Approximation of closed-loop prediction for dynamic real-time optimization calculations

Jamaludin, Mohammad Zamry; Swartz, Christopher L.E.

doi:10.1016/j.compchemeng.2017.02.037

Cited by 28 publications

(21 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A natural choice is to keep the reference trajectory constant over the DRTO execution interval,

Δ t_{DRTO}

. This strategy is an effective mechanism for reducing excessive variation in the computed set‐point trajectories; it was applied in Lam et al in reference trajectory optimization in a supervisory control scheme, as well as in the CL‐DRTO strategies in Jamaludin and Swartz …”

Section: Drto Formulationmentioning

confidence: 99%

“…While the CL‐DRTO formulation provides a more accurate representation of the plant and its associated control system than the open‐loop prediction counterpart, it is significantly more computationally intensive. In this section, we outline three approaches for approximating the closed‐loop prediction Hybrid Formulation .…”

Section: Drto Formulationmentioning

confidence: 99%

“…This strategy is an effective mechanism for reducing excessive variation in the computed set-point trajectories; it was applied in Lam et al [24] in reference trajectory optimization in a supervisory control scheme, as well as in the CL-DRTO strategies in Jamaludin and Swartz. [4][5][6][7] The resulting DRTO problem can in principle be solved using a sequential solution approach in which optimization iterations and closed-loop simulation are decoupled. However, in order to avoid potential difficulties with derivative discontinuities due to MPC input inequality constraints, we adopt a simultaneous solution strategy in which the MPC subproblems are replaced by their first-order KKT optimality conditions, [23] resulting in a single-level mathematical program with complementarity constraints (MPCC).…”

Section: Rigorous Closed-loop Formulationmentioning

confidence: 99%

“…In this section, we outline three approaches for approximating the closed-loop prediction. [5,6] (i) Hybrid Formulation. In this method, rigorous closed-loop prediction is applied over the first DRTO interval ( t DRTO ) The hybrid formulation therefore constitutes a multilevel optimization problem with n + 1 MPC optimization subproblems, as opposed to N subproblems in the rigorous formulation.…”

Section: Closed-loop Prediction Approximationmentioning

confidence: 99%

See 3 more Smart Citations

The utilization of closed‐loop prediction for dynamic real‐time optimization

Jamaludin

Swartz

2017

Can J Chem Eng

View full text Add to dashboard Cite

Real‐time optimization (RTO) is a layer within the hierarchical process automation architecture in which economically optimal set‐points are computed for the underlying plant control system. RTO calculations are traditionally based on steady‐state models, but an increasingly global and dynamic marketplace has led to the development of dynamic RTO (DRTO) strategies. Typical DRTO approaches optimize process input trajectories based on the open‐loop response dynamics of the process, with controller set‐point trajectories constructed from the resulting output response. This paper describes recent developments that utilize closed‐loop prediction in the DRTO calculations for MPC regulated processes. A rigorous closed‐loop DRTO problem is formulated as a multilevel dynamic optimization problem due to the inclusion of a sequence of MPC quadratic programming subproblems to generate the closed‐loop response dynamics. A simultaneous solution strategy is applied in which the MPC subproblems are replaced by their equivalent Karush‐Kuhn‐Tucker (KKT) optimality conditions, permitting reformulation of the original problem as a single‐level mathematical program with complementarity constraints (MPCC). Closed‐loop approximation techniques are proposed to reduce the dimension of the DRTO problem while maintaining good closed‐loop prediction accuracy. The performance of the proposed approaches is illustrated using case studies. Conclusions are drawn, and further research directions identified.

show abstract

“…A natural choice is to keep the reference trajectory constant over the DRTO execution interval,

Δ t_{DRTO}

Section: Drto Formulationmentioning

confidence: 99%

Section: Drto Formulationmentioning

confidence: 99%

Section: Rigorous Closed-loop Formulationmentioning

confidence: 99%

Section: Closed-loop Prediction Approximationmentioning

confidence: 99%

See 2 more Smart Citations

The utilization of closed‐loop prediction for dynamic real‐time optimization

Jamaludin

Swartz

2017

Can J Chem Eng

View full text Add to dashboard Cite

show abstract

“…To achieve feasible setpoints, the process dynamics are considered in the scheduling layer by using a model which represents the closed‐loop behavior of the process. This closed‐loop model is obtained either by embedding the necessary optimality conditions of the process in closed‐loop with a tracking controller or by using a data‐driven model to approximate closed‐loop behavior . The controller level is not altered by the top‐down approaches.…”

Section: Introductionmentioning

confidence: 99%

A flexible air separation process: 2. Optimal operation using economic model predictive control

et al. 2019

View full text Add to dashboard Cite

The penetration of renewable electricity promises an economic advantage for flexible operation of energy-intense processes. One way to achieve flexible operation is economic model predictive control (eNMPC), where an economic dynamic optimization problem is directly solved at controller level taking into account a process model and operational constraints. We apply eNMPC in silico to an air separation process with an integrated liquefier and liquid-assist operation. We use a mechanistic dynamic model as both controller model and plant surrogate. We conduct a closed-loop case study over a time horizon of 2 days with historical electricity prices and input disturbances. We solve the dynamic optimization problems in DyOS. Compared to the optimal steady-state operation, the eNMPC operating strategy gives a significant improvement of 14%. We further show that the eNMPC enables economic improvements similar to an idealized quasistationary scheduling. While the eNMPC provides control profiles qualitatively similar to those obtained from deterministic global optimization of quasistationary scheduling, the eNMPC satisfies the product purity constraints all the time whereas the quasistationary scheduling sometimes fails to do so. The eNMPC applies local optimization methods and achieves profiles similar to the scheduling solved using deterministic global optimization methods over the complete closed-loop simulation time horizon. K E Y W O R D S air separation unit, demand side management, direct single-shooting, economic model predictive control, integrated liquefication cycle 1 | INTRODUCTION The enhanced use of renewables, for example, onshore wind and photovoltaic, for electricity production results in fluctuating electricity prices. 1,2 Exploiting these fluctuations promises an economic advantage of flexibly operating electricity-intensive processes. There are two requirements: (a) a "flexible process", that is, a process with a wide operation range and without big losses of efficiency and (b) "flexible process operation", that is, exploiting the process flexibility in the operation. Thus, there is both economical and ecological incentive to take advantage of flexible process load adjustment as a reaction to changing market conditions. This is known as demandside management (DSM). 3 DSM has been applied to various process systems in the last decades, for example, by Ghobeity and Mitsos 4 and Brée et al. 5 Different concepts, recent advances and challenges of industrial DSM have been summarized by Zhang and Grossmann 6 and the rising need for flexible operation in context of the integration of renewable

show abstract

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

2021

View full text Add to dashboard Cite

Dynamic real‐time optimization (DRTO) is a supervisory strategy at the upper level of the industrial process automation architecture that computes economically optimal set‐point trajectories that are in turn passed on to the lower‐level model predictive control (MPC) for tracking. The economically optimal solution, in several process industries, could lead to operating the plant at or around an unstable steady state. The present article accounts for this by developing a closed‐loop DRTO (CL‐DRTO) formulation that enables handling unstable operating points via an underlying MPC with stability constraints. To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is embedded within the upper‐level DRTO. The resulting CL‐DRTO problem is reformulated by applying a simultaneous solution approach. The economic benefits realized by the proposed strategy are illustrated through applications to both linearized and nonlinear dynamic models for single‐input single‐output and multi‐input multi‐output continuous stirred tank reactor case studies.

show abstract

Approximation of closed-loop prediction for dynamic real-time optimization calculations

Cited by 28 publications

References 34 publications

The utilization of closed‐loop prediction for dynamic real‐time optimization

The utilization of closed‐loop prediction for dynamic real‐time optimization

A flexible air separation process: 2. Optimal operation using economic model predictive control

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

Contact Info

Product

Resources

About