H∞ criteria for robust actuator fault reconstruction for nonlinear systems in Takagi-Sugeno's form using sliding modes

In this paper, two criteria for robust actuator fault reconstruction with sliding mode observation for a class of uncertain nonlinear systems are derived. It is known, even though the sliding mode technique is robust against unknown but bounded uncertainties, that the quality of fault reconstruction under real conditions is not as good as assumed in the design stage. This is often due to the fact that the unmodeled dynamics and external disturbances have a greater variability and dimension as expected. Even if the dimension is known, it is formally limited by the existence condition for an exponentially stable error dynamics. Therefore, H∞ criteria are derived to obtain a threshold for the accuracy of fault reconstruction during sliding motion. The validity and applicability of the design approach is demonstrated by the inverted pendulum benchmark.

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

[2]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[3]  Halim Alwi,et al.  Robust fault reconstruction for linear parameter varying systems using sliding mode observers , 2014 .

[4]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[5]  Andreas Kroll,et al.  Robust adaptive fault detection using global state information and application to mobile working machines , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[6]  Bart De Schutter,et al.  Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models , 2010, Studies in Fuzziness and Soft Computing.

[7]  Andreas Kroll,et al.  Benchmark problems for nonlinear system identification and control using Soft Computing methods: Need and overview , 2014, Appl. Soft Comput..

[8]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[9]  Halim Alwi,et al.  Robust actuator fault reconstruction for LPV systems using sliding mode observers , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  Horst Schulte,et al.  Sensor Fault-Tolerant Control of a Drivetrain Test Rig via an Observer-Based Approach within a Wind Turbine Simulation Model , 2014 .

[11]  Ronald J. Patton,et al.  A Fault-Tolerant Control approach to friction compensation , 2009, 2009 European Control Conference (ECC).

[12]  Kazuo Tanaka,et al.  Fuzzy modeling via sector nonlinearity concept , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[13]  Horst Schulte,et al.  Diagnosis of Actuator Parameter Faults in Wind Turbines Using a Takagi-Sugeno Sliding Mode Observer , 2014 .

[14]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[15]  Florian Poschke,et al.  Fault reconstruction using a Takagi-Sugeno sliding mode observer for the wind turbine benchmark , 2014, 2014 UKACC International Conference on Control (CONTROL).

[16]  Horst Schulte,et al.  Control-oriented modelling of wind turbines using a Takagi-Sugeno model structure , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[17]  Horst Schulte,et al.  Observer-based estimation of pressure signals in hydrostatic transmissions , 2010 .

[18]  Horst Schulte,et al.  Actuator fault diagnosis and fault-tolerant control of wind turbines using a Takagi-Sugeno sliding mode observer , 2013, 2013 Conference on Control and Fault-Tolerant Systems (SysTol).

[19]  Kazuo Tanaka,et al.  A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer , 1994, IEEE Trans. Fuzzy Syst..

[20]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[21]  Horst Schulte,et al.  Takagi-Sugeno Sliding Mode Observer Design for Fault Diagnosis in Pitch Control Systems of Wind Turbines1 , 2012 .

[22]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

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

[24]  Dominic Gross,et al.  Design of sliding mode observers for TS fuzzy systems with application to disturbance and actuator fault estimation , 2010, 49th IEEE Conference on Decision and Control (CDC).