmeasurable premise variables is also provided. Since the design conditions reduce to a set of linear matrix inequalities that can be solved efficiently using the available software, an evident advantage of the proposed approach is its simplicity. The final part of the paper presents an academic example and a real application to a multi-tank system, which exhibit clearly the performance and effectiveness of the proposed strategy.Postprint (author's final draft

Robust fault estimation for stochastic Takagi-Sugeno fuzzy systems

Nowadays, industrial plants are calling for high-performance fault diagnosis techniques to meet stringent requirements on system availability and safety in the event of component failures. This paper deals with robust fault estimation problems for stochastic nonlinear systems subject to faults and unknown inputs relying on Takagi-Sugeno fuzzy models. Augmented approach jointly with unknown input observers for stochastic Takagi-Sugeno models is exploited here, which allows one to estimate both considered faults and full system states robustly. The considered unknown inputs can be either completely decoupled or partially decoupled by observers. For the un-decoupled part of unknown inputs, which still influence error dynamics, stochastic input-to-state stability properties are applied to take nonzero inputs into account and sufficient conditions are achieved to guarantee bounded estimation errors under bounded unknown inputs. Linear matrix inequalities are employed to compute gain matrices of the observer, leading to stochastic input-to-state-stable error dynamics and optimization of the estimation performances against un-decoupled unknown inputs. Finally, simulation on wind turbine benchmark model is applied to validate the performances of the suggested fault reconstruction methodologies

Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process

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

Integrated design of fault-tolerant control for nonlinear systems based on fault estimation and T-S fuzzy modelling

This paper proposes an integrated design of faulttolerant control (FTC) for nonlinear systems using Takagi-Sugeno (T-S) fuzzy models in the presence of modelling uncertainty along with actuator/sensor faults and external disturbance. An augmented state unknown input observer is proposed to estimate the faults and system states simultaneously, and using the estimates an FTC controller is developed to ensure robust stability of the closed-loop system. The main challenge arises from the bi-directional robustness interactions since the fault estimation (FE) and FTC functions have an uncertain effect on each other. The proposed strategy uses a single-step linear matrix inequality formulation to integrate together the designs of FE and FTC functions to satisfy the required robustness. The integrated strategy is demonstrated to be effective through a tutorial example of an inverted pendulum system (based on robust T-S fuzzy designs)