Davood Babaei Pourkargar

Control of dissipative partial differential equation systems using APOD based dynamic observer designs

This article focuses on output feedback control of distributed parameter systems with limited number of sensors employing adaptive proper orthogonal decomposition (APOD) methodology. The controller design issue is addressed by combining a robust state controller with a dynamic observer of the system states to reduce sensor requirements. The use of APOD methodology allows the development of locally accurate low-dimensional reduced order dynamic models (ROMs) for controller synthesis thus resulting in a computationally-efficient alternative to using large-dimensional models with global validity. The derived ROMs are subsequently employed for the design of dynamic observers and controllers. The proposed methods are successfully used to achieve the desired control objective of stabilizing the Kuramoto-Sivashinksy equation (KSE) at a desired state spatial profile.

Feedback control of linear distributed parameter systems via adaptive model reduction in the presence of device network communication constraints

We focus on model-based networked control of general linear dissipative distributed parameter systems, the infinite dimensional representation of which can be decomposed to finite-dimensional slow and infinite-dimensional fast and stable subsystems. The controller synthesis of such systems is addressed using adaptive proper orthogonal decomposition (APOD). Specifically, APOD is used to recursively construct locally accurate low dimensional reduced order models (ROMs). The ROM is included in the control structure to reduce the frequency of spatially distributed sensor measurements over the network by suspending communication. The main objective of the current work is to identify a criterion for minimizing communication bandwidth (snapshots transfer rate) from the distributed sensors to the control structure considering closed-loop stability. The proposed approach is successfully used to regulate the thermal dynamics in a tubular chemical reactor.

Output tracking of spatiotemporal thermal dynamics in transport-reaction processes via adaptive model reduction

We consider the output tracking problem of spatially distributed processes described by nonlinear dissipative partial differential equations (DPDEs). The infinite dimensional representation of such systems can be decomposed to finite dimensional slow and infinite dimensional fast and stable subsystems. To circumvent the important issues of controller and observer synthesis for large dimensional models of DPDEs, the controller and observer design is addressed using adaptive proper orthogonal decomposition (APOD) to recursively construct locally accurate low dimensional reduced order models. The effectiveness of the proposed control structure is successfully illustrated on an output tracking problem of thermal dynamics in a catalytic reactor to reduce hot spot temperature and manage the thermal energy distribution across reactor length using limited number of actuators and sensors.

Optimal decomposition for distributed optimization in nonlinear model predictive control through community detection

Abstract Distributed optimization, based on a decomposition of the entire optimization problem, has been applied to many complex decision making problems in process systems engineering, including nonlinear model predictive control. While decomposition techniques have been widely adopted, it remains an open problem how to optimally decompose an optimization problem into a distributed structure. In this work, we propose to use community detection in network representations of optimization problems as a systematic method of partitioning the optimization variables into groups, such that the variables in the same groups generally share more constraints than variables between different groups. The proposed method is applied to the decomposition of the optimal control problem involved in the nonlinear model predictive control of a reactor-separator process, and the quality of the resulting decomposition is examined by the resulting control performance and computational time. Our result suggests that community detection in network representations of the optimization problem generates decompositions with improvements in computational performance as well as a good optimality of the solution.

Non-parametric correlative uncertainty quantification and sensitivity analysis: Application to a Langmuir bimolecular adsorption model

We propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depends critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated.

Spatiotemporal response shaping of transport-reaction processes via adaptive reduced order models

We present a framework to address the dynamic response shaping question of nonlinear transport-reaction chemical processes. The spatiotemporal behavior of such processes can be described in the form of dissipative partial differential equations (PDEs), the modal infinite-dimensional representation of which can in principle be partitioned into two subsystems; a finite-dimensional slow and its complement infinite-dimensional fast and stable subsystem. The dynamic shaping problem is addressed via regulation of error dynamics between the process and a desired spatiotemporal behavior presented by a target PDE system. We approximate the infinite-dimensional nature of the systems via model order reduction; adaptive proper orthogonal decomposition (APOD) is used to compute and recursively update the set of empirical basis functions required by Galerkin projection to build switching reduced order models of the spatiotemporal dynamics. Then, the nonlinear output feedback control design is formulated by combination of a feedback control law and a nonlinear Luenberger type dynamic observer to regulate the error dynamics. The effectiveness of the proposed control approach is demonstrated on shaping the thermal dynamics of an exothermic reaction in a catalytic chemical reactor.

Low-dimensional adaptive output feedback controller design for transport-reaction processes

This paper focuses on adaptive output feedback control of transport-reaction processes described by semi-linear parabolic partial differential equations (PDEs) in the presence of unknown reaction parameters. Galerkin projection is applied to derive a low-dimensional reduced order model which employed as the basis for the adaptive controller design. The proposed control structure is a combination of a Lyapunov-based controller, an adaptation law and a static observer. The adaptation law is introduced to identify the unknown parameters while the static observer is employed to estimate the system modes required by the controller which cannot be measured directly from the process. The stability of the closed-loop system is shown using Lyapunov arguments. The effectiveness of the proposed low-dimensional adaptive output feedback control structure is illustrated on a tubular chemical reactor where the spatiotemporal dynamics of temperature and concentration are modeled by semi-linear parabolic PDEs. The control objective is considered to be thermal dynamics regulation in the presence of unknown heat of reaction.

Wave motion suppression in the presence of unknown parameters using recursively updated empirical basis functions

We focus on adaptive wave motion suppression of fluid flows in the presence of unknown parameters. The suppression problem is addressed by low-dimensional adaptive nonlinear output feedback controller synthesis. We employed adaptive proper orthogonal decomposition to recursively compute the set of empirical basis functions needed by the Galerkin projection to derive updated reduced order models that can be used as the basis for Lyapunov-based adaptive output feedback controller design. A static observer is applied to estimate the state modes of the system required by the adaptive controller. The effectiveness of the proposed adaptive wave motion suppression method is illustrated on a generalized form of the Korteweg-de Vries-Burgers (KdVB) equation which can adequately describe the wave motions in a wide range of fluid flow processes.