A Robust Adaptive Observer-Based Time Varying Fault Estimation

Document Type : Research Article


Dept. of Electrical Engineering, University of Technology, Baghdad, Iraq


This paper presents a new observer design methodology for a time varying actuator fault estimation. A new linear matrix inequality (LMI) design algorithm is developed to tackle the limitations (e.g. equality constraint and robustness problems) of the well known so called fast adaptive fault estimation observer (FAFE). The FAFE is capable of estimating a wide range of time-varying actuator fault signals via augmenting the Luenberger-observer by a proportional integral fault estimator feedback. Within this framework, the main contribution of this paper is the proposal of new LMI formulation that incorporates the use of  norm minimization: (a) to obviate the FAFE equality constraint in order to relax the design algorithm, (b) to ensure robustness against external disturbances, (c) to provide additional degrees of freedom to solve the infeasible optimization problem via assigning different proportional and integral fault estimator gains. Finally, a VTOL aircraft simulation example is used to illustrate the effectiveness of the proposed FAFE.


[1] S. Qikun, J. Bin, S. Peng, and L. Cheng-Chew, "Novel Neural Networks-Based Fault Tolerant Control Scheme With Fault Alarm," IEEE Trans. on Cybernetics, vol. 44, no. 11, pp. 2190-2201,2014.
[2] L. Ming, C. Xibin, and S. Peng, "Fuzzy-Model- Based Fault-Tolerant Design for Nonlinear
Stochastic Systems Against Simultaneous Sensor and Actuator Faults," IEEE Trans. on Fuzzy
Systems, vol. 21, no. 5, pp. 789-799, 2013.
[3] T. Jain, J. J. Yame, and D. Sauter, "A Novel Approach to Real-Time Fault Accommodation in
NREL's 5-MW Wind Turbine Systems," IEEE Trans. on Sustainable Energy, vol. 4, no. 4, pp.
1082-1090, 2013.
[4] M. Sami and R. J. Patton, "Active sensor fault tolerant output feedback tracking control for wind
turbine systems via T–S model," Engineering Applications of Artificial Intelligence, vol. 34, no.
0, pp. 1-12, 2014.
[5] M. Sami and R. J. Patton, "Active Fault Tolerant Control for Nonlinear Systems with Simultaneous
Actuator and Sensor Faults," Int. J. of Control,Automation, and Systems, vol. 11, no. 6, pp. 1149-
1161, 2013.
[6] R. J. Patton, L. Chen, and S. Klinkhieo, "An LPV pole-placement approach to friction compensation
as an FTC problem," Int. J. Appl. Math. Comput.Sci., vol. 22, no. 1, pp. 149–160, 2012.
[7] H. Alwi, C. Edwards, and A. Marcos, "Fault reconstruction using a LPV sliding mode observer
for a class of LPV systems," J. of the Franklin Institute, vol. 349, no. 2, pp. 510-530, 2012.
[8] X. Wei and M. Verhaegen, "Sensor and actuator fault diagnosis for wind turbine systems by using
robust observer and filter," Wind Energy, vol. 14,no. 4, pp. 491-516, 2011.
[9] M. Sami and R. J. Patton, "Global wind turbine FTC via T-S fuzzy modelling and control," 8th
IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Mexico City,
Mexico, 29-31 Aug 2012.
[10] M. Sami and R. J. Patton, "An FTC approach to wind turbine power maximisation via T-S fuzzy
modelling and control," 8th IFAC Symposium on Fault Detection, Supervision and Safety of
Technical Processes, Mexico City, Mexico, 29-31 Aug 2012.
[11] L. Zhang and A. Q. Huang, "Model-based fault detection of hybrid fuel cell and photovoltaic direct
current power sources," J. of Power Sources, vol. 196, no. 11, pp. 5197-5204, 2011.
[12] K. Zhang, B. Jiang, and V. Cocquempot, "Adaptive Observer-based Fast Fault Estimation,"
Int. J. of Control, Automation, & Systems, vol. 6,no. 3, pp. 320-326, June 2008.
[13] B. Jiang, K. Zhang, and P. Shi, "Integrated Fault Estimation and Accommodation Design for
Discrete-Time Takagi-Sugeno Fuzzy Systems With Actuator Faults," IEEE Trans. on Fuzzy
Systems, vol. 19, no. 2, pp. 291-304, 2011.
[14] M. Sami and R. J. Patton, "A Fault Tolerant Control Approach to Sustainable Offshore Wind
Turbines," in Wind Turbine Control and Monitoring, N. Luo, et al., Eds., ed: Springer,2014.
[15] K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix
Inequality Approach: John Wiley, 2001.
[16] M. C. M. Teixeira and S. H. Zak, "Stabilizing controller design for uncertain nonlinear systems
using fuzzy models," IEEE Trans. on Fuzzy Systems vol. 7, no. 2, pp. 133-142, 1999.
[17] H. D. Tuan, P. Apkarian, T. Narikiyo, and Y.Yamamoto, "Parameterized linear matrix inequality techniques in fuzzy control system design," IEEE Trans. on Fuzzy Systems, vol. 9, no.2, pp. 324-332, 2001.
[18] M. Corless and J. A. Y. Tu, "State and Input Estimation for a Class of Uncertain Systems," Automatica, vol. 34, no. 6, pp. 757-764, 1998.
[19] S. X. Ding, Model-based Fault Diagnosis Techniques Design Schemes, Algorithms, and Tools: Springer-Verlag, 2008.
[20] T. M. Guerra, A. Kruszewski, L. Vermeiren, and H. Tirmant, "Conditions of output stabilization for nonlinear models in the Takagi-Sugeno's form," Fuzzy Sets and Systems, vol. 157, no. 9, pp. 1248-1259, 2006.
[21] B. Mansouri, N. Manamanni, K. Guelton, A. Kruszewski, and T. M. Guerra, "Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed T–S models," Information Sciences, vol. 179, no. 4, pp. 446-457, 2009.