Sivakumar Pitchaiah

We address the problem of control of spatially distributed processes in the presence of measurement constraints. Specifically, we assume the availability of sensors that measure part of the state spatial profile. The measurements are utilized for the derivation and on‐demand update of reduced order models (ROM) based on an extension of the adaptive proper orthogonal decomposition (APOD) method using a snapshot reconstruction technique. The proposed Gappy‐APOD methodology constructs locally accurate low‐dimensional ROM thus resulting in a computationally efficient alternative to using a large‐dimensional ROM with global validity. Based on the low‐dimensional ROM and continuous measurements available from point sensors a Lyapunov‐based static output feedback controller is subsequently designed. The proposed controller design method is illustrated on an unstable process modeled by the Kuramoto‐Sivashinsky equation, when the designed controller successfully stabilizes the process even in the presence of model uncertainty. © 2012 American Institute of Chemical Engineers AIChE J, 59: 747–760, 2013

This work employs adaptive reduced order models (ROMs) in the design of model predictive controllers for stabilization of processes that are mathematically expressed as parabolic partial differential equation (PDE) systems. Initially, we construct a locally valid ROM of the PDE system employing the basis functions computed by applying an adaptive model reduction methodology called APOD on a small data ensemble. This ROM is then utilized in the design of model predictive controllers (MPC) under constraints on the control action. As periodic closed-loop process data becomes available (during closed-loop operation under the constructed MPC), we recursively update the ROM by employing our computationally efficient adaptive model reduction methodology thus extending the validity of ROM over the current operating region. The effects of employing the adaptive methodology on performance of MPC is studied. The design of such MPC controllers is illustrated by employing the methodology on numerical simulations.

This work addresses the problem of tracking and stabilization of FitzHugh-Nagumo equation (FHN) subject to Neumann boundary conditions via static output feedback control using adaptive model reduction methodology and specifically the adaptive proper orthogonal decomposition (APOD) approach. Initially, an ensemble of eigenfunctions is constructed based on a relatively small data ensemble using method of snapshots and Karhunen-Loève expansions (KLE). We then recursively update the eigenfunctions as additional data from the process become available periodically, thus relaxing the need for a representative ensemble in KLE. An accurate reduced-order model (ROM) is constructed and periodically refined via nonlinear Galerkin's method based on the eigenfunctions. Using the ROM and continuous measurements available from restricted number of sensors a static output feedback controller is subsequently designed. This controller is used achieve the desired control objective of stabilizing the FHN equation at a desired reference trajectory. The success of the adaptive model reduction and output-feedback controller design methodology are illustrated using computer simulations.

The problem of robust feedback control of spatially distributed processes described by highly dissipative partial differential equations (PDEs) is considered. Typically, this problem is addressed through model reduction where finite dimensional approximations to the original PDE system are derived. A common approach to this task is the Karhunen-Loeve expansion combined with the method of snapshots. To circumvent the issue of a priori availability of a sufficiently large ensemble of PDE solution data, we focus on the recursive computation of eigenfunctions as additional data from the process become available. Initially, an ensemble of eigenfunctions is constructed with a relatively small number of snapshots. The dominant eigenspace of this ensemble is then identified to compute the empirical eigenfunctions required for model reduction. This dominant eigenspace is reevaluated with the addition of new snapshots the dominant eigenspace is reevaluated and its dimensionality may increase or decrease. Because this dimensionality is typically small the computational burden is also small. This approach is applied to a representative example of dissipative PDEs, to demonstrate the effectiveness of the approach to design robust controllers.

This article focuses on dynamic output feedback and robust control of quasi linear parabolic partial differential equations (PDE) systems with time-varying uncertain variables. Especially processes that are described by dissipative PDEs are considered. The states of the process required for designing controllers are dynamically estimated from limited number of noisy process measurements employing an Extended Kalman filter. The issue of utilizing these estimated states in a robust controller to achieve the desired process objective is investigated. The controller design needs to address both model uncertainty and sensor noise. The methodology is employed on an representative example wherein the desired objective is to stabilize an unstable operating point in a catalytic rod, where an exothermic reaction occurs. A finite dimensional robust controller, utilizing dynamically estimated states, is used to successfully stabilize the process to an open-loop unstable steady-state.

The problem of online system identification and control of microscopic processes is considered. Traditionally, such processes are numerically simulated employing atomistic simulations. The unavailability of closed-form models to describe the evolution makes the controller design task challenging. A methodology is developed in which subspace algorithms for bilinear system identification are coupled with feedback linearization techniques with objective the online identification and control of microscopic processes. We illustrate the applicability of the proposed methodology on a Kinetic Monte Carlo (KMC) realization of a simplified surface reaction scheme that describes the dynamics of CO oxidation by O₂ on a Pt catalytic surface. The proposed controller successfully forces the process from one stationary state to another state.