Evaluating Optimization Objectives in Linear Quadratic Control Applied to Open Canal Automation

AbstractProportional-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 Kp and the integra...

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Bibliographic Details
Published in:Journal of water resources planning and management 2020-11, Vol.146 (11)
Main Authors: Zhong, Ke, Guan, Guanghua, Tian, Xin, Maestre, José María, Mao, Zhonghao
Format: Article
Language:English
Subjects:
Automatic control
Automation
Canals
Computational fluid dynamics
Control
Control methods
Controllers
Flow rates
Flow velocity
Fluid flow
Hydrodynamics
Linear quadratic regulator
Morphology
Optimization
Parameters
Proportional integral
Stability
Technical Papers
Time constant
Water level fluctuations
Water levels
Water resources management
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Summary:AbstractProportional-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 Kp and the integrational time constant Ti. 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.
ISSN:0733-9496
1943-5452
DOI:10.1061/(ASCE)WR.1943-5452.0001286