Closed‐loop dynamic real‐time optimization with stabilizing model predictive control
Real-time optimization (RTO) is a supervisory strategy at the upper level of the industrial
process automation architecture that computes optimal set-point trajectories
that are in turn passed on to the lower-level advanced controller for tracking. In recent
times, process industries have been operating plants in an increasingly dynamic
environment thus motivating the replacement of the traditional steady-state RTO
with a dynamic RTO (DRTO). Conventionally, the DRTO problem involved computing
optimal input trajectories without incorporating the e ects of the lower-level
controller that motivated the development of a closed-loop DRTO (CL-DRTO).
A previously published CL-DRTO strategy optimizes set-point trajectories based on
an economic cost function, while including the lower-level MPC calculations with
an assumption that the process is open-loop stable. But the economic optimum,
in certain process industries, could lead to operating the plant at or around an unstable
steady-state. Therefore, the goal of this research is to develop a CL-DRTO
formulation that enables handling unstable operating points via an underlying MPC
with stability constraints. In this work, we focus on a traditional two-layer DRTO
approach due to its close ties to the industrial automation architecture.
To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is
embedded within the upper-level DRTO, resulting in a multi-level dynamic optimization
problem. Subsequently, this optimization problem is reformulated by applying
a simultaneous solution approach. The economic bene ts realized by the proposed
strategy are illustrated through applications to both linearized and nonlinear dynamic
models for single-input single-output (SISO) and multi-input multi-output (MIMO)
CSTR case studies.