Parametric sensitivity functions for hybrid discrete/continuous systems

García-Galán, S.; Feehery, William F.; Barton, Paul I.

doi:10.1016/s0168-9274(98)00125-1

Cited by 113 publications

(103 citation statements)

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“…, N and u(t f ) = p N . The discontinuities in u make the dynamic model (2) a continuous-discrete hybrid dynamic system [28]. The discrete behavior potentially occurs at times t k , k = 1, .…”

Section: Problem Statement and Pertinent Backgroundmentioning

confidence: 99%

“…The computation of parametric sensitivities in a hybrid system where the switching times are a function of the parameters is involved and requires some assumptions for the system to ensure existence and uniqueness of the sensitivities [28]. Moreover, the parametric sensitivities are generally discontinuous over the switches [38], and additional computations are necessary to transfer the sensitivity values across the switches [28]. To avoid these numerical complications, the time transformation presented in [39,40] is used so that the switching times are fixed in the transformed formulation.…”

Section: U(t) U(t)mentioning

confidence: 99%

“…Accordingly, all the control switches are triggered at fixed times in the new time domain. This ensures existence and uniqueness of the parametric sensitivities and their continuity over the switches [28]. Despite the adaptive discretization strategy incorporated in Problem (22)- (27), the quality of the optimal solution can still depend on the resolutions set for the transient phases (N s and N d ).…”

Section: U(t) U(t)mentioning

confidence: 99%

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Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Sahlodin

Barton

2017

Processes

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Dynamic optimization offers a great potential for maximizing performance of continuous processes from startup to shutdown by obtaining optimal trajectories for the control variables. However, numerical procedures for dynamic optimization can become prohibitively costly upon a sufficiently fine discretization of control trajectories, especially for large-scale dynamic process models. On the other hand, a coarse discretization of control trajectories is often incapable of representing the optimal solution, thereby leading to reduced performance. In this paper, a new control discretization approach for dynamic optimization of continuous processes is proposed. It builds upon turnpike theory in optimal control and exploits the solution structure for constructing the optimal trajectories and adaptively deciding the locations of the control discretization points. As a result, the proposed approach can potentially yield the same, or even improved, optimal solution with a coarser discretization than a conventional uniform discretization approach. It is shown via case studies that using the proposed approach can reduce the cost of dynamic optimization significantly, mainly due to introducing fewer optimization variables and cheaper sensitivity calculations during integration.

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Section: Problem Statement and Pertinent Backgroundmentioning

confidence: 99%

Section: U(t) U(t)mentioning

confidence: 99%

Section: U(t) U(t)mentioning

confidence: 99%

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Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Sahlodin

Barton

2017

Processes

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“…The dynamic model including the stabilizing control structure presented in this section has been implemented in a dynamic simulator (JACOBIAN R , RES Group, Inc.), which is equipped with efficient methods to compute parametric sensitivities. 32,33 The decomposition strategy is derived from the approach from Douglas. 19 The time constants of the relevant processes at higher levels are slow and steady-state information can be used, whereas dynamic modeling has to be utilized at the lowest level to evaluate rejection of faster disturbances.…”

Section: Hierarchical Decomposition and Control Objectivesmentioning

confidence: 99%

Model‐based design of a plant‐wide control strategy for a continuous pharmaceutical plant

et al. 2013

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• This is the pre-peer reviewed version of the article which has been pub- AbstractThe design of an effective plant-wide control strategy is a key challenge for the development of future continuous pharmaceutical processes. This paper presents a case study for the design of a plant-wide control structure for a system inspired by an end-to-end continuous pharmaceutical pilot plant. A hierarchical decomposition strategy is used to classify control objectives. A plant-wide dynamic model of the process is used to generate parametric sensitivities, which provide a basis for the synthesis of control loops. Simulations for selected disturbances illustrate that the critical quality attributes (CQAs) of the final product can be kept close to specification in the presence of significant and persistent disturbances. Furthermore, it is illustrated how selected CQAs of the final product can be brought simultaneously to a new setpoint while maintaining the remaining CQAs at a constant value during this transition. The latter result shows flexibility to control CQAs independently of each other.

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“…The dynamic optimization problem is solved using a sequential approach, with the model simulated in the EcosimPro environment, coupled with a SQP optimization routine. Notice that the computation of the gradients can be performed safely, provided that the number of discontinuities does not change over the prediction horizon during its computation, Galan et al (1999), which is imposed by fixing a number of discrete changes over the horizon.…”

Section: Reverse Osmosis Plantsmentioning

confidence: 99%

Operation of Medium-size Reverse Osmosis Plants with Optimal Energy Consumption

Palacin¹,

Prada

Tadeo

et al. 2010

IFAC Proceedings Volumes

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This paper deals with the optimal operational strategy of a reverse osmosis (RO) plant for remote sites. The electricity supply to these plants comes usually from renewable energies (wind and solar), when they are not temporarily available, they are complemented by a diesel generator and batteries. The water demand of small settlements in arid regions suffers strong variations along a day. As the higher demand of water usually occurs when solar energy is more available, the operational expenses can be reduced by considering the RO plant as an active load. A good control strategy, will implement a variable operation point, taking into account the predictions of water demand, the expected variation of the available energy sources and the scheduling of cleaning operations in the RO plant, in order to optimize the energy use. In this paper a hybrid predictive control is proposed to implement this task. Simulations of a specific plant show that an adequate operation reduces the diesel energy consumption, while satisfying the variable water demand.

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Parametric sensitivity functions for hybrid discrete/continuous systems

Cited by 113 publications

References 0 publications

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Model‐based design of a plant‐wide control strategy for a continuous pharmaceutical plant

Operation of Medium-size Reverse Osmosis Plants with Optimal Energy Consumption

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