A Steady State Optimal Design of Artificial Induced Aeration in Polluted Streams by the Use of Pontryagin's Minimum Principle

Davidson, Burton; Bradshaw, Robert W.

doi:10.1029/wr006i002p00383

Cited by 16 publications

(6 citation statements)

References 2 publications

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“…As last remark, we point out that the plot (not reported here) of the left hand side term in (7) is positive where the control does not assume the extremal values 0 and u max and consequently a singular arc may exist.…”

Section: Optimal Time-profilesmentioning

confidence: 66%

On the Role of Inhibition Processes in Modeling Control Strategies for Composting Plants

Martalò

Bianchi

Buonomo

et al. 2020

SEMA SIMAI Springer Series

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We introduce a mathematical model for the composting process in biocells where several chemical phenomena, like the aerobic biodegradation, the hydrolysis of insoluble substrate and the biomass decay, occur. We investigate the best aeration strategies in presence of inhibition processes due to high concentrations of oxygen. Optimal stategries are obtained as result of a suitable optimal control problem. The dynamics exhibits an enhanced level of the oxygen concentration that guarantees the aerobic feature of the biodegradation process. Then, a nonlinear bioeconomic term is included in the objective functional to take into account of the external operational cost. The role of the economic cost in the control policy is analyzed and discussed.

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Section: Optimal Time-profilesmentioning

confidence: 66%

On the Role of Inhibition Processes in Modeling Control Strategies for Composting Plants

Martalò

Bianchi

Buonomo

et al. 2020

SEMA SIMAI Springer Series

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“…Using a numerical method, the aeration as a function of space and time that minimized the aeration rate and the DO deviation from a specified level was found. Davidson and Bradshaw (1970) did the same problem for the steady state case in which the DO level was described by an ordinary differential equation. The resulting solution gave the optimal steady state aeration rate as a function of distance along the stream.…”

Section: Section 2: Previous Resultsmentioning

confidence: 94%

Optimal estuary aeration: An application of distributed parameter control theory

Hullett

1974

Appl Math Optim

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A B S T R A C TThe use of artificial induced aeration has been suggested as a means for improving water quality. The task of controlling the aeration input rate to obtain maximum improvement with least cost is addressed as an optimization problem of a distributed parameter control system. A partial differential equation model for the dissolved oxygen balance in streams and estuaries is given, and a criterion functional is proposed in which the control can be found as the solution of an optimization problem in a Hilbert space. An analytic solution for the optimal feedback control of a stream aeration system is found, and a numerical algorithm for the estuary case is applied to an example using historical data from the Delaware estuary. The sensitivity of the control to system and input variations is discussed, and the dollar cost for the example is compared with costs for other suboptimal control schemes. A(x, t) =

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“…For T > 30øC, more than 100% treatment is required. This change demonstrates a new factor to be added to the thermal pollution syndrome [Davidson and Bradshaw, 1967]. Seasonal temperature changes or temperature changes caused by man-made devices (e.g., heated discharges) are thus seen to be an important factor in the optimization study.…”

Section: For Select Suboptimal Casesmentioning

confidence: 99%

Best combination of waste treatment and spatially distributed discharge of effluent

Mendiratta¹,

Davidson²

1972

Water Resources Research

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The optimal control theory based on Pontryagin's minimum principle has been applied to the problem of specifying the best combination of minimum percent BOD waste treatment and effluent distribution policies for a single plant on a specified polluted river segment. The analysis features a new dual water quality stream standard consisting of a minimum allowable DO concentration at every point in the river segment combined with a maximum allowable BOD concentration at a specified downstream point. The optimal BOD effluent distribution policies are compared with choice suboptimal effluent discharge patterns associated with best single point, best uniform, and best bang‐bang injection policies. The inequality constraints, the nonlinearities in the system model, and the synthesis of the optimal controls were handled in a direct manner by using the Pontryagin control theory principle combined with gradient search and penalty function techniques. The results of the study very definitely established certain guidelines for increasing the assimilative capacity of a given river segment through judicious combinations of minimum percent BOD waste treatment and continuous BOD effluent distribution or dumping patterns associated with single plant effluents. The systems analysis was made tractable by incorporating a no short‐circuit constraint into the dumping policies.

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A Steady State Optimal Design of Artificial Induced Aeration in Polluted Streams by the Use of Pontryagin's Minimum Principle

Cited by 16 publications

References 2 publications

On the Role of Inhibition Processes in Modeling Control Strategies for Composting Plants

On the Role of Inhibition Processes in Modeling Control Strategies for Composting Plants

Optimal estuary aeration: An application of distributed parameter control theory

Best combination of waste treatment and spatially distributed discharge of effluent

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