Constrained Active Fault Tolerant Control Based on Active Fault Diagnosis and Interpolation Optimization
Abstract
:1. Introduction
 (i)
 In terms of the implementation of AFD in AFTC, the test inputs used for modal separation are usually optimized online. For the smallscale systems, such computational requirements can be satisfied. However, as the number of system dimensions increases, the computational burden tends to become heavier, which often results in much longer delays of correct fault mode isolation. Recently, an effective solution was proposed in [27], where an implicit expression of the residual limit set is adopted and a constant auxiliary signal and the associated separation hyperplane used to separate the potential system modes are constructed offline. After a fault is detected, only the constant test signal is injected into the system and the current diagnostic observer. Then, the true system mode can be isolated by discriminating the position of the generated residuals in relation to the previously computed separation hyperplane. Given its advantages, such as simple implementation and fast isolation, this approach can provide an effective perspective for the design of control reconfigurations. Therefore, this paper will first attempt to adapt this active fault isolation approach to be integrated into the framework of AFTC to provide critical modal update information for timely regulation of constrained systems.
 (ii)
 In terms of the design of constrained active reconfiguration FTC, most MPCbased methods need to solve computationally intensive optimization problems online. Generally, this often places stringent requirements on the system scale, sample interval, and hardware controller performance. As an alternative solution to constrained optimization, the interpolation control (IC) methods exhibit excellent features [28,29,30]. The main idea is to optimize an interpolation coefficient in real time based on the updated system states and use this coefficient to make a smooth convex combination of a outer controller and a inner controller. The outer controller is used to enlarge the controllable feasible domain, while the inner controller is used to satisfy the given control performance requirements. In general, the inner controller is optimally designed offline, while the outer controller is determined online simultaneously when the interpolation coefficient is optimized. This method of offline designing some parameters of the controller in advance helps to reduce the online calculation burden. Moreover, the optimized interpolation coefficient enables a smooth transition between the inner–outer controllers and ensures a fast convergence of the states to the set point under the constraints. In particular, the associated optimization problem belongs to standard linear programming (LP), which can be readily solved in the practical implementation. Given these characteristics, the ICbased optimization can provide a good compromise among computational load, feasible region size, performance, etc. Therefore, the development of the IC strategy to solve the constrained AFTC problem would be very promising. To the authors’ knowledge, no relevant results have been reported.
2. System Description and Problem Formulation
3. Main Results
3.1. The Overall Scheme of the Proposed AFDBased Interpolation AFTC Method
3.2. AFD: Fault/Mode Change Detection and Isolation
3.3. Integrated Design of Observer and Unconstrained Controller
3.4. Constrained AFTC: Reconfigured Interpolating Control
3.5. The AFDBased Reconfigured Interpolation FTC Algorithm
Algorithm 1 AFDbased interpolation AFTC. 

4. Algorithm Verification by a Wastewater Treatment Plant Model
4.1. System Model and Parameters
4.2. Offline Design of AFD and AFTC According to Algorithm 1 and Relevant Validation
4.3. Simulation Results and Analysis of the above Designed AFDBased AFTC Method
4.4. MultiPerformance Comparison and Discussion of Active FaultTolerant Control Methods
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
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Method  Algorithm 1  [20]  [13]  [16]  

Performance  
Types of faults that can be handled  Component/actuator faults  Actuator fault  Actuator fault  Actuator fault  
Can active fault diagnosis be realized  Yes        
Number of observers used in real time  1      3  
Design principle of fault tolerant control  ${P}_{M}$based IC  Dualmode MPC  LMIbased MPC  ${P}_{M}$based MPC  
Expression of fault tolerant feasible domain  Polyhedral set  Polyhedral set  Ellipsoidal set  Ellipsoidal set  
Optimization problems to be solved  LP  QP  SDP  QP  
Can active constraint relaxation be achieved  Yes        
Extensibility of FTC method  General  General  High  General 
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Han, K.; Chen, C.; Chen, M.; Wang, Z. Constrained Active Fault Tolerant Control Based on Active Fault Diagnosis and Interpolation Optimization. Entropy 2021, 23, 924. https://doi.org/10.3390/e23080924
Han K, Chen C, Chen M, Wang Z. Constrained Active Fault Tolerant Control Based on Active Fault Diagnosis and Interpolation Optimization. Entropy. 2021; 23(8):924. https://doi.org/10.3390/e23080924
Chicago/Turabian StyleHan, Kezhen, Changzhi Chen, Mengdi Chen, and Zipeng Wang. 2021. "Constrained Active Fault Tolerant Control Based on Active Fault Diagnosis and Interpolation Optimization" Entropy 23, no. 8: 924. https://doi.org/10.3390/e23080924