FDI Robusta Para Sistemas LPV Mediante PIO

  • Adisson Ríos Universidad de los Andes

Resumen

Resumen: Considerando los sistemas lineales invariantes en el tiempo (LTI) continuos con incertidumbres politópicas, esta contribución presenta un método para la síntesis de filtros robustos de detección y diagnóstico de fallas. Tomando
ventaja de los reconstructores de entradas desconocidas, los filtros se diseñan como observadores proporcional-integral (PIO), considerando y resolviendo un problema de control por realimentación estática de la salida (SOF), donde la ganancia de realimentación corresponde a las matrices de diseño del PIO. El método está basado en condiciones de desempeño modificadas, establecidas a partir de las normas H2/H¥, las cuales se describen como desigualdades matriciales lineales, LMIs. La generación de los residuos, producto de los filtros robustos, se obtiene aplicando esas condiciones modificadas sobre los sistemas con perturbación desconocidas y sujetos a incertidumbres paramétricas. Los parámetros inciertos se suponen que pertenecen a un politopo. Las condiciones de desempeño H2/H¥ extendidas se obtienen por medio del lema de proyección. El diagnóstico de las fallas se alcanza en primer lugar, estableciendo condiciones, extendidas también, de detectabilidad y separabilidad. En segundo lugar, si esas condiciones se satisfacen, diseñando un banco de filtros, es decir, por multifiltraje, basado en PIOs. Para cada falla objeto de separación, se diseña un filtro. Para
ilustrar los resultados y el desempeño del multifiltraje, se presenta además, un ejemplo numérico.

 

Abstract: This paper presents a novel approach for robust fault detection and isolation (FDI), based on modifiedH2/H¥ performance conditions, which are described as LMIs. The FDI filters are designed as Proportional-Integral Observers (PIO), by considering and solution of Static Feedback Output (SOF) control problem, where the feedback gain contains the matrices of the PIO. The generation of the residues, as consequence of the outputs of the robust filters, is obtained applying these conditions modified on linear systems with unknown disturbance and parametric uncertainties. The uncertainty parameters are supposed to belong to a polytope. The extended H2/H¥ conditions are obtained by means of the well known projection lemma. Fault diagnosis is obtained, first of all, establishing extended conditions of detectability and separabilidad. Secondly, if these conditions are satisfied, designing a bank of filters based on PIO, which
is known as multifiltering. For each fault separation object, a filter is designed. Performance of the proposed synthesis technique is illustrated by numerical example.

Descargas

La descarga de datos todavía no está disponible.

Citas

R. Beard, “Failure accommodation in linear systems throught self-reorganization,” Ph.D. dissertation, Mass. Inst. Technol., 1971.

H. Jones, “Failure detection in linear systems,” Ph.D. dissertation, Mass. Inst. Technol., 1973.

E. Frisk and L. Nielsen, “Robust residual generation for diagnosis including a reference model for residual behavior,” Automatica, vol. 42, no. 3, pp. 437– 445, 2006.

M. L. Guillén, J. L. Paredes, and O. E. Camacho, “Detección y diagnóstico de fallas utilizando la transformada wavelet,” Ciencia e Ingeniería, vol. 25, no. 1, pp. 35–42, 2004.

H. Niemann, J. Stoustrup, and B. Shafai, “Fault detection using PI observers,” in Proc. of CONTROL 97, 1997.

B. Shafai, C. T. Pi, and S. Nork, “Robust fault detection using proportional integral observers,” inWorld Automation Congress, 2002.

J. Zhang, “Evaluation of observer structures with application to fault detection,” Master’s thesis, Northeastern University, Dep. of Electrical and Computer Eng., 2009.

M. Rodrigues, D. Theilliol, S. Aberkane, and D. Sauter,“Fault tolerant control design for polytopic LPV systems,” Int. J. Appl. Math. Comput. Sci., vol. 17, no. 1, pp. 27–37, 2007.

A. Casavola, D. Famularo, G. Franzè, and M. Sorbara, “A fault detection, filter-design method for linear parameter-varying systems,” Proc IMechE. Part

I: Journal of Systems and Control Engeneering, vol. 221, pp. 865–873, 2007, especial Issue on Fault Diagnosis and Fault-Tolerant Control.

A.Weng, R. Patton, and P. Cui, “Active fault-tolerant control of a double inverted pendulum,” Proc IMechE. Part I: Journal of Systems and Control Engeneering, vol. 221, pp. 895–904, 2007, especial Issue on Fault Diagnosis and Fault-Tolerant Control.

J. Bokor and G. Balas, “Detection filter design for LPV systems–a geometric approach,” Automática, vol. 40, pp. 511–518, 2004.

M.-A. Massoumnia, “A geometric approach to the synthesis of failure detection filters,” IEEE Trans. On Autom. Control, vol. 31, no. 9, pp. 839–846, 1986.

J. Bokor and G. Balas, “Linear parameter varying systems: A geometric theory and applications,” Comp. and Automation Research Institute, Hungary,

Tech. Rep., 2005.

W. Acuña and A. Ríos-Bolívar, “H2/H¥ multiobjectives for fault detection in uncertain polytopic systems,” in Proc. of 17th IFAC World Congress, vol. CDRom, Seoul, Korea, 2007, pp. We–290.

Z. Duan, J. Zhang, C. Zhang, and E. Mosca, “Robust H2 and H¥ filtering for uncertain linear systems,” Automatica, vol. 42, pp. 1919–1926, 2006.

E. Mazars, J. I.M., Z. Li, and A. Zolotas, “Fault detection and isolation filter design for systems subject to polytopic uncertainties,” in Proc. of the IEEE 15th Mediterranean Conf. On Control and Autom., Athens,

Grece, 2007, p. CDROM.

A. Casavola, D. Famularo, and Franzè, “A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: an LMI approach,” Automatica, vol. 41, pp. 1463–1472, 2005.

A. Ríos-Bolívar and W. Acuña, “Robust FDI in uncertain LTI systems: A multiobjective H2 􀀀 H¥ setting,” Int. J. of Electronics, Electrical and Communication Eng. (IJEECE), vol. 2, no. 1, pp. 25–45, 2010.

A. Y. Ríos, “Un filtro para detección robusta de fallas en sistemas lineales a tiempo discreto con incertidumbres estructuradas,” Ciencia e Ingeniería, vol. 28, no. 2, pp. 95–102, 2007.

A. Ríos-Bolívar, “On the design of PIO for LPV systems,” Revista Ciencia e Ingeniería (bajo consideración), 2014.

P. Apkarian, H. Tuan, and J. Bernussou, “Continuous-time analysis, eigenstructure assignment, andH2 synthesis with enhanced linear matrix

inequalities (LMI) characterizations,” IEEE Trans. on Autom. Control, vol. 46, no. 12, pp. 1941–1946, 2001.

C. Wei, “On applications of the projection lemma to analysis and design of continuous-time systems,” Master’s thesis, National Sun Yat-Set University,

M. Oliveira, J. Bernussou, and J. Geromel, “A new discrete-time robust stability condition,” Systems & Control Letters, vol. 37, pp. 261–265, 1999.

L. A. Morales, N. S. Sotomayor, and Y. Boada, “Control de seguimiento de trayectoria y paletización de un robot de tres grados de libertad tipo SCARA (selective compliance assembly robot arm),” Revista Politécnica,

vol. 33, no. 1, pp. 1–9, 2014.

A. Ríos-Bolívar, “Sur la synthèse de filtres de détection de défaillances,” Ph.D. dissertation, Université Paul Sabatier, Toulouse, 2001.

G. Angelis, “System analysis, modelling and control with polytopic linear models,” Ph.D. dissertation, Technische Universiteit Eindhoven, 2001.

Publicado
2015-02-28
Cómo citar
Ríos, A. (2015). FDI Robusta Para Sistemas LPV Mediante PIO. Revista Politécnica, 35(2), 58. Recuperado a partir de https://revistapolitecnica.epn.edu.ec/ojs2/index.php/revista_politecnica2/article/view/470