Continuous Stirred Tank Reactor Benchmark Research Articles

A Hierarchical approach for isolating sensor faults from un-stealthy attacks in large-scale systems

This paper proposes a novel hierarchical-adaptive threshold abnormal behavior discrimination scheme (HATAD) for Lipschitz nonlinear large-scale systems with disturbances and uncertain dynamics. Two layers of groups of interlinked observers, namely the supervisor and local layers, are designed. The local layer using open loop observers, switching technique, and local controllers is first developed to protect the physical system from the attack effects, where the proposed switching technique can connect the plant to the local controller under the attack conditions. At the supervisor layer, the main controllers and three types of observers are constructed to detect and discriminate the abnormal behaviors and determine the faulty unit. This architecture leads to less restrictive mathematical conditions and analyses, which ensure the stability and the L2−L∞ performance of the estimation error dynamics. To demonstrate the effectiveness of the proposed approach, a simulation study has been conducted on a large-scale system of two units of benchmark continuous stirred tank reactor (CSTR).

Data-Driven Sensor Fault Diagnosis Under Closed-Loop Control With Slow Feature Analysis

Recently, data-driven fault diagnosis techniques, especially multivariate statistical process monitoring methods, have been extensively investigated and widely applied to industries. Whether the monitored system is under closed- or open-loop control has a strong impact on the development of fault diagnosis strategies, but this point has not been taken seriously into consideration. This work aims to provide an effective data-driven method for sensor fault diagnosis under closed-loop control with modified slow feature analysis (SFA). The SFA is first revisited and compared with the well-known principal component analysis approach. Through theoretical analysis and an intuitive example, the influence of feedback control on sensor fault diagnosis is demonstrated, and to achieve successful detection, a strategy of incorporating more variables for monitoring is suggested. Then, based on SFA, a new sensor fault detection and classification method is developed. Its detectability analysis is carried out, based on which improved methods are proposed for efficient detection of incipient sensor faults. Finally, case studies on the continuous stirred tank reactor benchmark process demonstrate the effectiveness of the proposed method.

Steady-state target calculation integrating economic optimization for constrained model predictive control

Real-time optimization (RTO) in cascade model predictive control (MPC) is a classic two-layer architecture for economic optimization and dynamic control. The two-layer architecture is always integrated with steady-state target calculation (SSTC) to guarantee the feasibility of the control target. In this paper, we present a modified SSTC algorithm to recalculate the steady-state point for MPC when the optimal point calculated by RTO is no longer attainable. The proposed algorithm takes economic performance into account and retains the feasibility of solutions. Based on a classic SSTC formulation, ours has a new objective function with two terms, one for optimizing economic performance and the other for ensuring the feasibility. Moreover, the objective function of the proposed SSTC is rearranged, and the SSTC problem is formulated by quadratic programming, which can be solved in an instant for real applications. Furthermore, we provide a detailed 4-in-4-out model of the Fischer esterification reaction, which is similar to the benchmark continuous stirred tank reactor (CSTR) model, to demonstrate the effectiveness of our SSTC algorithm. The proposed algorithm is able to improve economic performances, whether a convex or non-convex economic cost function is concerned.

Robust NMPC using a model-error model with additive bounds to handle structural plant-model mismatch

Abstract We address the problem of robust nonlinear model predictive control (NMPC) under structural plant model mismatch in a multi-stage framework using a model-error model (MEM). Multi-stage NMPC models the presence of future feedback information in the predictions, hence it is less conservative than the other existing robust NMPC approaches. MEM consists of a stable linear model, an unknown nonlinear operator with bounded gain and a bounded additive mismatch. The computational burden of the proposed scheme is reduced by using two different approximations; 1. Constraint tightened multi-stage NMPC 2. Tube-enhanced multistage NMPC. Both the schemes are real-time implementable with a small loss in performance when compared to the standard multi-stage NMPC. The advantages of the proposed schemes are demonstrated for a benchmark continuous stirred tank reactor (CSTR) example.

Batch and Moving Horizon Estimation for Systems subjected to Non-additive Stochastic Disturbances

Abstract Nonlinear state estimation techniques for state dynamics involving additive discrete zero mean white noise have received considerable attention in the past. The probabilistic formulation of the conventional moving horizon estimation (MHE) is also developed under this simplifying assumption. In reality, the unmeasured disturbances affect the states and measurements in much more complex way and thus can not be treated in additive manner. In current work, we formally introduce a probabilistic formulation of MHE which can handle such nonlinear uncertainties in the state dynamics. The efficacy of the proposed MHE has been demonstrated by conducting stochastic simulation studies on a benchmark continuous stirred tank reactor (CSTR) system. It is found that the estimation performance of the proposed MHE formulation is comparable to estimation performance of a sampling based Bayesian estimator (unscented Kalman filter or UKF), which deals with non-additive disturbances systematically, and significantly better than the extended Kalman filter (EKF) that deals with non-additive disturbances through successive linearisation.

Simultaneous State and Parameter Estimation using Robust Receding-horizon Nonlinear Kalman Filter

Abstract Use of measurements corrupted with gross errors for state estimation leads to biased state estimates, which, in turn, deteriorates the performances of model based process monitoring and control schemes. In this work, with the aim of minimizing the effects of gross errors on state estimates, robust versions of receding horizon nonlinear Kalman filter (RNK) are developed by integrating M-estimators with RNK. Two M-estimators, viz. Huber’s fair function and Hampel’s redescending estimator, have been considered for incorporating robustness in RNK. The proposed robust RNK formulation is further used to develop a robust simultaneous state and parameter estimation scheme. The efficacies of the proposed estimation schemes have been demonstrated by conducting simulation studies on a benchmark continuous stirred tank reactor (CSTR) system. The simulation studies reveal that, the proposed robust RNK formulations are able to generate estimation performances comparable to that of robust moving horizon estimation (MHE) scheme. Further, the proposed robust RNK based state and parameter estimator is able to estimate drifting model parameter accurately even in the presence of biased temperature measurements.

Non‐linear system modelling based on NARX model expansion on Laguerre orthonormal bases

This study proposes a new representation of discrete Non-linear AutoRegressive with eXogenous inputs (NARX) model by developing its coefficients associated to the input, the output, the crossed product, the exogenous product and the autoregressive product on five independent Laguerre orthonormal bases. The resulting model, entitled NARX-Laguerre, ensures a significant parameter number reduction with respect to the NARX model. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the five Laguerre bases. Therefore, the authors propose to use the genetic algorithm to optimise the NARX-Laguerre poles, based on the minimisation of the normalised mean square error. The performances of the resulting NARX-Laguerre model and the proposed optimisation algorithm are validated by numerical simulations and tested on the benchmark Continuous Stirred Tank Reactor.

Implementing multivariate statistics-based process monitoring: A comparison of basic data modeling approaches

Abstract The development of large interconnected plants has brought the need for the development of active and accurate performance monitoring methods. The commonly used approach to this problem is implementing the multivariate statistics-based process monitoring (MSPM). In MSPM, data modeling methods play the central role in developing normal operation models, based on which the monitoring statistics can be used to track the process operating performance. This paper seeks to perform a comparison study on the commonly used data modeling methods in the MSPM field, including principal component analysis, partial least squares, and canonical correlation analysis, to provide users and practitioners with informative details such that useful guidance can be offered to select the preferable methods. The interconnections between each two of them are first investigated. Then, dynamic extensions based on their static formulations including how they modify and resolve objective functions are revealed. Using the simulated data from the continuous stirred tank reactor benchmark process and real industrial data from the hot strip rolling mill process, parts of theoretical results are validated.

A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality

A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality is proposed in this paper. The addressed approach is based on the fact that zonotopes are more flexible for representing sets than boxes in interval analysis. Then the solver of set inversion via interval analysis is extended to set inversion via zonotope geometry by introducing the novel idea of bisecting zonotopes. The main feature of the extended solver of set inversion is the bisection and the evolution of a zonotope rather than a box. Thus the shape of admissible domains for set inversion can be broadened from boxes to zonotopes and the wrapping effect can be reduced as well by using the zonotope evolution instead of the interval evolution. Combined with global optimization via interval analysis, the extended solver of set inversion via zonotope geometry is further applied to design control invariant sets for constrained nonlinear discrete-time systems in a numerical way. Finally, the numerical design of a control invariant set and its application to the terminal control of the dual-mode model predictive control are fulfilled on a benchmark Continuous-Stirred Tank Reactor example.

Nonlinear Model Based Predictive Control Using Wiener and Hammerstein Models

A nonlinear model based predictive control scheme is presented basing on Wiener and Harnmerstein models. The control algorithm that has been developed retains the characteristics of conventional (linear) model predictive control including capabilities to control time-invariant nonlinear processes. In order to estimate the j-step ahead output signal the q-th degree Wiener and Harnmerstein model is represented by Volterra-series. The optimal manipulated variable is calculated by minimizing the cost function depending on the j-step predictor.The nonlinear model predictive control algorithm is applied to two case studies of chemical processes. A pH neutralization process, the basic structure of which fits to a Wiener model, and a highly nonlinear benchmark CSTR (continuous stirred tank reactor), are examined.