When operating a post-combustion carbon capture system for power plants, specific requirements on CO2 capture fraction should be satisfied. But the operation is subject to disturbances caused by the fast load changing of power plants. Additionally, economic issue such as high energy consumption is a major bottleneck for the commercial application of carbon capture systems. Therefore, flexible operation and control strategies are required to improve the economic performance of carbon capture systems. In this study, we develop efficient control strategies for a solid sorbent based post-combustion carbon capture system using bubbling fluidized bed (BFB) adsorbers. Computationally efficient reduced dynamic models are used to reduce the computational cost for model-based control problems. A fast nonlinear model predictive control (NMPC) algorithm is utilized to enable the online control of the carbon capture system and state estimation is required to handle the prediction error given by the reduced model.
The model for the BFB adsorber is a one-dimensional, three-region, pressure-driven model developed by national energy technology laboratory (NETL), which considers axial variations in the solid phase and the bed hydrodynamics. The reactor’s hydrodynamic behavior is described by partial differential and algebraic equations (PDAEs), constructed from mass and heat conservation and hydrodynamic correlations. Detailed equations for steady-state and dynamic BFB model can be found in [1, 2]. After spatial discretization, the BFB model becomes a highly nonlinear and large scale differential and algebraic equation (DAE) system with over 10,000 equations. Considering the strong nonlinearity of the process, NMPC is used to efficiently control the carbon capture system.
Detailed first-principles BFB model can be applied for off-line optimization applications and give accurate description of the process behavior. For online control problem like NMPC, however, it requires a fast solution of dynamic optimization problems. In practice, solving NMPC problem with the original full scale BFB model can be time-consuming, which may lead to computational delay that will degenerate control performance and even destabilize the process. To reduce the computational cost for NMPC, dynamic reduced models of the BFB adsorber are developed using temporal and spatial reduction methods. From a temporal aspect, dynamic reduced models are generated using nullspace projection and eigenvalue analysis method to remove the fast dynamics of the system. From a spatial aspect, dynamic reduced models are developed using orthogonal collocation to reduce the size of the full scale model. The simulation time of the reduced dynamic models can be reduced by 70% while maintaining good prediction accuracy.
To enable online control and avoid computational delay, asNMPC is applied using the fast dynamic reduced models for the BFB adsorber, which is a sensitivity-based fast NMPC algorithm . The basic idea of asNMPC is to separate optimization problems into background and on-line calculations; the open loop NMPC optimization problem is solved within the sampling time using the predicted state as initial conditions and then a fast update of NLP solution is made based on NLP sensitivity once the actual state of the system is obtained. The online update only requires a single backsolve with fixed KKT matrix and thus it greatly reduces the online computational cost. To handle the uncertainty due to reduced model error and measurement noise, a formulation of moving horizon estimation (MHE) with output and state disturbances is used to reject the disturbances and achieve offset-free control behavior . After solving the modified MHE problem, both the optimal estimated states and the state and output disturbances are obtained. The predicted disturbances are then fed into NMPC to compensate for the uncertainty brought by model-plant mismatch and other disturbances. The proposed strategy can achieve good control performance in set point tracking under disturbances. Economic NMPC with reduced models will be studied to further improve the overall economic performance of the carbon capture system.
 Lee, Andrew, and David C. Miller. "A one-dimensional (1-d) three-region model for a bubbling fluidized-bed adsorber." Industrial & Engineering Chemistry Research 52.1 (2012): 469-484.
 Modekurti, Srinivasarao, Debangsu Bhattacharyya, and Stephen E. Zitney. "Dynamic Modeling and Control Studies of a Two-Stage Bubbling Fluidized Bed Adsorber-Reactor for Solid–Sorbent CO2 Capture." Industrial & Engineering Chemistry Research 52.30 (2013): 10250-10260.
 Zavala, Victor M., and Lorenz T. Biegler. "The advanced-step NMPC controller: Optimality, stability and robustness." Automatica 45.1 (2009): 86-93.
 Huang, Rui, Lorenz T. Biegler, and Sachin C. Patwardhan. "Fast offset-free nonlinear model predictive control based on moving horizon estimation." Industrial & Engineering Chemistry Research 49.17 (2010): 7882-7890.