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

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed methodPeer ReviewedPostprint (author's final draft

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Stabilization computation for a kind of uncertain switched systems using non-fragile sliding mode observer method

A non-fragile sliding mode control problem will be investigated in this article. The problem focuses on a kind of uncertain switched singular time-delay systems in which the state is not available. First, according to the designed non-fragile observer, we will construct an integral-type sliding surface, in which the estimated unmeasured state is used. Second, we synthesize a sliding mode controller. The reachability of the specified sliding surface could be proved by this sliding mode controller in a finite time. Moreover, linear matrix inequality conditions will be developed to check the exponential admissibility of the sliding mode dynamics. After that, the gain matrices designed will be given along with it. Finally, some numerical result will be provided, and the result can be used to prove the effectiveness of the method

Filtering for discrete-time nonhomogeneous Markov jump systems with uncertainties

This paper studies the problem of robust H1 filtering for a class of uncertain discrete-time nonhomogeneous Markov jump systems. The time-varying jump transition probability matrix is described by a polytope. By Lyapunov function approach, mode-dependent and variation-dependent H1 filter is designed such that the resulting error dynamic system is stochastically stable and has a prescribed H1 performance index. A numerical example is given to illustrate the effectiveness of the developed techniques

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance

Predictive control approaches to fault tolerant control of wind turbines

This thesis focuses on active fault tolerant control (AFTC) of wind turbine systems. Faults in wind turbine systems can be in the form of sensor faults, actuator faults, or component faults. These faults can occur in different locations, such as the wind speed sensor, the generator system, drive train system or pitch system. In this thesis, some AFTC schemes are proposed for wind turbine faults in the above locations. Model predictive control (MPC) is used in these schemes to design the wind turbine controller such that system constraints and dual control goals of the wind turbine are considered. In order to deal with the nonlinearity in the turbine model, MPC is combined with Takagi-Sugeno (T-S) fuzzy modelling. Different fault diagnosis methods are also proposed in different AFTC schemes to isolate or estimate wind turbine faults.The main contributions of the thesis are summarized as follows:A new effective wind speed (EWS) estimation method via least-squares support vector machines (LSSVM) is proposed. Measurements from the wind turbine rotor speed sensor and the generator speed sensor are utilized by LSSVM to estimate the EWS. Following the EWS estimation, a wind speed sensor fault isolation scheme via LSSVM is proposed.A robust predictive controller is designed to consider the EWS estimation error. This predictive controller serves as the baseline controller for the wind turbine system operating in the region below rated wind speed.T-S fuzzy MPC combining MPC and T-S fuzzy modelling is proposed to design the wind turbine controller. MPC can deal with wind turbine system constraints externally. On the other hand, T-S fuzzy modelling can approximate the nonlinear wind turbine system with a linear time varying (LTV) model such that controller design can be based on this LTV model. Therefore, the advantages of MPC and T-S fuzzy modelling are both preserved in the proposed T-S fuzzy MPC.A T-S fuzzy observer, based on online eigenvalue assignment, is proposed as the sensor fault isolation scheme for the wind turbine system. In this approach, the fuzzy observer is proposed to deal with the nonlinearity in the wind turbine system and estimate system states. Furthermore, the residual signal generated from this fuzzy observer is used to isolate the faulty sensor.A sensor fault diagnosis strategy utilizing both analytical and hardware redundancies is proposed for wind turbine systems. This approach is proposed due to the fact that in the real application scenario, both analytical and hardware redundancies of wind turbines are available for designing AFTC systems.An actuator fault estimation method based on moving horizon estimation (MHE) is proposed for wind turbine systems. The estimated fault by MHE is then compensated by a T-S fuzzy predictive controller. The fault estimation unit and the T-S fuzzy predictive controller are combined to form an AFTC scheme for wind turbine actuator faults

Super-Twisting-Algorithm-Based Terminal Sliding Mode Control for a Bioreactor System

This study proposes a class of super-twisting-algorithm-based (STA-based) terminal sliding mode control (TSMC) for a bioreactor system with second-order type dynamics. TSMC not only can retain the advantages of conventional sliding mode control (CSMC), including easy implementation, robustness to disturbances, and fast response, but also can make the system states converge to the equivalent point in a finite amount of time after the system states intersect the sliding surface. The chattering phenomena in TSMC will originally exist on the sliding surface after the system states achieve the sliding surface and before the system states reach the equivalent point. However, by using the super twisting algorithm (STA), the chattering phenomena can be obviously reduced. The proposed method is also compared with two other methods: (1) CSMC without STA and (2) TSMC without STA. Finally, the control schemes are applied to the control of a bioreactor system to illustrate the effectiveness and applicability. Simulation results show that it can achieve better performance by using the proposed method