Global stability results for systems under sampled‐data control

In this work sufficient conditions for uniform input‐to‐output stability and uniform input‐to‐state stability are presented for finite‐dimensional systems under feedback control with zero‐order hold. The conditions are expressed by means of single and vector Lyapunov functions. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonlinear observer design for state and disturbance estimation

A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov's auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor.     

An approach to mechanistic event recognition applied on monitoring organic matter depletion in SBRs

A fundamental practice in process engineering is monitoring the state dynamics of a system. Unfortunately, observability of some states is related to high costs, time, and efforts. The mechanistic event recognition (MER) aims to detect an event (defined as a change of the system with specific significance to the operation of the process) that cannot be directly observed but has some predictable effect on the dynamics of the systems. MER attempts to apply fault diagnosis techniques using mechanistic “recognition” models to describe the process. A systematic method for building recognition models using optimal experimental design tools is presented. As proof of concept, the MER approach to detect organic matter depletion in sequencing batch reactors, measuring only ammonia, dissolved oxygen, and nitroxides is applied. The event, that is, consumption of organic matter to a level below 50 gCOD/m³, was successfully detected even though microbial activity is known to continue after organic matter depletion. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3460–3472, 2014     

A Lyapunov approach for robust nonlinear state feedback synthesis

The authors apply the input/output linearization approach for nonlinear state feedback synthesis. The model uncertainty under consideration is a class of state model perturbations that satisfy appropriate matching conditions. The controller design uses a Lyapunov-based approach to guarantee uniform ultimate boundedness of the states and the output     

ISE-optimal nonminimum-phase compensation for nonlinear processes

This work concerns the optimal regulation of single-input–single-output nonminimum-phase nonlinear processes. The problem of calculation of an ISE-optimal, statically equivalent, minimum-phase output for nonminimum-phase compensation is formulated using Hamilton–Jacobi theory and the normal form representation of the nonlinear system. A Newton–Kantorovich iteration is developed for the solution of the pertinent Hamilton–Jacobi equations, which involves solving a Zubov equation at each step of the iteration. The method is applied to the problem of controlling a nonisothermal CSTR with Van de Vusse kinetics, which exhibits nonminimum-phase behaviour.     

Hidden Markov model based approach for diagnosing cause of alarm signals

When a fault occurs in a process, it slowly propagates within the system and affects the measurements triggering a sequence of alarms in the control room. The operators are required to diagnose the cause of alarms and take necessary corrective measures. The idea of representing the alarm sequence as the fault propagation path and using the propagation path to diagnose the fault is explored. A diagnoser based on hidden Markov model is built to identify the cause of the alarm signals. The proposed approach is applied to an industrial case study: Tennessee Eastman process. The results show that the proposed approach is successful in determining the probable cause of alarms generated with high accuracy. The model was able to identify the cause accurately, even when tested with short alarm sub-sequences. This allows for early identification of faults, providing more time to the operator to restore the system to normal operation.     

Nonlinear observer design for two-time-scale systems

A two-time-scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two-time-scale systems and presents two alternative nonlinear observer design approaches, one full-order and one reduced-order. The full-order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced-order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow-motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced-order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.     

Discrete-time nonlinear observer design using functional equations

The present research work proposes a new approach to the discrete-time nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer, the proposed approach develops a nonlinear analogue. The formulation of the discrete-time nonlinear observer design problem is realized via a system of first-order linear nonhomogeneous functional equations, and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory. The solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.