Design of robust predictive fault-tolerant control for Takagi-Sugeno fuzzy systems: Application to the twin-rotor system

The paper deals with the problem of robust predictive fault-tolerant control for non-linear discrete-time systems described by the Takagi-Sugeno models as well as application to the so-called Twin-Rotor system. Approach proposed in this paper is in fact series of three, i.e. it starts from fault estimation, which is subsequently compensated with a robust controller. While robust controller is designed without taking into account the input constraints, compensation feasibility is proven by introducing invariant set of states, which takes into account the input constraints. If the current state do not belong to a robust invariant set, appropriate predictive control actions are performed. This appealing phenomenon makes it possible to enlarge the domain of attraction, making the proposed approach an efficient solution for the fault-tolerant control. The final part of the paper shows an illustrative example of proposed approach to the Twin-Rotor system.

[1]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[2]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[3]  Bart De Moor,et al.  Unbiased minimum-variance input and state estimation for linear discrete-time systems , 2007, Autom..

[4]  Mustafa Ç. Pinar,et al.  On the S-procedure and Some Variants , 2006, Math. Methods Oper. Res..

[5]  Alex M. Andrew,et al.  Fault Diagnosis: Models, Artificial Intelligence, Applications , 2005 .

[6]  Jozef. Koscielny Jan Maciej. Jozef Korbicz Jan Maciej Kos Korbicz,et al.  Modeling, diagnostics and process control : implementation in the DiaSter system , 2010 .

[7]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[9]  Basil Kouvaritakis,et al.  Extended invariance and its use in model predictive control , 2005, Autom..

[10]  Marcin Mrugalski,et al.  An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection , 2013, Int. J. Appl. Math. Comput. Sci..

[11]  Marcin Witczak,et al.  State-Space GMDH Neural Networks for Actuator Robust Fault Diagnosis , 2012 .

[12]  Giorgio Battistelli,et al.  Design of state estimators for uncertain linear systems using quadratic boundedness , 2006, Autom..

[13]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[14]  Vicenç Puig,et al.  LMI-based strategies for designing observers and unknown input observers for non-linear discrete-time systems , 2007 .

[15]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[16]  Ryszard Rybski,et al.  Impedance Measurement With the D-Optimum Experimental Conditions , 2009, IEEE Transactions on Instrumentation and Measurement.

[17]  Marcin Witczak.  Modelling and Estimation Strategies for Fault Diagnosis of Non-Linear Systems: From Analytical to Soft Computing Approaches , 2007 .

[18]  Józef Korbicz,et al.  Active fault-tolerant control design for Takagi-Sugeno fuzzy systems , 2011 .

[19]  Vicenç Puig,et al.  A GMDH neural network-based approach to passive robust fault detection using a constraint satisfaction backward test , 2007, Eng. Appl. Artif. Intell..

[20]  Marcin Witczak,et al.  Design of an extended unknown input observer with stochastic robustness techniques and evolutionary algorithms , 2007, Int. J. Control.

[21]  Tomasz Szulc,et al.  Convex combinations of matrices — Full rank characterization , 1999 .

[22]  Vicenç Puig,et al.  A fault-tolerant control scheme for non-linear discrete-time systems: Application to the twin-rotor system , 2010 .

[23]  Akbar Rahideh,et al.  Mathematical dynamic modelling of a twin-rotor multiple input-multiple output system , 2007 .

[24]  Vicenç Puig,et al.  Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter , 2012, Int. J. Appl. Math. Comput. Sci..

[25]  Marcin Witczak,et al.  Robust and efficient predictive FTC: Application to wind turbines , 2013, 2013 Conference on Control and Fault-Tolerant Systems (SysTol).

[26]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[27]  Rolf Isermann,et al.  Fault-Diagnosis Applications: Model-Based Condition Monitoring: Actuators, Drives, Machinery, Plants, Sensors, and Fault-tolerant Systems , 2011 .

[28]  Marcin Witczak,et al.  Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear Systems , 2014 .

[29]  Rolf Isermann,et al.  Fault-Diagnosis Applications , 2011 .

[30]  Janina Decker,et al.  Fault Tolerant Control Systems Design And Practical Applications , 2016 .