State and Parameter Estimation in Closed-Loop Dynamic Real-Time Optimization

Abstract

To adapt to overarching objectives and changing demands, a plant automation system capable of real-time optimization and dynamic model predictions is desirable. Dynamic real-time optimization (DRTO) can achieve higher level objectives such as profitability, however RTO and DRTO schemes require a mechanism to utilize plant measurements to adapt the model to reflect changing conditions. This study proposes a novel integration of Kalman filter state and parameter estimation in which the impact of the controller and the plant response is accounted for in the DRTO. This closed-loop DRTO (CL-DRTO) approach is used to control a multi-input multi-output CSTR where a critical parameter is not measurable. The CSTR is optimized under economic and target tracking objectives, and is tested using two different control layers, PI-based and MPC-based. In the PI controlled CSTR, the proposed solution was compared to the ideal case of full state feedback and a common approach to dealing with mismatch: bias updating. The proposed Kalman filter estimator effectively handles noise and infeasible targets, surpassing bias updating in scenarios involving input saturation and increased measurement noise. The PI controlled CSTR is also tested with nonlinear models and an extended Kalman filter, demonstrating a method for controlling even highly nonlinear systems. In the MPC controlled CSTR, the Kalman filter is tested under input saturation and various disturbance sources. By using DRTO setpoints to guide the MPC towards targets, inputs can be maintained at their constrained bounds without directly accounting for these constraints in the MPC formulation or clipping the inputs directly. Under every scenario tested, the Kalman filter successfully estimated the unknown parameter and demonstrated excellent robustness. The proposed strategy’s ability to control nonlinear plants using linear models suggests potential scalability for larger, more complex systems.