LPV non-integer order model and control of an irrigation canal using gain scheduling technique

Abstract

Abstract—In this paper, a novel method for controlling mainirrigation canals with variable dynamic parameters is proposed.A non-integer order based gain-scheduling controller for canalsystems is presented. This controller takes into account thevariations of parameters in each operating point by using a linearparameter variable (LPV) non-integer order model obtained byfractional LPV identi cation. This non-integer controller hasbeen designed in accordance with the control input bound andassure closed loop poles placement desired in all the workingoperation canal range. This approach is validated in a pilot canalplant. Control results guarantee the desired performance andstability for slow parameters variation in the whole operationcanal range. I. INTRODUCTION Water is becoming a precious and very scarce resource inmany countries due to the increase of industrial and agricul-tural demands, as well as of the population. Irrigation is themain water consuming activity in the world, as it representsabout the 80% of the available fresh water consumption.There is growing interest for the application of advancedmanagement methods that prevent wastage and facilitate theef˚cient use of this vital resource.It is widely accepted that automation can lead to a betteref˚ciency of water management in many irrigation systemswith open canals, which are subjected to large losses. The useof an speci˚c control method depends on canal constructionproperties, the rules for delivery service, the type of waterdelivery, theavailabilityofcommunication between thecontrolcenter and automatic structures, the expectation of water usersand operation staff, and economic considerations. Automaticcontrol of water distribution in main irrigation canals can bejusti˚ed by improved service to clients, improved ef˚ciency inwater distribution, reduced overall operation costs, consider-abledecreasedinwaterlossesandincreasedsafetyexplotation.Designing an strategy leading to a practical and effectivecontrol of water distribution is an arduous task because hy-draulic behavior of irrigation canals shows that these systemsare distributed over long distances, with dynamics character-ized by important varying time delays, strong nonlinearities,numerous interactions between different consecutive subsys-tems and the existence of other dynamic parameters thatchange over the time during operation.For water distribution control in main irrigation canal poolsit is not necessary to know the downstream variations alongthe whole pool, but only at speci˚c points which depend on thecanal operation method that is being used. Considering this,a linear model with concentrated parameters and time delayis widely accepted to characterize in a suitable manner thedynamical behavior of an irrigation canal pool at each speci˚cpoint and to design a linear controller in each operating point[11].Bounded control is inherent to practical stabilization prob-lem: valves can only be operated between closed and open,tanks can only contain a ˚nite volume, etc. Actuator saturationcan severely degrade the closed loop system performance andsometimes even make the otherwise stable closed-loop systemunstable. Therefore, design of controllers for systems withbounds is an active area of research (see for instance booksof Hu and Lin [4] and Saberi [12]).The main topic of control strategies is to satisfy, the waterdemand of each consumer while guaranteeing a minimumdischarge all along the canal and spending a minimum watervolume from the upstream reservoir. An usual solution toreach these control objectives has been the use of conventionalPI controllers [1]. Other control schemes widely proposed tomodify the dynamics of systems characterized by large timedelays are based on the Smith Predictor (SP), which simpli˚esthe closed loop transfer function of the system, removing timedelay of the denominator and providing robustness to systemparameters changes. Recently fractional-order controllers havebeen applied to control effective water distribution in mainirrigation canal pool and they exhibit some advantages whendesigning robust control systems in the frequency domainfor processes whose parameters vary in a large range and,combined with SP, increasing the robustness to system gainvariations [3].In this paper, we apply some properties of the fractionalcalculus in order to design robust controllers in time domainto solve the problem of effective water distribution controlin irrigation canal pool. In particular, an LPV non-integerorder model is obtained by LPV non-integer identi˚cation andcontrol design for irrigation canal pool is proposed. In orderto test the control methology a real plant is used, that is, anexperimental canal prototype explained in the next Section.