Using the second-order information for reconfigurability analysis and design in the fault tolerant framework

The control reconfigurability measure defines the capability of a control system to allow recovery of performance when faults occur; therefore, it has been intended to be a tool for designing and synthesizing approaches in the fault tolerant control context. Reconfigurability depends on the controllability gramian, also known as the second-order information (SOI) in a broad sense. This paper proposes the assignation, by feedback, of the deterministic SOI in order to set the control reconfigurability of a given linear system. The theory concerned with this assignation is reviewed, then constructive theorems are given for finding constant feedback gains that approximate a required control reconfigurability for ease implementation. Also an unification of the reconfigurability measures proposed in the fault tolerance literature is given. Once the SOI is assigned by feedback, it can be computed online by using an identification method, which uses process input/output data. Results from simulation of the three tanks hydraulic benchmark, show that this approach can provide information about the system performance for fault tolerant purposes, thus online control reconfigurability computation and fault accommodation are considered. The approach presented in the paper gives an alternative for supervision taking into account the reconfigurability assigned by design

Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model

Generalized Functional Observer for Descriptor Nonlinear Systems—A Takagi-Sugeno Approach

This paper concerns the design of a generalized functional observer for Takagi–Sugeno descriptor systems. Furthermore, a generalized structure is herein introduced for purposes of estimating linear functions of the states of descriptor nonlinear systems represented into a Takagi–Sugeno descriptor form. The originality of the functional generalized observer structure is that it provides additional degrees of freedom in the observer design, which allows for improvements in the estimation against parametric uncertainties. The effectiveness of the developed design is illustrated by a nonlinear model of a single link robotic arm with a flexible link. A comparison between the functional generalized observer and the functional proportional observer is given to demonstrate the observer performances

Constant High-Gain Observer for a class of Triangular-Form Nonlinear System

[EN] In this article a continuous-discrete high-gain observer is presented to estimate the molar compositions in a distillation column for the Ethanol-Water mixture, by using the measurements of the temperatures in its plates. One of the main advantages of this observer is its constant gain, which is why its tuning depends only on choosing constant parameters that must satisfy some simple algebraic inequalities. The continuous-discrete observer presents a good pursuit of the process dynamics in spite of using less data than a purely discrete observer. The effectiveness of the proposed method is demonstrated using experimental data.[ES] En este artículo se presenta un observador de alta ganancia continuo-discreto para estimar las composiciones molares en una columna de destilación para la mezcla Etanol-Agua, empleando las mediciones de las temperaturas en los platos. Una de las principales ventajas de este observador es su ganancia constante, por lo que sintonizarlo depende únicamente de la elección de parámetros constantes que deben satisfacer algunas desigualdades algebraicas simples. El observador continuo-discreto presenta un buen seguimiento de la dinámica del proceso a pesar de usar menos datos que un observador puramente discreto. La efectividad del método propuesto es demostrado empleando datos experimentales.Aguilera-González, A.; Téllez-Anguiano, A.; Astorga-Zaragoza, CM.; Juárez-Romero, D.; Quintero-Mármol, E. (2010). Validación Experimental de un Observador de Alta Ganancia Constante Continuo-Discreto para una Columna de Destilación Binaria. Revista Iberoamericana de Automática e Informática industrial. 7(2):31-38. https://doi.org/10.1016/S1697-7912(10)70023-6313872Ben, S. (1997). Observation et commande de systemes non lineaires temps-discret. PhD thesis. Universite Claude Bernard-Lyon 1. Lyon, France.Deza, F., Busvelle, E., & Gauthier, J. P. (1992). Exponentially converging observers for distillation columns and internal stability of the dynamic output feedback. Chemical Engineering Science, 47(15-16), 3935-3941. doi:10.1016/0009-2509(92)85142-xHalvorsen, I. J., & Skogestad, S. (2000). DISTILLATION | Theory Of Distillation. Encyclopedia of Separation Science, 1117-1134. doi:10.1016/b0-12-226770-2/00631-1Hammouri, H., Targui, B., & Armanet, F. (2002). High gain observer based on a triangular structure. International Journal of Robust and Nonlinear Control, 12(6), 497-518. doi:10.1002/rnc.638Ibrir, S. (2007). Circle-criterion approach to discrete-time nonlinear observer design. Automatica, 43(8), 1432-1441. doi:10.1016/j.automatica.2007.01.012Jana, A. K., Nath Samanta, A., & Ganguly, S. (2006). Observer-based control algorithms for a distillation column. Chemical Engineering Science, 61(12), 4071-4085. doi:10.1016/j.ces.2006.01.043Murray-Gunther, A. (2003). Dynamic Mathematical Model of a Distillation Column. PhD thesis. University of Tenessee at Chattanooga.Nadri, M., Hammouri, H., & Astorga, C. (2004). Observer Design for Continuous-Discrete Time State Affine Systems up to Output Injection. European Journal of Control, 10(3), 252-263. doi:10.3166/ejc.10.252-263Perry, R.H. (1999). Perry's chemical engineer's handbook. 7 ed.Quintero-Marmol, E., Luyben, W. L., & Georgakis, C. (1991). Application of an extended Luenberger observer to the control of multicomponent batch distillation. Industrial & Engineering Chemistry Research, 30(8), 1870-1880. doi:10.1021/ie00056a029Shields, D. N., Ashton, S. A., & Daley, S. (2001). Design of nonlinear observers for detecting faults in hydraulic sub-sea pipelines. Control Engineering Practice, 9(3), 297-311. doi:10.1016/s0967-0661(00)00113-1Tronci, S., Bezzo, F., Barolo, M., & Baratti, R. (2005). Geometric Observer for a Distillation Column:  Development and Experimental Testing. Industrial & Engineering Chemistry Research, 44(26), 9884-9893. doi:10.1021/ie048751nYaz, E. E., Jeong, C. S., Bahakeem, A., & Yaz, Y. I. (2007). Discrete-time nonlinear observer design with general criteria. Journal of the Franklin Institute, 344(6), 918-928. doi:10.1016/j.jfranklin.2006.12.00

Observer for non‐linear systems with sampled measurements: Application to the friction factor estimation of a pipeline

Abstract This paper presents a new approach of the continuous‐discrete observer design for a class of uncertain state‐affine non‐linear systems. A high‐gain observer redesign is developed and analysed under insightful conditions. The proposed observer estimates the state vector by using system output measurements with long sampling times. This result is achieved by considering a persistent excitation condition that can be validated online. The performance of the proposed algorithm is evaluated under time‐varying sampled measurements to estimate the friction factor of a pipeline where the case of noisy sampled output measurements is also considered