The research done by the group centers around the development and application of concepts in optimization theory, operations research, and numerical methods for process design, analysis, and control.
Topic: Algorithm Improvements for IPOPT
Nonlinear programming (NLP) has become an essential tool for process systems engineering. As one of the most popular interior point NLP solvers, IPOPT is widely used because of its high performance. However, it still has several drawbacks. Dependent constraints are common in chemical process models but violate the regularity conditions, which may cause the interior point method to fail. 175 options built in IPOPT have been shown to be tightly related to the performance, but tuning the parameters is still an open question. In my project, we aim to improve IPOPT’s performance for dependent and ill-conditioned problems through algorithmic modifications and data-based options recommendation. First, three structured regularization methods have been developed to handle the dependent equality constraints and results show an average reduction of more than 50% of the iterations. In addition, we are developing a new restoration design to better handle ill-conditioned problems. An IPOPT online submission system is developed for the data-based options tuning.
Topic: Dynamic reduced order models for bubbling fluidized bed adsorbers
Spatially distributed first-principles process models can give an accurate physical description of chemical processes, but lead to large-scale models whose numerical solution is challenging and computationally expensive. Therefore fast reduced order models are required for model-based real-time applications, such as advanced process control and dynamic real-time optimization. In this work, we focus on the model reduction of a bubbling fluidized bed (BFB) adsorber, which is a key component of a post-combustion carbon capture system. From a temporal aspect, dynamic reduced models are generated using nullspace projection and eigenvalue analysis method, with a basic idea of quasi-steady state approximation for the states with fast dynamics. From a spatial aspect, dynamic reduced models are developed using orthogonal collocation and proper orthogonal decomposition to reduce the size of the rigorous model. Finally, a computationally efficient and accurate dynamic reduced order model is developed for the BFB adsorber by combining temporal and spatial model reduction techniques, which is suitable for an online optimization-based control strategy.
Topic: Reduced Order Model (ROM)-based optimization for energy systems
As multi-scale modeling and advanced simulation technologies mature, it is desirable to utilize their predictive power in process design and optimization. However, these models present unique challenges for traditional optimization frameworks. A popular approach is to fit an algebraic surrogate model to these complex functions. However, small errors in the regression can result in a large deviation from the true optimum. We are developing trust region algorithms capable of adaptively controlling this error during the optimization process to provably converge to the true optimum.
Our current system of interest is the oxycombustion power generation process. In this process, the boiler is not easily described by algebraic models, so will model it use a hybrid zonal boiler model that integrates the radiation equation in 3D. This boiler model will be integrated into an equation oriented process optimization framework using trust region methods.
Topic: Dynamic Real-Time Optimization (DRTO)
Model predictive control (MPC) is an optimization based form of control that has many applications in the chemical industry. The mathematic programming formulation of the problem allows for an easy way to handle multiple-input-multiple-output systems, as well as state and control variable constraints. Furthermore, nonlinear model predictive control (NMPC) extends MPC to make use of a nonlinear dynamic model in order to ensure accuracy across a wider range of states.
Our goal is to ensure good performance when this technology is applied to large-scale chemical processes. In particular, we are interested in the stability of NMPC in the presence of disturbances. Specific areas of research include calculating predictive state trajectory bounds in order to quantify robust stability, as well as reformulations of the nonlinear programming (NLP) optimization problems that allow for robust stability even in pathological cases.
We are also interested in economic nonlinear model predictive control (e-NMPC) in which the process economics are optimized directly. This modification leads to new complications in the stability analysis, and there are many open questions in this area.
Topic: Pressure swing adsorption optimization strategies for CO2 capture
Pressure swing adsorption (PSA) has received recent attention as a potential process for economically removing CO2 from flue and/or shifted syngas for carbon capture and storage. We apply state-of-the-art methods for PSA optimization using a superstructure-based approach; this allows simultaneous selection of PSA cycle steps and optimization of operating parameters (feed flow rate, recycle fractions, bed pressures, etc.). The partial differential equation bed models are discretized with finite volumes in space and two flux limiters are compared. Sparse linear solvers are implemented to accelerate the integration of bed models and direct sensitivity equations, which are interfaced to MATLAB. The PSA optimization approach is demonstrated on CO2/H2 separation case studies for an integrated gasification combine cycle power plant, and solved by sequential quadratic programming solvers.
Topic: Modeling and optimal grade transitions for polypropylene processes in fluidized bed reactors
Gas phase polymerizations using fluidized bed reactors are widely implemented in industry. We present a set of differential and algebraic equations to simulate this process for producing polypropylene. Kinetic models based on multisite catalysts (Ziegler-Natta) are used for propylene and ethylene copolymerization. This work will lead to the grade transition optimization, shortening the transition time by manipulating operation conditions.
Topic: Advanced Optimal Control Strategies for Bubbling Fluidized Beds
Bubbling Fluidized Bed (BFB) models have been previously created for CO2 capture. Such models contain Partial Differential Equations to model the mass and energy balances for different regions inside the bed. Additionally there are Algebraic Equations to model the hydrodynamics, equations of state, etc. This leads to a system of Partial Differential Equations (PDAE) that can be handled through an implicit high order discretization scheme like collocation.
The availability of such models and new algebraic modeling languages like Pyomo, make possible the implementation of Non-Linear Model Predictive Control (NMPC) strategies for the BFB.
The goals of the project are to generate steady and dynamic state models for the BFB with generic discretization schemes and to implement fast NMPC and state estimation strategies.
Topic: Multistage Nonlinear Model Predictive Control under Uncertainty
Model Predictive Control (MPC) has been widely used in process control industry mainly because it can deal with constraints and multiple-input-multiple-output. However, the system performance deteriorates under the influence of uncertainty. The current robust MPC techniques are often shy of applications due to either model conservativeness or formidable computational effort. In order to improve this situation, we present a multistage nonlinear model predictive control (NMPC) to serve as a non-conservative robust NMPC scheme. Multistage NMPC models the uncertainty evolution with a scenario tree structure that exploits the degree of freedom by allowing future control inputs to adjust accordingly to future available information.
Currently, our case study is based on a nonlinear CSTR example with a setpoint tracking objective with one uncertain parameter. The performance of multistage NMPC has been compared to standard NMPC and no-recourse robust NMPC, and the result shows that multistage NMPC is a promising framework to account for plant uncertainty. The effect of different robust horizons has also been discussed.