Design of PI Controllers for Irrigation Canals Based on Linear Matrix Inequalities

Abstract

A new Proportional-Integral (PI) tuning method based on Linear Matrix Inequalities (LMIs) is presented. In particular, an LMI-based optimal control problem is solved to obtain a sparse feedback that provides the PI tuning. The ASCE Test Canal 1 is used as a case study. Using a linearised model of the canal, different tunings for the design of the PI controller are developed and tested using the software Sobek. Furthermore, the proposed method is also compared with other tunings proposed for the same canal available in the literature. Our results show that the proposed method reduces by half the maximum errors with respect to other assessed alternatives and minimizes undesired mutual interactions between canal pools. Also, our method improves the optimality degree of the PI tuning by 30%. Therefore, it is concluded that the LMI based PI controllers lead to satisfactory performance in regulating water levels and canal flows/structure outflows, outperforming other tested alternatives, thus becoming a useful tool for irrigation canal control.

Parameter optimization of PID controller for water and fertilizer control system based on partial attraction adaptive firefly algorithm

“…The results showed that the control effect of RBF-PID is more precise and steady than PID control. Teresa Arauz et al 23 designed a PI controller based on linear matrix inequality (LMI) to solve the optimal control issue. Simulation results presented that the novel controller can improve the control effect by 30% and can effectively control the irrigation canal water level.…”

Modeling and control in open-channel irrigation systems: A review

“…For example, Burt et al (1998) establish methods and strategies for tuning upstream PI controllers; Litrico and Georges (1999) compare the performance of a PID controller with a pole placement controller with Smith Predictor; investigate the convenience between using a PI controller to maintain a fixed upstream level or a fixed downstream level; van Overloop et al ( 2005) modify a PI controller with a firstorder filter with the aim to reduce resonant oscillations that are induced from neighbor channels; Lozano et al (2010) evaluate the performance between a downstream PI controller and a distant downstream PI controller; Figueiredo et al (2013) test a PI downstream controller in a system with fourth channels; Bolea et al (2014c), in a real system, assess the behavior of a PI controller designed from a Muskingum model and other from an integrator delay; recently, Arauz et al (2020); Ke et al (2020) present two PI tuning methods, that have been designed using the integrator delay modeling approach. It is important to realize that the control strategy proposed by Arauz et al (2020) has been tested in specialized software (SOBEK), showing that optimally tuned PI controllers are successful for level regulation of OCIS. Other studies simply use the PID controllers to compare the performance of more sophisticated control strategies (e.g., Malaterre and Khammash 2003;Zheng et al 2019).…”

Irrigation canal control using enhanced fuzzy SARSA learning

“…Various model-free and model-based controllers have been used to control the structures in irrigation canals that include the canal environment and incorporating a canal simulator. A proportional integral derivative (PID) controller is a classic and simple controller used successfully in many fields of engineering; for example, a proportional integral (PI) controller was designed to control an irrigation canal (Arauz et al, 2020) using linear matrix inequalities, showing satisfying results. Another controller is an Model Predictive Control (MPC) that is a robust controller used widely in the literature (Shahdany & Roozbahani, 2016;Shahdany et al, 2018Shahdany et al, , 2019.…”