(421b) Robust Detection of Mode Transitions in Hybrid Process Systems with Measurement Sampling Constraints

With the extensive use of automated control systems in modern chemical plants, a great deal of emphasis is being placed on process safety and reliability issues because of the increased likelihood of faults, such as malfunctions of process equipment and/or control instrumentation, which can undermine the stability and integrity of the entire system if not detected and handled appropriately. Not surprisingly, the problems of monitoring and fault detection in dynamic process systems have been the subject of considerable research interest over the past few decades in both the academic and industrial circles in process control (e.g., [1], [2]). A careful examination of the existing literature on process monitoring, however, shows that the majority of existing methods have been developed for purely continuous processes. Yet, many chemical processes are characterized by strong interactions between continuous dynamics and discrete events, and are more appropriately modeled as hybrid systems. Compared with the efforts on the analysis and control of hybrid systems, the monitoring problem has received less attention. Examples of important contributions in this direction include the design of switched state estimation schemes for switched linear systems [3], as well as the development of fault diagnosis algorithms using hybrid automata theory [4] and statistical data-based methods [5].

Recently, we developed in [6] an integrated approach for fault detection and monitoring of a class of hybrid process systems modeled by switched nonlinear systems with control actuator faults, uncertain continuous dynamics and uncertain mode transitions. A robust hybrid monitoring scheme that distinguishes reliably between faults, mode transitions and uncertainty was developed using tools from unknown input observer theory and results from Lyapunov stability theory. A key idea of this approach was to design a set of dedicated mode observers that facilitate the identification of the active mode without information from the controllers and render the residuals insensitive to the faults and uncertainties within the constituent subsystems. Beyond uncertainty and hybrid dynamics, measurement sampling is another key issue that requires attention in the design of the monitoring and control systems. In practice, measurements of the process outputs are typically available from the sensors at discrete time instances and not continuously. The transmission frequency is typically dictated by the inherent limitations on the data collection and processing capabilities of the measurement sensors. These limitations can also arise from sensor-controller communication constraints in networked control systems where the sensor data are transmitted over a shared finite communication channel. Due to these limitations, the design and implementation of the monitoring and control system are further complicated in that the ability of the system to accurately monitor the evolution of the process and implement correct, yet prompt, control actions will be impaired by discrete measurement sampling, and this might lead to performance deterioration or even loss of stability.

Motivated by these considerations, we present in this work a methodology for the robust detection and identification of mode transitions in hybrid process systems subject to measurement sampling constraints. We design an integrated monitoring and control system that consists of a family of Lyapunov-based feedback controllers that enforce closed-loop stability in the absence of sampling constraints, a bank of mode observers that run in parallel to the process for all times and a supervisor that switches synchronously between the different controllers. To compensate for measurement unavailability, a model of each mode of the hybrid system is embedded within the mode observer to provide estimates of the output measurements between sampling instances. The discrepancy between the output of the observer and that of the process is used as a residual to identify the active mode and detect mode transitions. The state of the model is then updated and reset using the actual measurements whenever they become available from the sensors. Using unknown input observer design techniques, the mode observers are designed so that the identification of the active mode and the detection of mode transitions are insensitive to the effects of uncertainties within the constituent modes. The overall closed-loop system is formulated as a switched jump system and analyzed, leading to a set of uncertainty decoupling conditions as well as an explicit characterization of the minimum allowable sampling rate that ensures that the observer residual corresponding to the active mode converges to, and remains, zero until a mode transition takes place. Using this characterization, a mode transition can be detected whenever the residual for the active mode deviates from the expected behavior. Once the active mode is identified, the supervisor activates the corresponding controller to stabilize the new mode of the hybrid system. Finally, the efficacy and implementation of the proposed methodology are demonstrated using a chemical process example that involves switching between different operating modes.

References:

[1] Venkatasubramanian, V., R. Rengaswamy, K. Yin and S. Kavuri, ``Review of process fault detection and diagnosis - Part I: Quantitative model-based methods," Comp. Chem. Eng., 27:239-311, 2003.

[2] Ghantasala, S. and N. H. El-Farra, ``Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems," Automatica, 45:2368-2373, 2009.

[3] Alessandri, A., M. Baglietto and G. Battistelli, ``Luenberger observers for switching discrete-time linear systems," Inter. J. Contr., 80:1931-1943, 2007.

[4] Zhao, F., X. Koutsoukos, H. Haussecker, J. Reich and P. Cheung, ``Monitoring and fault diagnosis of hybrid systems," IEEE Trans. Syst. Man. Cybern. Part B-Cybern., 35:1225-1240, 2005.

[5] Jin, X. and B. Huang, ``Robust identification of piecewise/switching autoregressive exogenous process," AIChE J., in press.

[6] Hu, Y. and N. H. El-Farra, ``Robust fault detection and monitoring of hybrid process systems with uncertain mode transitions," Proceedings of 49th IEEE Conference on Decision and Control, submitted, Atlanta, GA, 2010.