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In this paper, a new approach to fault detection and diagnosis that is based on correspondence analysis (CA) is proposed. CA is a powerful multivariate technique based on the generalized singular value decomposition. The merits of using CA lie in its ability to depict rows as well as columns as points in the dual lower dimensional vector space. CA has been shown to capture association between various features and events quite effectively. The key strengths of CA, for fault detection and diagnosis, are validated on data involving simulations as well as experimental data obtained from a laboratory-scale setup.

The total least-squares technique has been extensively used for the identification of dynamic systems when both the inputs and outputs are corrupted with noise. However, the major limitation of this technique has been the difficulty in identifying the actual and stable model parameters when the collinearity in the causal data block leads to several “small” singular values. This paper proposes a novel multivariate tool, namely, the augmented principal components analysis (APCA), to deal with collinearity problems under the errors-in-variables formulation. On the basis of the level of noise in each measured variable, the proposed technique is divided further into simple and generalized augmented principal components. Some of the errors-in-variables- and least-squares-based methods available in the literature have been shown as special cases of this APCA-based technique. The efficacy of the new technique over other conventional methods has been illustrated through representative case studies taken from the literature.

The prefilter-based control-relevant identification (CRI) scheme proposed by Rivera et al. [IEEE Trans. Autom. Control 1992, 37 (7), 964−974] for single-input/single-output (SISO) systems estimates a model of the system that matches the true system dynamics in a range of frequencies that are important and relevant for closed-loop performance. In this paper, an extension of this approach is proposed for the CRI of multi-input/multi-output (MIMO) systems by partitioning the overall system into individual multi-input/single-output (MISO) structures. Furthermore, CRI methodologies proposed hitherto have not examined the issue of accurate identification of the steady-state gain. In this paper, the importance of achieving good steady-state gain match is emphasized, and a method is proposed to identify a control-relevant model that has a good match, at steady state (zero frequency), as well as in the control-relevant frequency band, with the true plant. The effect of the proposed control-relevant prefiltering on the identification of the high- and low-gain directions is also analyzed in this paper. The proposed methodology is validated using simulations on representative problems from the literature and on a paper machine problem.

The design of disturbance classification and accommodation techniques for complex chemical systems is generating considerable research interest. In this work, we propose to employ a pattern recognition method, viz., the fuzzy clustering, to classify disturbances. Various operating modes of the plant, including normal and anticipated/measured fault modes, are represented as clusters in a suitable dynamic clustering space. The key idea is to classify any unmeasured disturbance in terms of nominal and known disturbance modes by assigning the appropriate membership to these known clusters. For the rejection of the unmeasured disturbances, the deployment of composite controllers that are built by fuzzy aggregation of the individual controller actions is proposed. Validation results using closed-loop simulation involving a simple illustrative single-input−single-output control loop and also a nonlinear, multivariable continuous stirred tank reactor are presented to demonstrate the validity of the methodology in classification and accommodation of unmeasured steplike disturbances.

A novel and more comprehensive formulation of the optimal control problem that reflects the operational requirements of a typical industrial fermentation has been proposed in this work. This formulation has been applied to a fed-batch bioreactor with three control variables, i.e., feed rates of carbon source, nitrogen source, and an oxygen source, to result in a 148.7% increase in product formation. Xanthan gum production using Xanthomonas campestris has been used as the model system for this optimization study, and the liquid-phase oxygen supply strategy has been used to supply oxygen to the fermentation. The formulated optimization problem has several constraints associated with it due to the nature of the system. A robust stochastic technique, differential evolution, has been used to solve this challenging optimization problem. The infinite dimensional optimization problem has been approximated to a finite dimensional one by control vector parametrization. The state constraints that are path constraints have been addressed by using penalty functions and by integrating them over the total duration to ensure a feasible solution. End point constraints on final working volume of the reactor and on the final residual concentrations of carbon and nitrogen sources have been included in the problem formulation. Further, the toxicity of the oxygen source, H2O2, has been addressed by imposing a constraint on its maximum usable concentration. In addition, the initial volume of the bioreactor contents and feed concentrations have been handled as decision variables, which has enabled a well-grounded choice for their values from the optimization procedure; adhoc values are normally used in the industry. All results obtained by simulation have been validated experimentally with good agreements between experimental and simulated values.

Chemical plants exhibit nonlinear dynamics that need to be captured accurately for model-based control. This paper focuses on a frequency-domain-based, control-relevant model reduction strategy for nonlinear process plants. The generalized frequency response function proposed for the nonlinear plants has been used to analyze the characteristics of nonlinear structures in the frequency domain, from a control-relevant viewpoint. Control-relevant model reduction is sought by minimizing the mismatch between a higher order, nonlinear proxy plant and candidate reduced order nonlinear model structures. The minimization is proposed to be done by prefiltering of identification data to shape the mismatch in a control-relevant manner. For these prefilters as well, candidate linear and nonlinear structures are evaluated and an algorithm to design the prefilters to reflect the servo and regulatory performance specifications is proposed. The model reduction methodology is used along with a nonlinear internal model control (NIMC) algorithm and is demonstrated on a simple simulation as well as on a representative nonlinear chemical reactor studied in the literature.

In this work, we propose a new method to model and control complex nonlinear dynamic systems. The suggested scheme employs an output curve methodology to determine the initial set of dynamic clustering spaces. The choice of the optimal dynamic clustering space is made through an analysis of cross validation performance and other indicative indices. A fuzzy clustering methodology for dynamic-model building is proposed. The relative advantages of the proposed adaptive fuzzy clustering method over other segregation methods are highlighted. For online control, a smooth internal model-switching strategy based on fuzzy methods is proposed and shown to be superior to other methods hitherto proposed in the literature. Two control structures based on the proposed methodology are discussed. The efficacy of the proposed fuzzy modeling and control schemes are demonstrated through several representative illustrative examples and by application to a high-purity distillation process.

The identification of nonlinear models for chemical processes solely from experimental data is described in this paper. The canonical variate analysis (CVA) technique that has served well in the identification of empirical linear process models is extended to construct data-based bilinear models in an iterative fashion. Numerous examples involving engineering systems are included to illustrate the practicality of the suggested approach for bilinear model identification. Finally, the use of the identified nonlinear models for control is demonstrated using the example of a simulated paper machine headbox system.