Real-Time Optimization (RTO) and Model Predictive Control (MPC) are important technologies for optimal process operation in the chemical and refining industry. Both NMPC and dynamic real-time optimization (D-RTO) allow the incorporation of first principle process models, which lead to on-line optimization strategies consistent with higher-level tasks, including scheduling and planning. Moreover, with recent advances in dynamic modeling, simulation and optimization, dynamic optimization has seen increasing industrial application, particularly for inherently transient processes. However, more detailed dynamic optimization models that reflect complex reaction and separation phenomena and multi- stage dynamic operation still need to be addressed - and solved as time-critical, on-line applications. Here, a major concern is that computational times needed to solve these large-scale optimizations lead to feedback delays in implementation that can degrade performance and possibly destabilize the process.
This project addresses these issues and enables the realization of fast on-line dynamic optimization with first principle models. The PI plans to develop a class of sensitivity-based algorithms that separate dynamic optimization into background calculations, where most of the computation is performed, and on-line calculations, where a perturbed problem is solved very quickly. On-line computations are thus reduced by several orders of magnitude and become very fast, even for large, complex nonlinear models. These formulations are to be developed both for NMPC as well as state and parameter moving horizon estimation (MHE).
Intellectual Merit
The intellectual merit of this activity deals with the development and analysis of sensitivity-based on-line optimization with first principle dynamic models, particularly Advanced-Step NMPC and MHE. The work should lead to nonlinear model predictive control and on-line dynamic optimization for large-scale chemical processes without the limitations of computational feedback delay. The research also deals with extensions to multi-stage dynamic optimization for tighter integration of planning and scheduling decisions, and robust problem formulations to deal with model mismatch and unmeasured disturbances. This approach will be extended to moving horizon estimation (MHE) problems. MHE strategies for nonlinear models have significant advantages over observers and Kalman filters, but their realization requires application of fast optimization strategies.
Broader Impacts
Broader impacts include the application of this approach on two challenging industrial applications. These include a large-scale polymer process with detailed on-line reactor models and dynamic multi-stage operation, including grade changes. The PI will also consider on-line dynamic optimization strategies for gas separation processes. Characterized by load changes and dynamics with strong nonlinearities, performance of these systems can be greatly improved through efficient NMPC and MHE strategies. These concepts will also be integrated within a comprehensive optimization and modeling environment. Finally, graduate training is emphasized as a key component. Included in the educational plan are industrial internships and the development of courses and materials related to Enterprise Wide Optimization.
Outcomes for Nonlinear Model Predictive Control with First Principle Models This project developed the advanced-step concepts for both NMPC and state estimation using fast optimization algorithms and NLP sensitivity. This combination leads to the realization of on-line optimization with negligible performance loss and computational delay. Key accomplishments of this project are the publication of a book on Nonlinear Programming and dynamic optimization, and a powerful software package, called sIPOPT that integrates with the IPOPT solver and efficiently generates NLP sensitivities. This open source code is available through www.coin-or.org. In addition, the project dealt with a sophisticated derivation and analysis of advanced step concepts for moving horizon estimation (MHE), detailed analysis of arrival costs for (MHE) and a fast update of covariance matrices for MHE arrival costs, based on NLP sensitivity. Moreover, superior performance of advanced step NMPC has been demonstrated and benchmarked on several large-scale processes. We have developed a novel way of including the arrival cost based on non-normal statistics with MHE controllers, including particle filters, unscented Kalman filters and Ensemble Kalman filters. We have shown that this strategy has superior performance to Kalman Filter updating approaches as well as previous MHE strategies. This work has also been extended to quickly evaluate and update covariance and expected values using a nonlinear variant of Kalman Smoothing. This approach makes use of IPOPT sensitivity tools described above and is described in detail in a reprint listed below. Finally, this grant was supplemented by a travel grant in the amount of $23,505 to refine and apply dynamic optimization and NMPC strategies to natural gas plants as well as eutrophication processes, i.e., unwanted, accelerated algae growth in lakes and other aquatic sources. Working with colleagues at PLAPIQUI, Argentina, this travel grant allowed us to form a strong collaboration that leverages and increases research strengths in both groups through the development of optimization models, strategies and challenging applications. References [1] L. T. Biegler. Nonlinear Programming: Concepts, Algorithms and Applications to Chemical Processes. SIAM, Philadelphia, PA, 2010. [2] F. D’Amato, A. Kumar, R. Lopez-Negrete, and L. T. Biegler. Fast nonlinear model predictive control:formulation and industrial process applications. CPC VIII Conference, 2012. [3] J. Ignacio Laiglecia, Rodrigo Lopez-Negrete, M. Soledad Diaz, and Lorenz T. Biegler. A simultaneous dynamic optimization approach for natural gas processing plants. Foundations of Computer Aided Process Operations, 2012. [4] R. Lopez-Negrete. Nonlinear Programming Sensitivity Based Methods for Constrained State Estimation. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, 2011. [5] R. Lopez-Negrete and L. T. Biegler. A moving horizon estimator for multi-rated measurements based on nonlinear programming sensitivity, Journal of Process Control, 2012. [6] R. Lopez Negrete, S. Patwardhan, and L. T. Biegler. Constrained particle filter approach for approximation of the arrival cost in moving horizon estimation. Journal of Process Control, 21:909–919, 2011. [7] H. Pirnay, R. Lopez-Negrete, and L. T. Biegler. Optimal sensitivity based on Ipopt, Mathematical Programming Study, in press, 2012.
