One-layer gradient-based MPC + RTO strategy for unstable processes: a case study of a CSTR system

Closed‐loop dynamic real‐time optimization with stabilizing model predictive control

“…Accurate approximation strategies to approximate the closed‐loop prediction with a reduced computational time (without any significant loss of information) have been devised by Jamaludin and Swartz 9 . More recently, a one‐layer gradient‐based RTO framework was proposed for unstable processes in Santana et al 10 In this approach, the optimal control law is calculated based on an approximation of the gradient of the economic function. They circumvent the issue of evaluating two optimization problems by adding the approximation of the gradient of the convex economic function to a stabilizing infinite horizon MPC cost with a terminal constraint.…”

A stabilizing gradient-based economic MPC for unstable processes: toward the enlargement of the domain of attraction

“…The performance of hierarchical control schemes can be improved if the control layer can directly access the economic performance of the system (Hinojosa et al, 2017). Such strategies can be classified as one-layer hierarchical control schemes with economic objectives, whose resulting strategies with stabilizing properties can be formulated as (Santana et al, 2020): (i) nonlinear optimization problems that directly solve an economic objective function, the so-called EMPC (Economic Model Predictive controller); and (ii) MPC+RTO controllers, which include into the cost function an additional term related to the economic performance.…”

“…Focusing on MPC+RTO strategies, Alvarez and Odloak (2014) proposed an infinite horizon MPC with zone control that drives open-loop stable systems towards its economic optimal condition, in which stabilizing properties are based on slacked terminal equality constraints, and the economic term is an approximation of the gradient of a convex gradient function. Santana et al (2020) extended this work for unstable systems, also applying slacked terminal equality constraints to ensure both stability and feasibility. An advantage of these strategies is the lack of need to know the economic optimal steady-state in advance, due to the usage of set-point targets as decision variables in the zone control formulation.…”

“…An advantage of these strategies is the lack of need to know the economic optimal steady-state in advance, due to the usage of set-point targets as decision variables in the zone control formulation. On the other hand, the Hessian matrix of the economic function can not be zero, and the state-space model applied by Santana et al (2020), based on an analytical step response of the system, include more states than the canonical Jordan decomposition. Thus, in order to constrain unstable states it is needed more terminal equality constraints than a formulation based on the Jordan decomposition.…”

Metodologia de sintonia para controladores preditivos utilizando funções de sensibilidade

“…O intuito do projeto foi conceber uma metodologia que possuísse aplicabilidade na arquitetura típica de controladores preditivos. Sugere-se que para trabalhos futuros sejam estudadas formas de traduzir a metodologia de sintonia para sistemas que adaptem a aplicação de controladores preditivos para sistemas complexos, como aqueles relacionados à variação de ganho (Grimble;Majecki, 2018) ou a sistemas instáveis (Santana et al, 2020).…”