The thesis contains 6 chapters which are organized as follows.
• Chapter 2: In this chapter, a new direct adaptive robust controller is designed using a back- stepping technique augmented with an adaptive second order sliding mode control strategy to compensate actuator failures in nonlinear systems with norm bounded modeling uncertainties.
Output transient performance improvement is achieved through finite time convergence of the error variable obtained at the last coordinate of backstepping. Different from other ARC strate- gies, it separately estimates the fault parameters and the upper bound on modeling uncertainties.
Compared to ASMC, the most celebrated ARC method, input usage is decreased by the use of a second order sliding mode controller; without compromising the robustness and asymptotic stability of output tracking both in nominal and post failure scenarios.
• Chapter 3: A multiple model based backstepping controller with two layer adaptation is pro- posed in the context of FTC of nonlinear uncertain systems. The problem of adaptive compensa- tion of infinite actuator failures is discussed followed by proofs which show the inability of direct adaptive control strategies and the method proposed in Chapter 2, to ensure stable solutions in
ring actuator failures apart from system uncertainties followed by transient performance analysis.
The quantification of transient performance is provided to show the performance superiority over single model adaptive control. Following the results, the proposed AMMFTC is applied to non- linear coupled MIMO systems to compensate finite actuator failures and ensure enhancement of transient and steady state output performance.
• Chapter 4: A new finite time adaptation based controller (FTAC) is designed to ensure finite time output nominal performance recovery and promising transient behavior both at start-up and post failure instances. The proposed FTAC is then extended for applications to compensate infinite actuator failures followed by a rigorous stability proof to arrive at the boundedness of tracking error in the absolute sense. The theoretical results are justified through simulation results. Thereafter, the proposed adaptive controller with finite time adaptation is adopted in the design of FTC for a MIMO coupled nonlinear system. An involved analysis followed by simulation and experimental results demonstrate the proficiency of the control algorithm.
• Chapter 5: This chapter proposes a novel finite time converging adaptive disturbance observer based backstepping controller for nonlinear uncertain systems. The system uncertainties and those induced due to actuator failures do not require any kind of parametrization for DOB based estimation and backstepping control. Rigorous stability analysis proves the closed loop signal boundedness and global asymptotic stability of the tracking error in the event of infinite and finite actuator failures for all time. Fast and exact disturbance estimation at steady state are indeed very important to the improvement of output transient and steady state performance.
The bidirectional interactions between control-DOB estimator pair is reduced to a unidirectional interaction from the observer to the controller and hence the separation principle is satisfied which offers more design freedom into FE design.
• Chapter 6: In this section, the conclusions from all the proposed adaptive FTC methodologies are discussed. These inferences are followed by several useful recommendations for future research in adaptive FTC and applications.
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Adaptive Robust Fault Tolerant Controller (ARFTC) Design for Nonlinear Uncertain Systems with Actuator Failures
Contents
2.1 Introduction . . . 22 2.2 Adaptive Robust Fault Tolerant Controller (ARFTC) . . . 23 2.3 Summary . . . 45
2.1 Introduction
The objective of this chapter is to propose a fault tolerant controller ensuring enhanced post fault transient performance in conjunction with the issue of reaching a trade-off between improved transients and control effort respectively. Robustness towards modeling uncertainties is another design require- ment of the proposed controller. The essence of exploring the complimentary relation between two different control methodologies is the main driving force behind the synthesis of the proposed control algorithm. The main contribution lies in the proposed design of an adaptive second order sliding mode controller embedded in a backstepping framework for FTC design of uncertain nonlinear systems. The designed FTC scheme has been specifically aimed for potential applications in aircraft control. Further, a systematic and rigorous closed loop stability analysis of the proposed control scheme has been con- ducted which suggests an improvement in post fault transient performance using the proposed design methodology. The benefits of both backstepping [69] and sliding mode [97] controllers are encashed in the proposed approach. Moreover, to the best of the authors’ knowledge, there are no results available pertaining to the defined objective of this work in accommodating actuator faults and failures in ad- dition to system uncertainties. The proposed methodology offers numerous advantages.
The proposed control strategy is applicable to both linear and nonlinear systems affected by matched or mismatched uncertainties which may not be necessarily linearly parameterized. In addition, failure induced mismatched perturbations and exogenous disturbances are also tackled faithfully by the proposed controller. Unlike the backstepping based methodologies proposed in [5,32,54,65,98,99], the proposed control strategy neither requires trajectory initialization nor resorts to an increment in the virtual control gains for the improvement in post fault tracking error performance. The contribu- tion of this study relative to SMC based fault tolerant controllers [19, 20, 44, 61] is that the proposed design totally eradicates intruding matched and mismatched uncertainties (rather than minimizing) due to actuator failures without any control reallocation scheme requiring an explicit detection and isolation of such uncertain eventualities. In addition, robustness towards modeling uncertainties is also guaranteed. The proposed scheme attains the desired control objective for uncertain nonlinear systems yielding improved post fault transients with a considerably lower control energy requirement compared to the schemes based on control allocation and adaptive sliding mode control [4, 29, 30]. Moreover, the proposed control input is smooth with no chattering and therefore expected to satisfy physical constraints more effectively in comparison to the existing SMC based FTC strategies for aircraft sys- tems, making it suitable for practical applications. It is to be noted that while using an ASMC based FTC strategy, an increase in the values of the sliding surface coefficient may improve the initial tran- sient response of the system. However, in consequence, the post fault output transient performance degrades resulting in high overshoots which is strictly undesirable in safety critical systems. Further, no detailed investigations regarding ASMC based control of nonlinear systems in the face of actuator failures have been reported in literature. Moreover, no rigorous analysis of the transient performance is available in literature to give an insight as to how the post fault transients can be improved. In contrast to multiple model based adaptive approaches to FTC [22, 23, 100, 101], the proposed control methodology does not require any knowledge about the bounds of the failure nor does it depend on any switching logic for controller reconfiguration in the event of unanticipated actuator failures. The
proposed control scheme utilizes two adaptive laws to distinguish between actuator faults/failures and uncertainties/disturbances. In practice, sliding motion is never ideal and hence the adaptive estimates here can be unbounded. Hence, in the proposed controller, the adaptive laws are formulated suitably to ensure boundedness of adaptation and thereby prevent overestimation. Compared to traditional backstepping based methods and dynamic surface control (DSC) based techniques [66], the proposed control scheme reduces the computational complexity without compromising on the asymptotic stabil- ity of the output error dynamics. Moreover, in the proposed control technique, the discontinuous sign function is made to act on the time derivative of the control input resulting in a continuous control signal and hence chattering is totally eliminated.
The proposed scheme is applied to pitch control problem of a nonlinear longitudinal model of a large transport aircraft (Boeing 747-100/200), potentially affected by parametric uncertainties, sudden ac- tuator faults, float and lock-in-place failures. Simulation studies confirm that the proposed controller yields satisfactory tracking performance and fast nominal performance recovery under fault and fail- ures, thereby outperforming the basic approaches based on backstepping and sliding mode ideologies individually.
The chapter is organized as follows. Firstly the dynamics of the considered nonlinear systems with actuator failures are described in Section 2.2.1. Thereafter, the objective of the proposed actuator FTC with the inherent assumptions is formulated in Section 2.2.2. The proposed design procedure and stability analysis of the proposed controller are explained in Sections 2.2.3-2.2.4. In Section 2.2.5, simulation studies are performed by applying the proposed controller to longitudinal control of a Boeing 747-100/200 aircraft. Finally, the solution proposed for the FTC problem and its design attributes are summarized in Section 2.2.6.