John D. Hedengren

Initialization Strategies for Optimization of Dynamic Systems

Abstract For dynamic optimization applications, real-time solution reliability is improved if there is an initialized prior solution that is sufficiently close to the intended solution. This paper details several initialization strategies that are useful for obtaining an initial solution. Methods include warm start from a prior solution, linearization, structural decomposition, and an incremental unbounding of decision variables that leads up to solving the originally intended problem. Even when initialization is not required to solve a dynamic optimization problem, a staged initialization approach sometimes leads to an overall faster solution time when compared to a single optimization attempt. Several challenging optimization problems are detailed that include a high-index differential and algebraic equation pendulum model, a standard reactor model used in many benchmark tests, a tethered aerial vehicle, and smart grid energy storage. These applications are representative of a larger class of applications resulting from the simultaneous approach to optimization of dynamic systems.

Optimal Trajectory Generation using Model Predictive Control for Aerially Towed Cable Systems

This paper studies trajectory generation for a mothership that tows a drogue using a flexible cable. The contributions of this paper include model validation for the towed cable system described by a lumped mass extensible cable using flight data, and optimal trajectory generation for the towed cable system with tension constraints using model predictive control. The optimization problem is formulated using a combination of the squared error and L1-norm objective functions. Different desired circular trajectories of the towed body are used to calculate optimal trajectories for the towing vehicle subject to performance limits and wind disturbances. Trajectory generation for transitions from straight and level flight into an orbit is also presented. The computational efficiency is demonstrated, which is essential for potential real-time applications. This paper gives a framework for specifying an arbitrary flight path for the towed body by optimizing the action of the towing vehicle subject to constraints.

Dynamic optimization of a solar thermal energy storage system over a 24 hour period using weather forecasts

A solar thermal power plant is used as a case study for dynamic heat integration with thermal energy storage. Findings show that thermal energy storage gives the system the ability to make the power dispatchable. Additionally, by solving a 24-hour dynamic optimization problem where the plant temperatures and power output are variable allows the system to capture and harvest a higher percentage of solar energy, with the most benefit occurring on mostly cloudy days. The solar energy captured increases 64% from 4.75 MWh to 7.80 MWh using this scheme. Hybrid plant operation and the ability to bypass the storage tanks further improve the system performance.

Moving Horizon Estimation and Control for an Industrial Gas Phase Polymerization Reactor

Moving horizon estimation (MHE) has been applied to an industrial gas phase polymerization reactor to improve estimates of current states and parameters. MHE is compared to implicit dynamic feedback (IDFtrade). With MHE, there is improved estimation of unmodeled disturbances in the UNIPOLtrade polyethylene plant. The UNIPOLtrade technology is licensed by Univation, a joint venture between ExxonMobil and Dow. The polymerization reactor and plant model is a large-scale set of differential and algebraic equations (DAEs) posed in open equation form. The DAE model is converted to algebraic equations by orthogonal collocation and solved with the MHE objective function in a simultaneous optimization. NOVAtrade, an active-set sparse NLP solver, is used to converge the problem that has 46,870 variables, 18 complementarity conditions, and a Jacobian sparsity of 0.01%. This large, sparse optimization problem is initiated every 5 minutes to update the model as new plant measurements become available and prior to the control optimization. The same plant model is used for nonlinear model predictive control (MPC) with 10 manipulated variables (MVs) and 26 controlled variables (CVs). In this case, a significant advantage is that with MHE a simpler rigorous model suffices for the application of nonlinear MPC.

Approximate Nonlinear Model Predictive Control with In Situ Adaptive Tabulation

In situ adaptive tabulation (ISAT) is applied to store and retrieve solutions of nonlinear model predictive control (NMPC) problems. ISAT controls approximation error by adaptively building the database of NMPC solutions with piecewise linear local approximations. Unlike initial state or constraint parameterized constrained quadratic programming (QP) solutions, ISAT approximates NMPC solutions within a specified tolerance, thereby easing the dimensionality difficulties of these other techniques. In the limit, as the specified tolerance is reduced to zero and for linear models with quadratic objective functions, ISAT becomes an adaptive version of state parameterized storage and retrieval of mp-QP problems.

Dynamic Parameter Estimation and Optimization for Batch Distillation

Abstract This work reviews a well-known methodology for batch distillation modeling, estimation, and optimization but adds a new case study with experimental validation. Use of nonlinear statistics and a sensitivity analysis provides valuable insight for model validation and optimization verification for batch columns. The application is a simple, batch column with a binary methanol–ethanol mixture. Dynamic parameter estimation with an l1-norm error, nonlinear confidence intervals, ranking of observable parameters, and efficient sensitivity analysis are used to refine the model and find the best parameter estimates for dynamic optimization implementation. The statistical and sensitivity analyses indicated there are only a subset of parameters that are observable. For the batch column, the optimized production rate increases by 14% while maintaining product purity requirements.

Model predictive control with a rigorous model of a Solid Oxide Fuel Cell

Degradation of Solid Oxide Fuel Cells (SOFCs) can be minimized by maintaining reliability parameters during load changes. These reliability parameters are critical to maintain power generation efficiency over an extended life of the SOFC. For SOFCs to be commercially viable, the life must exceed 20,000 hours for load following applications. This is not yet achieved because transient stresses damage the fuel cell and degrade the performance over time. This study relates the development of a dynamic model for SOFC systems in order to predict optimal manipulated variable moves along a prediction horizon. The model consists of hundreds of states and parameters that permit tracking of a realistic response. Previously, this detailed model was too computationally intensive to run in parallel with the SOFC process. The contribution of this paper is an application study to enable a large-scale simulation model to be used in Model Predictive Control (MPC) without simplification. Such a technology permits real time calculation of controller moves while loads are followed during operation. The contribution demonstrates the assumptions and approach necessary to provide real-time calculations for optimal predictive control operations using a rigorous model of the SOFC process. Large-scale process models are rarely employed in real-time control because of the prohibitive computational expense necessary to complete the calculations within the specified cycle time. An efficient model based predictive controller reduces operational fluctuations related to the startup and shutdown conditions, without exceeding reliability limits in the cells.

Investigating the impact of Cryogenic Carbon Capture on power plant performance

Cryogenic Carbon Capture (CCC) is a CO2 mitigation process that can be integrated into existing baseline and load following fossil-fueled power plants. This process consumes less energy than conventional chemical absorption and includes energy storage capability. The CCC process has a fast response time to load changes to allow higher utilization of intermittent renewable power sources to be used at a grid-scale level in the power sector. The impact of the CCC process on the performance and operating profit of a single fossil-fueled power generation unit is studied in this paper. The proposed system (power production from wind, coal, and natural gas) meets the total electricity demand with 100% utilization of the available wind energy. The operational strategy for the hybrid energy-carbon capture system and the change in the performance of the hybrid system due to the seasonal changes are also examined in this paper. A sensitivity analysis is implemented to investigate the change in operating strategy of the hybrid system based on the relative fraction of wind energy adoption. The optimal wind energy adoption factor in the proposed system is obtained.

Evolutionary View Planning for Optimized UAV Terrain Modeling in a Simulated Environment

This work demonstrates the use of genetic algorithms in optimized view planning for 3D reconstruction applications using small unmanned aerial vehicles (UAVs). The quality of UAV site models is currently highly dependent on manual pilot operations or grid-based automation solutions. When applied to 3D structures, these approaches can result in gaps in the total coverage or inconsistency in final model resolution. Genetic algorithms can effectively explore the search space to locate image positions that produce high quality models in terms of coverage and accuracy. A fitness function is defined, and optimization parameters are selected through semi-exhaustive search. A novel simulation environment for evaluating view plans is demonstrated using terrain generation software. The view planning algorithm is tested in two separate simulation cases: a water drainage structure and a reservoir levee, as representative samples of infrastructure monitoring. The optimized flight plan is compared against three alternate flight plans in each case. The optimized view plan is found to yield terrain models with up to 43% greater accuracy than a standard grid flight pattern, while maintaining comparable coverage and completeness.

Advanced Deepwater Monitoring System

This study investigates new methods to improve deepwater monitoring and addresses installation of advanced sensorson ”already deployed” risers, flowlines, trees, and other deep water devices. A major shortcoming of post installed monitoring s ystems in subsea is poor coupling between the sensor and structure. This study provided methods to overcome this problem. Both field testing in subsea environments and laboratory tes ting were performed. Test articles included actual flowline p ipe and steel catenary risers up to twenty-four inches in diamet er. A monitoring device resulting from this study can be install ed in-situ on underwater structures and could enhance product ivity and improve safety of offshore operations. This paper de tails the test results to determine coupling methods for attachin g fiber optic sensor systems to deepwater structures that have alre ady been deployed. Subsea attachment methods were evaluated in a forty foot deep pool by divers. Afterword, structural test ing