Abstract
Engineering systems are vulnerable to different kinds of faults. Faults may compromise safety, cause sub-optimal operation and decline in performance if not preventing the whole system from functioning. Fault tolerant control (FTC) methods ensure that the system performance maintains within an acceptable level at the occurrence of the faults. These techniques cannot be successful if the necessary redundancy does not exist in the system. Fault recoverability which is also known as control reconfigurability is a mathematical measure which quantifies the level of redundancy in connection with feedback control. Fault recoverability provides important and useful information which could be used in analysis and design. However, computing fault recoverability is numerically expensive. In this paper, a new approach for computation of fault recoverability for bilinear systems is proposed. This approach uses cross-gramian and reduces the computations significantly. The contribution of this paper is twofold. Firstly the concept of cross-gramian is extended to support discrete-time bilinear systems and an iterative algorithm for cross-gramian computation is proposed. Secondly a cross-gramian based approach for computation of fault recoverability is proposed which reduces the computational burden significantly. The proposed results are used for an electro-hydraulic drive to reveal the redundant actuating capabilities in the system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Antoulas, A. C. (2005). Approximation of large-scale dynamical systems (Vol. 6). Siam.
d’Alessandro, P., Isidori, A., & Ruberti, A. (1974). Realization and structure theory of bilinear dynamical systems. SIAM Journal on Control, 12(3), 517–535.
Deutscher, J. (2005). Nonlinear model simplification using L 2-optimal bilinearization. Mathematical and Computer Modelling of Dynamical Systems, 11(1), 1–19.
Dorissen, H. (1989). Canonical forms for bilinear systems. Systems & Control Letters, 13(2), 153–160.
Gugercin, S., & Antoulas, A. C. (2004). A survey of model reduction by balanced truncation and some new results. International Journal of Control, 77(8), 748–766.
Guo, L., Schöne, A., & Ding, X. (1994). Control of hydraulic rotary multi-motor systems based on bilinearization. Automatica, 30(9), 1445–1453.
Guo, L., & Schwarz, H. (1989). A control scheme for bilinear systems and application to a secondary controlled hydraulic rotary drive. Paper Presented at the Proceedings of the 28th IEEE Conference on Decision and Control, p. 989.
Harris, T., Seppala, C., & Desborough, L. (1999). A review of performance monitoring and assessment techniques for univariate and multivariate control systems. Journal of Process Control, 9(1), 1–17.
Mohler, R. R. (1991). Nonlinear systems, volume II: Applications to bilinear control: Englewood-cliffs. New Jersey: Prentice-Hall.
Patton, R. J. (1997). Fault-tolerant control systems: The 1997 situation. Paper presented at the IFAC symposium on fault detection supervision and safety for technical processes.
Schwarz, H., Dorissen, H., & Guo, L. (1988). Bilinearization of nonlinear systems. Systems Analysis and Simulation, 46, 89–96.
Schwarz, H., & Ingenbleek, R. (1994). Observing the state of hydraulic drives via bilinear approximated models. Control Engineering Practice, 2(1), 61–68.
Shaker, H. R. (2013). Control reconfigurability of bilinear systems. Journal of Mechanical Science and Technology, 27(4), 1117–1123.
Shaker, H. R., & Komareji, M. (2012). Control configuration selection for multivariable nonlinear systems. Industrial and Engineering Chemistry Research, 51(25), 8583–8587.
Shaker, H. R., & Tahavori, M. (2011). Control reconfigurability of bilinear hydraulic drive systems. Paper presented at the International Conference on Fluid Power and Mechatronics (FPM).
Shaker, H. R., & Tahavori, M. (2013). Frequency-interval control configuration selection for multivariable bilinear systems. Journal of Process Control, 23(6), 894–904.
Shaker, H. R., & Tahavori, M. (2014a). Frequency-interval model reduction of bilinear systems. Automatic Control, IEEE Transactions on, 59(7), 1948–1953.
Shaker, H. R., & Tahavori, M. (2014b). Time-interval model reduction of bilinear systems. International Journal of Control, 87(8), 1487–1495.
Svoronos, S., Stephanopoulos, G., & Aris, R. (1980). Bilinear approximation of general non-linear dynamic systems with linear inputs. International Journal of Control, 31(1), 109–126.
Wu, N. E., Zhou, K., & Salomon, G. (2000). Control reconfigurability of linear time-invariant systems. Automatica, 36(11), 1767–1771.
Zhang, L., Lam, J., Huang, B., & Yang, G.-H. (2003). On gramians and balanced truncation of discrete-time bilinear systems. International Journal of Control, 76(4), 414–427.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Shaker, H.R. (2017). Fault Recoverability Analysis via Cross-Gramian. In: Zhang, D., Wei, B. (eds) Mechatronics and Robotics Engineering for Advanced and Intelligent Manufacturing. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-33581-0_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-33581-0_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33580-3
Online ISBN: 978-3-319-33581-0
eBook Packages: EngineeringEngineering (R0)