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

Ke Zhong, Guanghua Guan*, Xin Tian, José María Maestre, Zhonghao Mao

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)


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 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.

Original languageEnglish
Article number04020087
Number of pages12
JournalJournal of Water Resources Planning and Management
Issue number11
Publication statusPublished - 2020


  • Canal automation
  • Constant downstream water-level regulation
  • Linear quadratic regulator (LQR)
  • Optimal control
  • Proportional-integral (PI) control


Dive into the research topics of 'Evaluating Optimization Objectives in Linear Quadratic Control Applied to Open Canal Automation'. Together they form a unique fingerprint.

Cite this