Fault estimation and fault-tolerant control for discrete-time dynamic systems

In this paper, a novel discrete-time estimator is proposed, which is employed for simultaneous estimation of system states, and actuator/sensor faults in a discrete-time dynamic system. The existence of the discrete-time simultaneous estimator is proven mathematically. The systematic design procedure for the derivative and proportional observer gains is addressed, enabling the estimation error dynamics to be internally proper and stable, and robust against the effects from the process disturbances, measurement noise, and faults. Based on the estimated fault signals and system states, a discrete-time fault-tolerant design approach is addressed, by which the system may recover the system performance when actuator/sensor faults occur. Finally, the proposed integrated discrete-time fault estimation and fault-tolerant control technique is applied to the vehicle lateral dynamics, which demonstrates the effectiveness of the developed techniques

Discrete-Time Observer Design for Sensorless Synchronous Motor Drives

This paper deals with the speed and position estimation of interior permanent-magnet synchronous motor (IPM) and synchronous reluctance motor (SyRM) drives. A speed-adaptive full-order observer is designed and analyzed in the discrete-time domain. The observer design is based on the exact discrete-time motor model, which inherently takes the delays in the control system into account. The proposed observer is experimentally evaluated using a 6.7-kW SyRM drive. The analysis and experimental results indicate that major performance improvements can be obtained with the direct discrete-time design, especially if the sampling frequency is relatively low compared to the fundamental frequency. The ratio below 10 between the sampling and fundamental frequencies is achieved in experiments with the proposed discrete-time design.Peer reviewe

An LMI Approach to Discrete-Time Observer Design with Stochastic Resilience

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant or the measurement model. The present work addresses the important problem of stochastic resilience or non-fragility of a discrete-time Luenberger observer which is the maintenance of convergence and/or performance when the observer is erroneously implemented possibly due to computational errors i.e. round off errors in digital implementation or sensor errors, etc. A common linear matrix inequality framework is presented to address the stochastic resilient design problem for various performance criteria in the implementation based on the knowledge of an upper bound on the variance of the random error in the observer gain. Present results are compared to earlier designs for stochastic robustness. Illustrative examples are given to complement the theoretical results

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

Resilient Observer Design for Discrete-Time Nonlinear Systems with General Criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based resilient observer design approach is presented to guarantee the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of bounded perturbations on the gain. Some simulation examples are included to illustrate the proposed design methodology

H ∞ sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

Copyright @ 2012 John Wiley & SonsIn this paper, the H ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme

H∞ observer design for a class of nonlinear discrete systems

Necessary and sufficient conditions are presented under which a discrete-time autonomous system with outputs is locally diffeomorphic to an output-scaled linear observable system or an output-scaled nonlinear system in the observer form. As a consequence of such characterizations, the nonlinear observer design problem is studied for a broader class of discrete-time nonlinear systems by using the exact linearization technique that is based on the differential geometric approac

A hybrid observer for practical observability of linear stochastic systems

This paper focuses on the problem of observability and observer design for linear stochastic systems. To introduce our idea, we first construct an idealistic observer. This idealistic observer is not causal as it requires perfect knowledge of the Brownian motion. However, after introducing an a posteriori method to reconstruct the variations of the Brownian motion in discrete time, we propose a realistic hybrid observer which approximates the idealistic observer. The performance of this hybrid observer can be made arbitrarily close to that of the idealistic observer. Numerical simulations illustrate the results of the paper

Observers Design for a Class of Lipschitz Discrete-Time Systems with Time-Delay

The observer design problem for nonlinear time-delay systems becomes more and more a subject of research in constant evolution Germani et al. (2002), Germani & Pepe (2004), Aggoune et al. (1999), Raff & Allgöwer (2006), Trinh et al. (2004), Xu et al. (2004), Zemouche et al. (2006), Zemouche et al. (2007). Indeed, time-delay is frequently encountered in various practical systems, such as chemical engineering systems, neural networks and population dynamic model. One of the recent application of time-delay is the synchronization and information recovery in chaotic communication systems Cherrier et al. (2005). In fact, the time-delay is added in a suitable way to the chaotic system in the goal to increase the complexity of the chaotic behavior and then to enhance the security of communication systems. On the other hand, contrary to nonlinear continuous-time systems, little attention has been paid toward discrete-time nonlinear systems with time-delay. We refer the readers to the few existing references Lu & Ho (2004a) and Lu & Ho (2004b), where the authors investigated the problem of robust H∞ observer design for a class of Lipschitz time-delay systems with uncertain parameters in the discrete-time case. Their method show the stability of the state of the system and the estimation error simultaneously. This chapter deals with observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay. The main result lies in the use of a new structure of the proposed observer inspired from Fan & Arcak (2003). Using a Lyapunov-Krasovskii functional, a new nonrestrictive synthesis condition is obtained. This condition, expressed in term of LMI, contains more degree of freedom than those proposed by the approaches available in literature. Indeed, these last use a simple Luenberger observer which can be derived from the general form of the observer proposed in this paper by neglecting some observer gains. An extension of the presented result to H∞ performance analysis is given in the goal to take into account the noise which affects the considered system. A more general LMI is established. The last section is devoted to systems with differentiable nonlinearities. In this case, based on the use of the Differential Mean Value Theorem (DMVT), less restrictive synthesis conditions are proposed