Sridharakumar Narasimhan

New nonlinear residual feedback observer for fault diagnosis in nonlinear systems

The increased complexity of plants and the development of sophisticated control systems have necessitated the parallel development of efficient Fault Detection and Isolation (FDI) systems. This paper discusses a model based technique, viz., observers for detecting and isolating parametric and sensor faults. In this paper, a novel diagonal nonlinear residual feedback observer is proposed which is valid for a certain class of nonlinear systems where, subject to other conditions, the state depends nonlinearly on the fault. A number of typical chemical engineering systems can be represented by models of this form. The structure of the observer ensures that the residuals are diagonally affected by the faults. Conditions for exact decoupling of residuals are presented and convergence of the observer in the presence of step faults is proved using Lyapunov like analysis. Multiple observers and a decision logic module are used for FDI when there are un-monitored faults. Results are presented from numerical simulations of an illustrative example and a typical chemical engineering system: a counter-current heat exchanger.

Robust sensor network design for fault diagnosis

An appropriately designed sensor network is crucial for the success of any fault diagnostic strategy. Strategies for optimally locating sensors based on reliability-maximization and cost-minimization exist. While reliability and cost criteria have been used in selecting optimal sensor networks, the robustness of the network to uncertainties/errors in the underlying model and probability data have not been considered. In this article, we present robustness enhancing criteria for the design of sensor networks for reliable fault diagnosis. Robustness to modeling errors is incorporated by choosing a distributed sensor network. Robustness to available probability data is incorporated by minimizing the unreliability of fault detection with uncertain probability data. These criteria are incorporated in a lexicographic manner along with the overall reliability-maximization and cost-minimization objectives in a single optimization problem. Solution to this optimization problem results in a solution that is most reliable, robust and cost minimal in a lexicographic sense. The utility of the proposed approaches is demonstrated through the Tennessee Eastman case study.

Optimal output selection for control of batch processes

Near-optimal control of batch processes can often be obtained using simple feedback structures. The maximum gain rule for selection of good outputs for feedback control is extended to nonlinear tracking problems, such as found in control of batch processes.

Plant Friendly Input Design: Convex Relaxation and Quality

A common practice in a system identification exercise is to perturb the system of interest and use the resulting data to build a model. The problem of interest in this contribution is to synthesize an input signal that is maximally informative for generating good quality models while being “plant friendly,” i.e., least hostile to plant operation. In this contribution, limits on input move sizes are the plant friendly specifications. The resulting optimization problem is nonlinear and nonconvex. Hence, the original plant friendly input design problem is relaxed which results in a convex optimization problem. We formulate a SemiDefinite Programme using the theory of generalized Tchebysheff inequalities to derive tight bounds on the quality of relaxation. Simulations show that the relaxation results in more plant friendly input signals.

Multi-objective optimal input design for plant friendly identification

In optimal input design problems, the designer seeks to solve for maximally informative inputs to be used as perturbation signals in system identification experiments. Plant- friendly identification experiments are those that satisfy plant or operator constraints on experiment time, input and output amplitudes or input move sizes. These have been reported to be in direct conflict with requirements for good identification. Hence plant-friendly input design is inherently multi-objective in nature. In this contribution, we present the use of two well known techniques of multi-objective optimization to solve for a plant friendly input design where the plant friendly objective is to keep input move sizes low. We relax the constraint on the input move sizes by constraining the variance of the move size instead. Both techniques result in convex optimization problems which can be solved efficiently using powerful algorithms.

Structural Properties of Gene Regulatory Networks: Definitions and Connections

The study of gene regulatory networks is a significant problem in systems biology. Of particular interest is the problem of determining the unknown or hidden higher level regulatory signals by using gene expression data from DNA microarray experiments. Several studies in this area have demonstrated the critical aspect of the network structure in tackling the network modelling problem. Structural analysis of systems has proved useful in a number of contexts, viz., observability, controllability, fault diagnosis, sparse matrix computations etc. In this contribution, we formally define structural properties that are relevant to Gene Regulatory Networks. We explore the structural implications of certain quantitative methods and explain completely the connections between the identifiability conditions and structural criteria of observability and distinguishability. We illustrate these concepts in case studies using representative biologically motivated network examples. The present work bridges the quantitative modelling methods with those based on the structural analysis.

Unsupervised Segmentation of Cervical Cell Images Using Gaussian Mixture Model

Cervical cancer is one of the leading causes of cancer death in women. Screening at early stages using the popular Pap smear test has been demonstrated to reduce fatalities significantly. Cost effective, automated screening methods can significantly improve the adoption of these tests worldwide. Automated screening involves image analysis of cervical cells. Gaussian Mixture Models (GMM) are widely used in image processing for segmentation which is a crucial step in image analysis. In our proposed method, GMM is implemented to segment cell regions to identify cellular features such as nucleus, cytoplasm while addressing shortcomings of existing methods. This method is combined with shape based identification of nucleus to increase the accuracy of nucleus segmentation. This enables the algorithm to accurately trace the cells and nucleus contours from the pap smear images that contain cell clusters. The method also accounts for inconsistent staining, if any. The results that are presented shows that our proposed method performs well even in challenging conditions.

Approximate dynamic programming based control of hyperbolic PDE systems using reduced-order models from method of characteristics

Abstract Approximate dynamic programming (ADP) is a model based control technique suitable for nonlinear systems. Application of ADP to distributed parameter systems (DPS) which are described by partial differential equations is a computationally intensive task. This problem is addressed in literature by the use of reduced order models which capture the essential dynamics of the system. Order reduction of DPS described by hyperbolic PDEs is a difficult task as such systems exhibit modes of nearly equal energy. The focus of this contribution is ADP based control of systems described by hyperbolic PDEs using reduced order models. Method of characteristics (MOC) is used to obtain reduced order models. This reduced order model is then used in ADP based control for solving the set-point tracking problem. Two case studies involving single and double characteristics are studied. Open loop simulations demonstrate the effectiveness of MOC in reducing the order and the closed loop simulations with ADP based controller indicate the advantage of using these reduced order models.

Economic back-off selection based on optimal multivariable controller

Abstract This paper discusses the minimum backed off operating point selection problem based on process economics. In this work, we consider the case where the nominal operating point is not completely constrained, i.e., there are some unconstrained degrees of freedom or manipulations available. In this regard, we propose a stochastic formulation that ensures feasible dynamic operating region within the prescribed confidence limit. Furthermore, the formulation also finds a suitable multivariable controller to achieve economic benefits. The problem is nonlinear and non-convex and hence an iterative solution procedure is proposed such that at each step in the iteration, a convex problem is solved. Finally, the approach is illustrated using an evaporation process.

Explicit MPC with output feedback using self-optimizing control

Abstract Model predictive control (MPC) is a favored method for handling constrained linear control problems. Normally, the MPC optimization problem is solved on-line, but in ‘explicit MPC’ an explicit precomputed feedback law is used for each region of active constraints (Bemporad et al., 2002). In this paper we make a link between this and the ‘self-optimizing control’ idea of finding simple policies for implementing optimal operation. The ‘nullspace’ method (Alstad and Skogestad, 2007) generates optimal variable combinations, c = u – Kx , which for the case with perfect state measurements are equivalent to the explicit MPC feedback laws, where K is the optimal state feedback matrix in a given region. More importantly, this link makes it possible to derive explicit feedback laws for cases with (1) state measurement error included and (2) measurement (rather than state) feedback. We further show how to generate optimal low-order controllers for unconstrained optimal control, also in the presence of noise.