Fast hierarchical economic optimization of dynamic systems

This project studies ways for optimizing operation of processes whose operating conditions change with time. Examples include optimizing agile operation of a chemical processes, or house heating in smart grids, where the energy prices are constantly changing. The idea is to use available inputs like heating/cooling, or valves in such a way that the operational cost is minimized, not only at the current time, but also taking future predictions into account. In this project we do this by using a process model (digital twin) which is repeatedly optimized numerically to find the optimal operation strategy. Using the process model, we compute the optimal setpoint values for selected variables in a control layer below. This lower control layer adjusts the inputs such that the selected variables stay at their optimal values. For good performance, it is critical that the optimization problem can be solved fast enough, otherwise, the operation decisions are made on outdated information. The main results so far have been in the development of fast and efficient numerical algorithms that can solve the large-scale optimization problem in real-time, such that the decisions are not based on outdated information. The developed algorithm is based on a path-following method and provides fast approximate solutions to the optimization problem. This algorithm was further developed to handle uncertainty. This is done in a multi-stage scenario framework, that takes all possible present and future realizations of the uncertainty into account.

Dette prosjektet bidro vesentlig til å forstå hvordan rask modell prediktiv regulering kan gjennomføres ved hjelp av en sensitivitetsbasert numerisk «path-followingmetode». Det ble opparbeidet en ny kompetanse, i vår forskningsgruppe, som førte til at slike metoder også ble anvendt i andre prosjekter (e.g. SFI Subpro, der metoden blir tatt i bruk, og videreutviklet). Det forventes at metoden som ble utviklet i dette prosjektet kommer til å anvendes innen relaterte områder, som å beregne optimal drift under usikre parametere. Som langfristige effekter forventer vi at optimaliseringsbaserte reguleringsstrategier blir brukt oftere, fordi den optimale løsningen kan beregnes og implementeres i sanntid. Prosjektet bidro også til å styrke samarbeidet med Carnegie Mellon University, USA, og har lagt et godt fundament for videre samarbeid.

The research in this project is focused on finding strategies and developing tools for optimizing dynamic behavior and transients in complex systems. It is part of a larger activity on optimal operation methods in the process systems group at the Department of Chemical Engineering at NTNU. In practice, most implementations of optimal operation are realized in a hierarchical control structure, where an upper layer does the online economic optimization on a slow time-scale, and passes the optimal setpoint trajectories to a fast lower layer which adapts the plant inputs to follow the trajectories. The problem of designing a hierarchical control structure for economic optimization with intended transients is considered an industrially very important problem (Scattolini, 2009). In control structure design, decisions are made on what variables to control in which layer (e.g. Skogestad, 2000). While for steady state optimization there exist approaches for designing hierarchical control structures (Skogestad 2000), there are no systematic methods and guidelines for the more difficult case of dynamic optimization, and there are very few theoretical results in this area. The first objective of this project is to combine the offline optimization paradigm of self-optimizing control with the paradigm of online optimization, to find a systematic method for designing a hierarchical control structure for optimizing dynamic performance of a chemical plant. The second objective is to study a fast sensitivity-based path-following algorithm that is used in the optimization layer, and to establish a robust stability proof for a system which is optimized by this algorithm. In particular, we will add a corrector element to our previously developed predictor algorithm, study its convergence, and develop a stability proof based on input to state stability arguments. This project is meant to fund 1 postdoc; if no suitable candidate is found, a PhD student will be employed instead.