(16c) Isolation and Handling of Sensor Faults in Nonlinear Process Systems

Automatic control technologies have been widely used in industrial processes, leading to improved efficiency and profitability. Their successful implementation is based on the reliability of actuating and sensing equipment, which are subject to faults that take place due to various reasons. The equipment abnormalities can lead to failures to meet product quality specifications, safety hazards to facilities and personnel, and damages to the environment in the absence of appropriately designed monitoring and fault-handling systems. Therefore, an accurate and timely detection of a fault and identification of the location of the faulty equipment is of great importance to reducing the effect of faults through the implementation of corrective control action. This realization has motivated significant research efforts to the development of fault detection and isolation (FDI) techniques.

Existing results on FDI include those that mainly use information embodied in plant data or a process model. In the data-based approach, abnormal behavior is detected using statistical monitoring techniques (see, e.g., [1, 2]). In particular, faults are reported when detection statistics exceed the limits for normal operation. Faults then can be isolated by using contribution plots [3, 4] or through comparison with additional data on past faults (see, e.g., [5]). The other approach to FDI is based on an explicit use of first-principles or identification models, where the analytic redundancy contained in the process model is used to generate residuals as fault indicators. A fault is reported when a residual breaches its threshold, and isolated according to certain isolation logic. The problem of FDI has been studied extensively for linear systems (see [6] for a survey).

For nonlinear process systems, there has been a significant body of work on detection and isolation of actuator faults. In a geometric approach, a nonlinear FDI filter is designed to solve the fundamental problem of residual generation (see [7]). Dedicated residuals are generated for fault isolation by exploiting the structure of the system (see [8]). Adaptive estimation techniques are used to handle unstructured but bounded modeling uncertainty for FDI of a class of Lipschitz nonlinear systems (see, e.g., [9]). To enhance data-based fault isolation, a feedback control law has recently been designed to enforce a closed-loop structure by decoupling the dependency between certain process variables (see, e.g., [10]). More recently, a method that compares the estimate of the actual input to its prescribed value has been proposed, where the estimate is obtained with the consideration of bounded parametric uncertainty (see [11]).

Compared to actuator faults, there exist limited results on detection and isolation of sensor faults. This problem has been studied for Lipschitz nonlinear systems (see, e.g., [12, 13]). In [12], a nonlinear state observer is designed to generate state estimates by using a single sensor. The fault isolation logic, however, is only limited to systems with three or more outputs. The method developed in [13] utilizes adaptive estimation techniques to deal with unstructured but bounded uncertainty for FDI. A sliding mode observer is designed to reconstruct or estimate faults by transforming sensor faults into pseudo-actuator faults (see [14]). This approach, however, requires a special system structure, and there is a limitation on system nonlinearity that can be handled. While a bank of observers are used to isolate sensor faults in [15], the observer gain is obtained through the first order approximation of the nonlinear dynamics. Therefore, the performance of the FDI design is subject to the type of nonlinearities. In summary, the problem of sensor FDI stands to gain from further results on designs that explicitly consider system nonlinearity in the FDI filter design.

As sensor faults are concerned, observers are typically required to fully or partly recover the system state. The design of observers, however, is a challenging problem for nonlinear process systems. In the context of output feedback control, high-gain observers are known to have good convergence properties (see, e.g., [16, 17]). Most existing results, however, rely on a special system structure for the system to be in to begin with, or after an appropriate transformation. To generalize the application of this type of observers, a model predictive control formulation has been studied in [18], where the discrete nature of the control implementation is exploited to relax the system structure required in the standard high-gain observer design. This generalization, however, is developed under the assumption of the locally Lipschitz continuity of the control input in the system state. Note that this assumption is hard to verify, especially under controllers such as model predictive control where the control law is not explicit but results from the solution to an optimization problem.

Motivated by the above considerations, this work considers the problem of isolation and handling of sensor faults in nonlinear process systems subject to input constraints. To this end, a high-gain observer design is first presented, which expands the class of nonlinear systems to which this type of observers can be applied. The convergence property of the observer and practical stability of the closed-loop system in the absence of faults are established under standard assumptions without assuming the locally Lipschitz continuity of the control input in the system state. Exploiting the enhanced applicability of the observer design, a sensor fault isolation scheme is then proposed, which uses a bank of high-gain observers. Each observer is driven by a subset of the measured outputs, for which residuals are generated that capture the differences between a state estimate and its expected trajectory. A fault is isolated when all the residuals breach their thresholds except for the one generated without using the erroneous measurements. After a fault is isolated, the state estimate generated using measurements from the healthy sensors is used by the controller to continue nominal operation. The implementation of the proposed fault isolation and handling framework subject to uncertainty and measurement noise is illustrated using a chemical reactor example.

References

[1] J. V. Kresta, J. F. MacGregor, and T. E. Marlin. Multivariate statistical monitoring of process operating performance. Can. J. Chem. Eng., 69:35–47, 1991.

[2] S. J. Qin. Statistical process monitoring: Basics and beyond. J. Chemometrics, 17:480–502, 2003.

[3] J. F. MacGregor, C. Jaeckle, C. Kiparissides, and M. Koutoudi. Process monitoring and diagnosis by multiblock PLS methods. AIChE J., 40:826–838, 1994.

[4] J. Yu. A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes. Chem. Eng. Sci., 68:506–519, 2012.

[5] S. Yoon and J. F. MacGregor. Fault diagnosis with multivariate statistical models part I: Using steady state fault signatures. J. Proc. Contr., 11:387–400, 2001.

[6] P. M. Frank. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results. Automatica, 26:459–474, 1990.

[7] C. De Persis and A. Isidori. A geometric approach to nonlinear fault detection and isolation. IEEE Trans. Automat. Contr., 46:853–865, 2001.

[8] P. Mhaskar, C. McFall, A. Gani, P. D. Christofides, and J. F. Davis. Isolation and handling of actuator faults in nonlinear systems. Automatica, 44:53–62, 2008.

[9] X. Zhang, M. M. Polycarpou, and T. Parisini. Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation. Automatica, 46:290–299, 2010.

[10] B. J. Ohran, D. Munoz de la Pena, J. F. Davis, and P. D. Christofides. Enhancing data-based fault isolation through nonlinear control. AIChE J., 54:223–241, 2008.

[11] M. Du, J. Nease, and P. Mhaskar. An integrated fault diagnosis and safe-parking framework for fault-tolerant control of nonlinear systems. Int. J. Rob. & Non. Contr., 22:105–122, 2012.

[12] R. Rajamani and A. Ganguli. Sensor fault diagnostics for a class of non-linear systems using linear matrix inequalities. Int. J. Contr., 77:920–930, 2004.

[13] X. Zhang. Sensor bias fault detection and isolation in a class of nonlinear uncertain systems using adaptive estimation. IEEE Trans. Automat. Contr., 56:1220–1226, 2011.

[14] X.-G. Yan and C. Edwards. Sensor fault detection and isolation for nonlinear systems based on a sliding mode observer. Int. J. Adapt. Contr. & Sign. Process., 21:657–673, 2007.

[15] M. Mattei, G. Paviglianiti, and V. Scordamaglia. Nonlinear observers with H_∞performance for sensor fault detection and isolation: a linear matrix inequality design procedure. Contr. Eng. Prac., 13:1271–1281, 2005.

[16] A. N. Atassi and H. K. Khalil. A separation principle for the stabilization of a class of nonlinear systems. IEEE Trans. Autom. Contr., 44:1672–1687, 1999.

[17] N. H. El-Farra, P. Mhaskar, and P. D. Christofides. Output feedback control of switched nonlinear systems using multiple Lyapunov functions. Syst. & Contr. Lett., 54:1163–1182, 2005.

[18] R. Findeisen, L. Imsland, F. Allgöwer, and B. A. Foss. Output feedback stabilization of constrained systems with nonlinear predictive control. Int. J. Rob. & Non. Contr., 13:211–227, 2003.