This paper deals with the fault-tolerant control (FTC) problem for a class of linear time-invariant systems with time-varying actuator faults and uncertainties. For more general consideration, the faults and uncertainties are supposed to depend on the states of systems and unknown constant bounds. For the sake of eliminating the effects of such state-dependent faults and uncertainties automatically, a switching control strategy which is formulated by a sign function is designed to configure controller based on system’s states. And some adjustable control parameters are updated via designing adaptive laws. Based on the information from switching function and the adaptive estimation mechanism, the robust adaptive controllers are constructed to compensate for the effects of faults and uncertainties. Through Lyapunov functions and adaptive schemes, the asymptotic stability of the resulting adaptive FTC uncertain system can be achieved. The effectiveness of the proposed design is illustrated via a rocket fairing structural-acoustic model.

In recent years, the safety, reliability, and validity of practical systems have attracted growing attention. However, during the operation of systems, the occurrence of some critical and unpredictable faults of system components, especially in actuators and sensors, is unavoidable and intolerable. As we know, actuators afford the operating function of the whole system. In the event of an actuator fault, the traditional feedback control design may result in unsatisfactory performance of systems or even cause other catastrophic consequence. Thus, fault-tolerant control (FTC) designs are necessary to make the system have capability of tolerating potential actuator faults and to improve the safety and reliability of systems.

In the existing literatures, there are many valuable research results on fault-tolerant control designs in time-delay systems [

Recently, as adaptive technique has capability of quick and automatic response for estimating unknown parameters at each instant, there has been a growing interest in designing active FTC schemes for systems based on adaptive methods. The faults of loss actuator effectiveness and parameterizable stuck-actuator faults were studied in [

It should be mentioned that the compensation of uncertainties have not been fully considered in the existing robust FTC literature, though some works considered the robust fault-tolerant compensation control with external disturbances in [

In this paper, a novel switching adaptive method is proposed to solve the robust fault-tolerant control compensation problem of a class of uncertain linear systems. Similar to the adaptive controllers designed in [

The rest of the paper is organized as follows. The robust fault-tolerant control problem formulation is described in Section

In this paper, we consider that a linear time-invariant uncertain continuous-time model captured the following state-space equation:

Similar to [

According to the practical case, the occurrence of time-varying unparametrizable faults may be related to the current system states. Thus, we assume that the unparametrizable stuck fault in (

Here, we define the following sets:

Taking actuator faults (

Hence, considering actuator faults (

Here, we consider the case of state-feedback fault-tolerant controller design. Thus, we assume that all the states of system are available at every instant and all pairs

For any vector

Then, the main objective of this paper is to construct a robust adaptive state feedback controller

For the sake of eliminating the effects of actuator faults and uncertainties completely, a switching adaptive control strategy is proposed in this section. Some adaptive laws are designed to construct the controller with the estimation signals of the unknown actuator failure parameters and upper bound of uncertainties. Then, the asymptotically stable results of the closed-loop FTC system via state feedback are presented in Theorem

Consider a linear time-invariant uncertain FTC model described by (

Therefore, substituting (

On the other hand, we denote that

In the following, we denote a solution of the closed-loop system and the error system by

Consider the adaptive closed-loop system described by (

For the adaptive closed-loop system described by (

According to the definition of

Thus, by the light of the inequality of (

On the other hand, according to the definition of (

Then, it follows from (

Hence, it is easy to see that

Theorem

Consider uncertain system (

Similar to the proof of Theorem

From the fact of

Since

Then, it follows from (

Hence, it indicates that, for any

Theorem

From Theorems

Consider uncertain system (

The proof of this corollary is omitted. It is quite similar to the one of Theorem

From Theorems

Actually, several methods have been proposed to completely compensate for the effects of time-varying matched perturbations and redundant actuator faults (e.g., [

Similar to [

With the similar simulation of [

For the sake of verifying the effectiveness of the proposed adaptive method, the simulations are given with the following parameters and initial conditions:

The following faulty case is considered in the simulations; that is, before 8 second, the systems operate in normal case and the uncertainties

Figure

Response curves of the system’s states

Response curves of the adaptive adjustable control parameters

This paper presents a switching adaptive method for robust fault-tolerant control problem of actuator faults and compensation in continuous-time linear systems. The fault model of normal operation, loss of effectiveness, outage, and stuck are considered, and the bias-/stuck-actuator faults and system uncertainties are supposed to be satisfying a state-dependent condition. The switching robust adaptive control schemes are constructed based on a sign function and some updating adaptation laws which are used to estimate the controller parameters on line. The proposed state feedback controllers can automatically compensate the fault and uncertainty effects and guarantee the asymptotically stable of the system. A numerical example has shown the effectiveness of the proposed method.

One of the further research topics is to eliminate the assumption of knowing the dependency rate of states

This work is supported by the National Natural Science Foundation (Grant nos. 61104029, 61273155, and 61203087), Program for Liaoning Excellent Talents in University (LNET) (Grant no. LJQ2013122), the science and technology plan of Liaoning Province (2011219011), the Natural Science Foundation of Liaoning Province (Grant no. 201202156), and the Scientific Research Foundation for Doctor of Liaoning Province (Grant no. 20121040).

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