Ioannis Bonis

Multiple Model Predictive Control of Dissipative PDE Systems

Model predictive control (MPC) is a popular strategy, often applied to distributed parameter systems (DPSs). Most DPSs are approximated by nonlinear large-scale models. Using it directly for control applications is problematic because of the high associated computational cost and the nonconvexity of the underlying optimization problem. In this brief, we build on the notion of multiple MPC, combining it with equation-free model reduction techniques, to identify the (relatively low-dimensional) subspace of slow modes and obtain a local reduced-order linear model. This procedure results in an input/output framework, enabling the use of black-box deterministic and stochastic simulators. The set of linear low-dimensional models obtained off-line along the reference trajectories are used for linear MPC, either with off-line gain scheduling or with online identification of the reduced model. In the former approach, the decision to use the model in real time is taken a priori, whereas in the latter a local model is computed online as a function of a set stored in a model bank. The two approaches are discussed and validated using case studies based on a tubular reactor, a highly nonlinear dissipative partial differential equation system exhibiting instabilities and multiplicity of state.

A Reduced Linear Model Predictive Control Algorithm for Nonlinear Distributed Parameter Systems

Abstract A novel model reduction-based framework for linear Model Predictive Control (MPC) of Distributed Parameter Systems is presented. It exploits the separation of scales exhibited in many systems of engineering interest. It is based on the online, adaptive identification of the dominant modes of the system using the Arnoldi method. The low-dimensional dominant subspace corresponding to those modes is exploited for the linearization of the model. Only low-dimensional Jacobian and sensitivity matrices are involved in this framework. They are projections of the original matrices onto the dominant subspaces, computed efficiently with numerical directional perturbations. The low-order linear model from this procedure is utilized in the context of a MPC scheme. The efficiency of the proposed methodology is illustrated using a temperature tracking control of a tubular reactor which also involves measurement noise and disturbances.

Linear MPC based on data-driven Artificial Neural Networks for large-scale nonlinear distributed parameter systems

Process controller synthesis with detailed models is a challenging task, which may lead to many advantageous closed-loop features. Model reduction such as Proper Orthogonal Decomposition (POD) and (adaptive) linearization can be applied to tackle with the arising problems, whereas process data can be directly used to build accurate models via training of artificial neural networks (ANN). In this contribution, we present two methodologies we have recently developed, which combine ANN with POD, for use in the context of MPC: the process at hand is represented as a sum of products of time- varying coefficients (computed with ANN) with the POD basis functions computed from plant “snapshots”. The resulting accurate model can be used in NMPC, or trajectory piecewise linearization along a reference path can be applied on the ANN, yielding a series of linear models, suitable for linear MPC.

A Model Reduction-Based Optimisation Framework for Large-Scale Simulators Using Iterative Solvers

Abstract A novel gradient-based optimisation framework for large-scale steady-state input output simulators is presented. The method uses only low-dimensional Jacobian and reduced Hessian matrices calculated through on-line model-reduction techniques. The typically low-dimensional dominant system subspaces are adaptively computed using efficient subspace iterations. The corresponding low-dimensional Jacobians are constructed through a few numerical perturbations. Reduced Hessian matrices are computed numerically from a 2-step projection, firstly onto the dominant system subspace and secondly onto the subspace of the (few) degrees of freedom. The tubular reactor which is known to exhibit a rich parametric behaviour is used as an illustrative example.

Detailed Multi-dimensional Modeling of Direct Internal Reforming Solid Oxide Fuel Cells.

Abstract Fuel flexibility is a significant advantage of solid oxide fuel cells (SOFCs) and can be attributed to their high operating temperature. Here we consider a direct internal reforming solid oxide fuel cell setup in which a separate fuel reformer is not required. We construct a multidimensional, detailed model of a planar solid oxide fuel cell, where mass transport in the fuel channel is modeled using the Stefan‐Maxwell model, whereas the mass transport within the porous electrodes is simulated using the Dusty‐Gas model. The resulting highly nonlinear model is built into COMSOL Multiphysics, a commercial computational fluid dynamics software, and is validated against experimental data from the literature. A number of parametric studies is performed to obtain insights on the direct internal reforming solid oxide fuel cell system behavior and efficiency, to aid the design procedure. It is shown that internal reforming results in temperature drop close to the inlet and that the direct internal reforming solid oxide fuel cell performance can be enhanced by increasing the operating temperature. It is also observed that decreases in the inlet temperature result in smoother temperature profiles and in the formation of reduced thermal gradients. Furthermore, the direct internal reforming solid oxide fuel cell performance was found to be affected by the thickness of the electrochemically‐active anode catalyst layer, although not always substantially, due to the counter‐balancing behavior of the activation and ohmic overpotentials.

Multiscale Modelling of Spillover Processes in Heterogeneous Catalytic Systems

Abstract In this work, a multi-scale model of an electrochemically promoted catalytic system is formulated. The model accounts for the controlled migration of backspillover species [O δ- - δ+] from the support to the catalytic surface, when potential is applied between the catalyst and a counter electrode in a solid electrolyte cell. This metal-support interaction leads to a significant alteration of the catalytic activity. To the best of our knowledge, a systematic multi-scale model, which simulates the chemical and electrochemical processes taking place in electrochemically promoted catalytic systems, has not been developed yet. The proposed multi-scale model couples a macroscopic model based on commercial CFD software and an in-house developed efficient implementation of the kinetic Monte Carlo method (kMC) for the simulation of CO oxidation over a deposited on Yttria-Stabilized Zirconia (YSZ) Pt electrode.

Steady-state constrained optimisation for input/output large-scale systems

A model reduction-based, constrained optimisation algorithm for large-scale, steadystate systems is presented. The proposed technique belongs to the reduced Hessian class of methods and involves only low-order Jacobian and Hessian matrices. The reduced Jacobians are computed as projections onto the dominant subspace of the system and are calculated adaptively by numerical directional perturbations. The reduced Hessians are computed the same way, based on a 2-step projection scheme, firstly onto the dominant subspace of the system and secondly onto the subspace of the independent variables. The inequality constraints are handled using constraint aggregation functions. A more efficient version of the proposed algorithm is also presented. The behaviour of the proposed scheme is illustrated through two illustrative case studies including both equality and inequality constraints.