(299d) Model-Based Fault Diagnosis and Fault Tolerant Control for Safety-Critical Chemical Reactors

In safety-critical chemical reactors with potential hazards, reaction kinetics and heat transfer parameters are usually known and a mathematical model is available. It is then meaningful to base fault detection and isolation algorithms on the first-principles model as opposed to statistics, so that physically meaningful residual signals are generated from material and/or energy balances not closing, leading to reliable fault diagnosis. Also, in order to maintain the safety of the entire system, it is necessary to take appropriate control action based on the mathematical model and the identified faults, so as to minimize their impact and thus ensure safe operation. In the present work, these ideas will be formulated and illustrated through a CSTR case study involving the liquid phase oxidation of alkylpyridine with hydrogen peroxide.

Fault detection and isolation in linear systems have been studied extensively¹ and recently, there have been generalizations to a large class of nonlinear systems^2,3. The approach involves designing a set of disturbance-decoupled linear residual generators, each one becoming active only when a specific fault occurs^2,3.

Once an abnormal event happens and the corresponding fault is detected and isolated, appropriate control action must be taken in order to prevent severe consequences caused by the fault. Re-tuning the controller and/or changing the manipulated input could be involved in the control action. The concepts of Dynamic Safe Set (DSS)⁴, defined as a maximal admissible set, and Dynamic Safety Margin (DSM)⁴, defined as the distance from the boundary of the DSS, play a critical role in formulating and designing the control strategy. Monitoring the position of the system in the interior of the DSS, including the size of the DSM, provides criteria for adapting control action in after the occurrence of an abnormal event.

Alkylpyridine N-oxidation with hydrogen peroxide as the oxidizer is an important synthesis step for pharmaceutical intermediates and other useful organic chemicals. This reaction is highly exothermic with possible decomposition of hydrogen peroxide generating oxygen, raising safety concerns. Inherently safer operation conditions were studied based on the boundary diagrams⁵. Recent research has shown that continuous operation in a CSTR is advantageous in controllable temperature profiles and concentration homogeneity, suitable for this specific reaction⁶.

In this work, we first study detectability in two groups of faults during the operation of the CSTR: jacket coolant inlet temperature and jacket coolant flow rate; reactant feed ratio and FT-IR sensor faults. We have found that one fault from each group can be effectively isolated via appropriate residual generators, despite persistent disturbances in the reaction rate, both in open loop and in closed loop under temperature control manipulating jacket coolant flow rate or jacket coolant inlet temperature. During the operation of the reactor, state estimates from a nonlinear observer track the system in state space and determine the corresponding DSS. The proposed fault tolerant control strategy monitors the DSM (distance of the system state from the boundary of the DSS) and, when it gets below a certain limit as a result of an abnormal event, the controller parameters are retuned and/or the manipulated input is switched. Simulation results show the effectiveness of the proposed fault tolerant control strategy in dealing with cooling system and sensor faults.

(1) Ding, S. X. Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools; Springer Science & Business Media, 2008.

(2) Venkateswaran, S.; Liu, Q.; Wilhite, B. A.; Kravaris, C. Design of Linear Residual Generators for Fault Detection and Isolation in Nonlinear Systems. Int. J. Control 2022, 95 (3), 804–820.

(3) Venkateswaran, S.; Sheriff, M.Z.; Wilhite, B. A.; Kravaris, C. C. Design of Functional Observers for Fault Detection and Isolation in Nonlinear Systems in the presence of noises. J. Process Control. 2021, 108, 68-85.

(4) Venkidasalapathy, J. A.; Kravaris, C. Safety-Centered Process Control Design Based on Dynamic Safe Set. J. Loss Prev. Process Ind. 2020, 65, 104126.

(5) Westerterp, K. R.; Lewak, M.; Molga, E. J. Boundary Diagrams Safety Criterion for Liquid Phase Homogeneous Semibatch Reactors. Ind. Eng. Chem. Res. 2014, 53 (14), 5778–5791.

(6) Cui, X.; Mannan, M. S.; Wilhite, B. A. Towards Efficient and Inherently Safer Continuous Reactor Alternatives to Batch-Wise Processing of Fine Chemicals: CSTR Nonlinear Dynamics Analysis of Alkylpyridines N-Oxidation. Chem. Eng. Sci. 2015, 137, 487–503.