Shankar Narasimhan S

Given a state space model together with the state noise and measurement noise characteristics, there are well established procedures to design a Kalman filter based model predictive control (MPC) and fault diagnosis scheme. In practice, however, such disturbance models relating the true root cause of the unmeasured disturbances with the states/outputs are difficult to develop. To alleviate this difficulty, we reformulate the MPC scheme proposed by K.R. Muske and J.B. Rawlings [Model predictive control with linear models, AIChE J. 39 (1993) 262-287] and the fault tolerant control scheme (FTCS) proposed by J. Prakash, S.C. Patwardhan, and S. Narasimhan [A supervisory approach to fault tolerant control of linear multivariable systems, Ind. Eng. Chem. Res. 41 (2002) 2270-2281] starting from the innovations form of state space model identified using generalized orthonormal basis function (GOBF) parameterization. The efficacy of the proposed MPC scheme and the on-line FTCS is demonstrated by conducting simulation studies on the benchmark shell control problem (SCP) and experimental studies on a laboratory scale continuous stirred tank heater (CSTH) system. The analysis of the simulation and experimental results reveals that the MPC scheme formulated using the identified observers produces superior regulatory performance when compared to the regulatory performance of conventional MPC controller even in the presence of significant plant model mismatch. The FTCS reformulated using the innovations form of state space model is able to isolate sensor as well as actuator faults occurring sequentially in time. In particular, the proposed FTCS is able to eliminate offset between the true value of the measured variable and the setpoint in the presence of sensor biases. Thus, the simulation and experimental study clearly demonstrate the advantages of formulating MPC and generalized likelihood ratio (GLR) based fault diagnosis schemes using the innovations form of state space model identified from input output data. © 2005 Elsevier Ltd. All rights reserved.

In this work, we have developed a reduced order model relevant for fault diagnosis and control. This model is combined with a generalized likelihood ratio (GLR) method and integrated with fault tolerant control schemes developed earlier. Simulation studies of an ideal binary distillation column show that the use of reduced order model improves the diagnostic performance thereby leading to improved fault tolerance. Furthermore, the proposed strategy is also computational more efficient. In inferential control, such as the use of temperature measurements to infer product compositions, the proposed fault tolerant control scheme performs better than the conventional control scheme when various soft faults occur. © 2008 Canadian Society for Chemical Engineering.

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization and control. Since many chemical processes often exhibit nonlinear dynamics, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed to improve the data quality. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. Recently a recursive estimation technique for nonlinear dynamic processes has been proposed which combines the merits of EKF and NDDR techniques. This technique, named as Recursive Nonlinear Dynamic Data Reconciliation (RNDDR), provides state and parameter estimates that satisfy bounds and other constraints imposed on them. However, the estimate error covariance matrix in RNDDR is computed in the same manner as in EKF, that is, the effects of both nonlinearity and constraints are neglected in the computation of the estimate error covariance matrix. A relatively new method known as the Unscented Kalman Filter has been developed for nonlinear processes, in which the statistical properties of the estimates are computed without resorting to linearization of the nonlinear equations. This leads to improved accuracy of the estimates. In this paper, we combine the merits of the Unscented Kalman Filter and the RNDDR to obtain the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) technique. This technique addresses all concerns arising due to the presence of nonlinearity and constraints within a recursive estimation framework, resulting in an efficient, accurate and stable method for real-time state and parameter estimation for nonlinear dynamic processes. © 2006 Elsevier Ltd. All rights reserved.

Model predictive control (MPC) schemes are typically developed under the assumption that the sensors and actuators are free from faults. Attempts to develop fault-tolerant MPC schemes have mainly focused on dealing with hard faults, such as sensor or actuator failures, process leaks, etc. However, soft faults such as biases or drifts in sensors or actuators are more frequently encountered in the process industry. Occurrences of such faults can lead to degradation in the closed loop performance of the MPC controller. Since MPC controllers are typically used to control key operations in a chemical plant, this can have an impact on safety and productivity of the entire plant. The conventional approach to dealing with such soft faults in MPC formulations is through the introduction of additional artificial states to the model. The main limitation of this approach is that number of artificial extra states introduced cannot exceed the number of measurements. This implies that it is necessary to have a priori knowledge of which subset of faults are most likely to occur. In this paper, an active on-line fault-tolerant model predictive control (FTMPC) scheme is proposed by integrating state space formulation of MPC with the fault detection and identification (FDI) method based on generalized likelihood ratios. The fact that both these schemes use a Kalman filter as their basis facilitates tight integration of these two components. The main difference between the conventional MPC formulation and FTMPC formulation is that the bias corrections to the model are made as and when necessary and at qualified locations identified by the FDI component. The FTMPC eliminates offset between the true values and set points of controlled variables in the presence of a variety of faults while conventional MPC does not. Also, the true values of state variables, manipulated inputs, and measured variables are maintained within their imposed bounds in FTMPC, while in conventional MPC, these may be violated when soft faults occur. These advantages of the proposed scheme are demonstrated using simulation studies on a CSTR process and experimental studies conducted on the temperature control of a coupled two tank heater system. © 2005 American Chemical Society.

Dynamic simulation models of gas pipeline networks can be used for on-line applications such as state estimation, leak detection, etc. A prime requirement for such models is computational efficiency. In this paper, a transfer function model of a gas pipeline is used as a basis for developing a dynamic simulator for gas pipeline networks. The simulator is incorporated in a data reconciliation framework, which is ideally suited for on-line state estimation based on all available measurements of pressures and flow rates. The American Gas Association (AGA) model is used for making realistic computations of the gas compressibility. Accuracy and computational efficiency of the proposed method are evaluated by comparing our results with those obtained using a fully nonlinear second-order accurate finite difference method. The ability of the proposed approach for obtaining accurate state estimation from noisy measurements is demonstrated through simulations on an example network. We also demonstrate the use of the proposed approach for estimating an unknown demand at any node by exploiting the redundancy in measurements. © 2006 American Chemical Society.

The quality of multivariate calibration (MVC) models obtained depends on the effective treatment of errors in spectral data. If errors in different absorbance measurements are correlated and have different variances, then the Maximum Likelihood Principal Component Regression (MLPCR) (Wentzell et al., Anal. Chem. 69 (1997), 2299-2311) is an optimal approach which gives a more accurate MVC model. However, this approach requires either complete knowledge of the error covariances or replicated measurements of all spectra from which an estimate of error covariances can be obtained. We propose a method for developing MVC models from non-replicated measurements when errors in different absorbances are independent, but can have different unknown variances. The core of the proposed approach is an Iterative Principal Component Analysis method which simultaneously estimates the lower dimensional spectral subspace and all the error variances. Application of this approach to simulated and experimental data sets demonstrates that the quality of the model obtained using the proposed method is better than that obtained using PCR, and is comparable to the accuracy of the model obtained using MLPCR. © 2006.

Faults lead to loss of productivity and in rare cases, loss of human lives. Therefore fault diagnosis is a critical task for increased reliability and safety. There are a variety of techniques that have been proposed in the literature for fault diagnosis. A comprehensive diagnostic problem is one which involves parametric changes in the presence of sensor failures and controller or actuator malfunction. In this paper we describe a diagnostic framework that integrates qualitative models with quantitative estimation to address the comprehensive diagnostic problem. The comprehensive diagnostic framework presented in this paper can be studied as four modules. The first module, also referred to as the diagnostic module, uses qualitative techniques to generate a hypotheses set of all possible root causes. In this paper we study a signed directed graph based qualitative model for the generation of hypotheses. The second module, called the hypothesis generator intelligently constructs and reorders the candidate hypothesis sets. The third module is the nonlinear estimation module, which estimates the relevant parameters in the candidate hypothesis. The fourth module performs statistical testing of the estimation results to either validate or invalidate the hypothesis. The efficacy of the proposed framework is demonstrated on simulation examples. © 2007 Institution of Chemical Engineers.

The accuracy of a multivariate calibration (MVC) model for relating concentrations of multicomponent mixtures to their spectral measurements depends on effective handling of errors in the measured data. For the case when error variances vary along only one mode (either along mixtures or along wavelengths), a method to estimate the error variances simultaneously along with the spectral subspace was developed by Narasimhan and Shah (Control Engineering Practice, 16, (2008), 146-155). This method was exploited by Bhatt et al. (Chemom. Intell. Lab. Syst., 85, (2007), 70-81) to develop an iterative principal component regression (IPCR) MVC model, which was shown to be more accurate than models developed using PCR. In this work, the IPCR method is extended to deal with measurement errors whose variances vary along both modes, by using a factored noise model. As a first step, an iterative procedure is developed to estimate the error variance factors along with the spectral subspace, which is subsequently used in developing the regression model. Using simulated and experimental data, it is shown that the quality of the MVC model developed using the proposed method is better than that obtained using PCR, and is as good as the model obtained using Maximum Likelihood PCR, which requires knowledge of the error variances. For dealing with large data sets, a sub-optimal approach is also proposed for estimating the large number of error variances. © 2009 Elsevier B.V. All rights reserved.

There is growing realization that on-line model maintenance is the key to realizing long term benefits of a predictive control scheme. In this work, a novel intelligent nonlinear state estimation strategy is proposed, which keeps diagnosing the root cause(s) of the plant model mismatch by isolating the subset of active faults (abrupt changes in parameters/disturbances, biases in sensors/actuators, actuator/sensor failures) and auto-corrects the model on-line so as to accommodate the isolated faults/failures. To carry out the task of fault diagnosis in multivariate nonlinear time varying systems, we propose a nonlinear version of the generalized likelihood ratio (GLR) based fault diagnosis and identification (FDI) scheme (NL-GLR). An active fault tolerant NMPC (FTNMPC) scheme is developed that makes use of the fault/failure location and magnitude estimates generated by NL-GLR to correct the state estimator and prediction model used in NMPC formulation. This facilitates application of the fault tolerant scheme to nonlinear and time varying processes including batch and semi-batch processes. The advantages of the proposed intelligent state estimation and FTNMPC schemes are demonstrated by conducting simulation studies on a benchmark CSTR system, which exhibits input multiplicity and change in the sign of steady state gain, and a fed batch bioreactor, which exhibits strongly nonlinear dynamics. By simulating a regulatory control problem associated with an unstable nonlinear system given by Chen and Allgower [H. Chen, F. Allgower, A quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability, Automatica 34(10) (1998) 1205-1217], we also demonstrate that the proposed intelligent state estimation strategy can be used to maintain asymptotic closed loop stability in the face of abrupt changes in model parameters. Analysis of the simulation results reveals that the proposed approach provides a comprehensive method for treating both faults (biases/drifts in sensors/actuators/model parameters) and failures (sensor/ actuator failures) under the unified framework of fault tolerant nonlinear predictive control. © 2008 Elsevier Ltd. All rights reserved.