Robust adaptive fault tolerant control for a process with actuator faults
Introduction
Due to increasing high performance demand and production efficiency requirements, industrial processes, which are inherently nonlinear and multivariable systems, become more complex and component fault occurrence is inevitable. Therefore, resilience to system malfunctioning that stems from actuator, sensor and structural faults becomes one of the most important requirements of today’s industrial world. In order to make the system gain such ability, a fault tolerant control (FTC) design needs to be considered. Recently, FTC systems is an active research area and the design of such reliable control systems draws a great deal of interest [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. The field is generally classified as active or passive FTC depending on the presence of a reconfiguration mechanism in the control structure. An active FTC, as the name suggests, has a variable structure and mostly needs a fault detection and diagnosis (FDD) unit that locates the fault and supplies its estimated magnitude. For instance, in the case of an actuator fault, active FTC is able to accommodate both anticipated and unanticipated faults with acceptable performance degradation thanks to its real-time decision-making and controller reconfiguration properties. It can deal with beyond design basis failures as long as FDD scheme works properly [7]. An important drawback of active FTC, in this instance, is that the reconfigurable controller design is highly dependent on FDD module information and system performance deterioration as a result of an increase in FDD reaction time beyond a critical level [12]. It is possible to bypass the aforementioned drawback and resulting system uncertainties by using an adaptive control method in the design of FTC. Since the method is so called “self-reconfigurable”, it does not need a reconfiguration mechanism depending highly on FDD module [13]. For that purpose, one solution is using the adaptive control as an auxiliary controller so as to cope with actuator faults while the core controller continues to maintain performance specifications. A significant amount of studies are available for this combined control approach in FTC literature [13], [14], [15], [16], [17], [18]. Linear quadratic control, model following, feedback linearization, backstepping, model predictive control, sliding mode and eigenstructure assignment are some design methods combined with adaptive control. Jin [18] presented an adaptive FTC scheme for MIMO nonlinear systems with actuator faults. A time varying Barrier Lyapunov Function (BLF) is proposed together with an auxiliary system analyzing the effect of input constraints. Estimation error boundedness for faults is proved and output tracking performance with an acceptable error is guaranteed. Chen and Tao [19] presented an adaptive neural fault-tolerant control scheme by using backstepping technique for a class of uncertain nonlinear large-scale systems. They considered the case of unknown dead zone, partial additive/multiplicative actuator faults and external disturbances. Wang et al. [20] proposed a robust adaptive FTC scheme without need a fault detection/diagnosis of actuation faults for distributed consensus problem of multi-agent systems. The control scheme consists of a robust control and an adaptive control that updates crucial parameters for the purpose of compensating partial loss of actuation effectiveness and uncontrollable actuator faults. Mao et al. [21] addressed an adaptive failure compensation problem for high-speed trains with actuator failures. For both the healthy piecewise constant system and the system with actuator failures, the adaptive controller structure and conditions are derived to achieve plant-model matching. The controller designed such that it does not require the known bounds of failures. System stability and asymptotic state tracking are proved.
The second solution is to use adaptive approach in the design of main control of FTC with some proper modifications in order to compensate actuator faults system uncertainties and external disturbances. Tong et al. [22], developed an adaptive fuzzy decentralized output feedback FTC for unknown nonlinear large-scale systems with lock-in-place and loss of effectiveness type actuator faults. The method solves the control problem without direct requirement of the state measurement thanks to a fuzzy adaptive observer structure and relaxes the restrictive state availability assumption. Tong et al. [23] investigated an adaptive fuzzy FTC for uncertain stochastic nonlinear systems with actuator failures and unmodeled dynamics. Authors showed that the method solve the robustness problem of unmodeled dynamics and stochastic disturbances in addition to actuator faults. Li et al. [24] studied adaptive fuzzy FTC for SISO nonlinear systems with actuator failures. They investigated a solution to both adaptive optimal control problem and actuator failure tolerance in nonaffine nonlinear structure. Another option here is to use model reference adaptive control thanks to its model following property forcing the system to preserve nominal plant behavior despite an actuation fault [25], [26], [27], [28], [29]. Besides, if a multivariable industrial process is the case, the method is able to deal with interaction effects resulting from actuator faults. On the other hand, adaptive control estimation algorithms generally need the system parameters to change slowly enough for a decent output tracking which causes poor system performance as a result of faults that may cause abrupt and dramatic changes in system parameters. The first solution that comes to mind is to increase adaptive learning rates ending up with achieving fast adaptation. However, an update law subjected to high learning rates makes the overall system performance even worse as a consequence of high frequency oscillations in control signal resulting with excitations of unmodeled dynamics of the plant [30], [31], [32]. In order to eliminate possible high frequency oscillations and improve transient of MRAC both in normal operation and in a case of actuator fault, one must modify generic MRAC [33], [34], [35]. Furthermore, actuator fault tolerance for a multivariable adaptive control brings extra uncertainties in the controlled system structure and limits the performance of MRAC as a consequence of restrictive conditions of high frequency gain (HFG) matrix and adequate knowledge of the system interactor matrix. As a result, MRAC design requires solutions to the aforementioned issues in addition to requirements of maximal plant uncertainty parameterization and robust parameter adaptation to recover the system performance in an acceptable level.
In this paper, a multivariable quadruple tank process is considered as a case study for real-time application of adaptive fault compensation control. The system is a benchmark process which allows applying various control designs including centralized and decentralized multivariable control, minimum and non-minimum phase control and nonlinear control. In advance, the structure of the system gives us the opportunity of testing FDD algorithms related with actuator and sensor fault tolerance, hardware and analytical redundancy for FTC applications. Comparing with the existing results, the main contributions of this study can be summarized as follows: (1) This paper studies a robust adaptive FTC for an uncertain MIMO process system exposed to actuator faults and additionally considers practical implementation issues as well; such as sensor noises, external disturbances and unparametrizable actuator failures. Although the authors in [36], [37] also studied robust adaptive FTC, some issues are leaved unsolved such as absence of analytical solution of control algorithm in real time application, robustness for only actuator fault cases and priori knowledge of some control parameters that limits overall system performance. (2) Since we consider a multi-input process system, a centralized multivariable MRAC with output feedback framework is chosen for output tracking despite the presence of actuator fault regardless of time and duration. This structure requires less plant information than a state feedback approach as in [38]. The interaction effects of faults of multivariable process are compensated by using decoupled model following property of the control approach. (3) Multivariable adaptive control issues related with the restricted knowledge of the system HFG matrix in a case of fault are solved by using a simple decomposition method relaxing this restriction and allowing more robust system to parameter variations. Note that a similar solution is given in [39] however it requires a control reparametrization and leads to a more complex control algorithm. (4) Since the mentioned factorization allows increasing adaptive rule gains freely, unlike restrictive gain selection in studies [36], [38], [40], changing update gains in a wide range allows us to integrate a modification that is first proposed in our previous work [8]. The modification eliminates poor post-fault transient of adaptive control systems as a result of suppressing the control signal oscillations under high adaptation gain conditions while the existing results in [36], [41], [42], [43] does not consider such improvement.
This paper is organized as follows: In Section 2, the problem formulation of a multivariable system under actuator fault condition is presented. In Section 3, firstly, the essential conditions of designing a multivariable MRAC are given then, robustness and performance improvements that make the controller gain fault tolerance ability are presented. In Section 4, the process description, modeling and practical implementation results are presented. In Section 5, the study is concluded with final remarks.
Section snippets
Problem formulation
Consider the following linear presentation of a plant with m-inputs and m-outputs: with and . For output feedback control design, transfer matrix of the system is considered. Although we study in time domain, for the sake of simplicity in calculations, a mixture of time and Laplace domain is used throughout the paper. When there is no actuator fault, we describe the controlled plant as: Where is the system input vector. The control
Adaptive fault tolerant control designs
In this section, we start with giving basics of direct model reference controller that is fundamental to FTC scheme proposed in this paper. Output feedback direct MRAC structure with known parameters can be written as: where the parameters of controller are with with v being the observability index of plant and the regressor vector contains reference inputs, plant
Real system applications
In this section, it is aimed to prepare robust adaptive fault tolerant control scheme to a real-time application and by using a benchmark system, present the acquired results in a comparative way considering aforementioned design approaches.
Conclusion
In this paper, practical implementation of a multivariable robust adaptive FTC is studied. A quadruple tank process setup with actuator faults is used as a case study. In addition to fault consideration, possible structural challenges of designing a multivariable MRAC are pointed out along with the other issues such that the system has coupling disturbance, sensor noise and unmodeled dynamics. Some robustness and performance modifications are then integrated to multivariable MRAC. Closed-loop
CRediT authorship contribution statement
Mehmet Arıcı: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Visualization. Tolgay Kara: Writing - review & editing, Supervision, Project administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work is supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK), through project 116E020.
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