Discussion on Muskingum versus Integrator-Delay Models for Control Objectives

Abstract

A comparative study about two models, Muskingum and integrator-delay (ID) models, for canal control is presented. The former is a simplified hydrological model which is very simple and extensively used in hydraulic engineering for simulation and prediction. The latter is also a model with physical meaning and is widely used for irrigation canals control. Due to a lack of general awareness of Muskingum prediction model in regulation from the control community, authors present this comparative study with the ID control model. Both models have been studied and analyzed for control purposes. This study has been carried out and validated in a real irrigation canal, at Aghili irrigation district in Iran, using two traditional control approaches, PID with feedback and predictive control. The results demonstrate the advantages and drawbacks of both models, showing the benefits and limitations of using the widespread Muskingum model among the hydraulics scientific community for control design.

Modeling and real-time control of urban drainage systems: A review

“…This model is an approximation that relates backwater effects when a tank-delay model is used. In [109], a comparative study between Muskingum and integrator-delay models is presented.…”

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

“…Therefore, in the literature, the integrator delay model is one of the most reported modeling strategy for OCIS, which has been used for control design in multiple studies (e.g. Wahlin 2004;Litrico and Fromion 2004c,a;Koenig et al 2005;van Overloop et al 2005;Litrico and Fromion 2006b;Litrico et al 2007;van Overloop et al 2008a;Litrico and Fromion 2009;van Overloop et al 2010a;Horváth et al 2014;Bolea et al 2014c;Van Overloop et al 2014;Horváth et al 2015b,a;Zheng et al 2019).…”

“…Several studies that use PID controllers to maintain a fixed level in the OCIS have been reported. 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.…”