Evaluating Optimization Objectives in Linear Quadratic Control Applied to Open Canal Automation
Publication: Journal of Water Resources Planning and Management
Volume 146, Issue 11
Abstract
Proportional-integral (PI) control, as one of the most popular classic control methods, has been applied widely to the real-world practice of canal automatic control. The performance of a PI controller largely depends on two key parameters, namely the proportional constant and the integrational time constant . Rather than tuning these parameters empirically or in terms of the canal morphology, this study proposes a linear quadratic regulator (LQR) to determine their optimal values. The proposed LQR utilizes an integrator delay model to represent the hydrodynamics of open canals in order to minimize changes in water levels and flow rates. In addition, the weights for the optimization objective in the LQR are determined by an optimized quadratic performance indicators estimate (OQPIE), using the precalculated nondimensional integrated square of error and nondimensional integrated absolute discharge change as well as inherent designed parameters, which potentially impact the stability of system states. In this way, the LQR can fit various canal automation applications, especially for low-gradient canals. The optimal PI controller was tested on two different-scaled canals. Results showed that the objective was met satisfactorily, and stability can be reached in hours.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request (all simulation data of test cases).
Acknowledgments
The authors thank Albert J. Clemmens, US Arid Land Agricultural Research Center, for fruitful discussions about and constructive suggestions for the study. The authors also are grateful to the anonymous reviewers for their valuable comments. The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Nos. 51979202, 51439006 and 51009108), the National Key R&D Program of China (Grant No. 2016YFC0401810), and Project C3PO of the Spanish MEC (Grant No. DPI2017-86918-R).
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Journal of Water Resources Planning and Management
Volume 146 • Issue 11 • November 2020
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© 2020 American Society of Civil Engineers.
History
Received: Jun 24, 2019
Accepted: May 26, 2020
Published online: Sep 10, 2020
Published in print: Nov 1, 2020
Discussion open until: Feb 10, 2021
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