Fault detection, diagnosis and tolerant control for non-Gaussian stochastic distribution systems using a rational square-root approximation model

Stochastic Distribution Control (SDC) systems are a group of systems where the outputs considered are the measured Probability Density Functions (PDFs) of the system output whilst subjected to a normal crisp input. The purpose of the control algorithm design of such systems is to choose a control input such that the PDF of the system output can follow a prespecified PDF as close as possible. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper a non-linear adaptive observer-based fault diagnosis algorithm is proposed to diagnose the fault in the dynamic part of such systems. Using the estimation to the unknown fault, a fault tolerant control via a controller reconfiguration is proposed, where it has been shown that a good output PDF tracking can still be realised when fault occurs in the system. A simulated example is given to illustrate the use of the proposed algorithm.

[1]  Paul M. Frank,et al.  Fault diagnosis in dynamic systems: theory and application , 1989 .

[2]  Lei Guo,et al.  Generalized discrete-time PI control of output PDFs using square root B-spline expansion , 2005, Autom..

[3]  Hong Wang,et al.  Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions , 2000 .

[4]  Visakan Kadirkamanathan,et al.  Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems , 2001, IEEE Trans. Syst. Man Cybern. Part C.

[5]  D Zhou,et al.  REAL-TIME DETECTION AND DIAGNOSIS OF "PARAMETER BIAS" FAULTS FOR NONLINEAR SYSTEMS , 1993 .

[6]  D Zhou.  A NEW APPROACH TO SENSOR FAULT DETECTION AND DIAGNOSTICS OF NONLINEAR SYSTEMS , 1995 .

[7]  Charalambos D. Charalambous,et al.  Maximum likelihood parameter estimation from incomplete data via the sensitivity equations: the continuous-time case , 2000, IEEE Trans. Autom. Control..

[8]  R. Srichander,et al.  Stochastic stability analysis for continuous-time fault tolerant control systems , 1993 .

[9]  M. Mariton.  Detection delays, false alarm rates and the reconfiguration of control systems , 1989 .

[10]  Robert H. Chen,et al.  A generalized least-squares fault detection filter , 2000 .

[11]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems: Modelling and Control , 2000 .

[12]  Jason L. Speyer,et al.  Optimal stochastic fault detection filter , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[13]  Hong Wang,et al.  Shaping of output PDF based on the rational square-root b-spline model , 2005 .

[14]  Charalambos D. Charalambous,et al.  Conditional densities for continuous-time nonlinear hybrid systems with applications to fault detection , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[15]  Hong Wang,et al.  Recent Developments in Stochastic Distribution Control/A Review , 2003 .

[16]  Jason L. Speyer,et al.  Optimal stochastic fault detection filter , 2003, Autom..

[17]  Youmin Zhang,et al.  Stochastic stability analysis of fault-tolerant control systems in the presence of noise , 2001, IEEE Trans. Autom. Control..

[18]  Lei Guo,et al.  PID controller design for output PDFs of stochastic systems using linear matrix inequalities , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  R. Braatz,et al.  Identification of particle-particle interactions in suspension polymerization reactors , 2005, Proceedings of the 2005, American Control Conference, 2005..

[20]  Michèle Basseville,et al.  On-board Component Fault Detection and Isolation Using the Statistical Local Approach , 1998, Autom..