SYSTEMS ENGINEERING FOR IRRIGATIONSYSTEMS: SUCCESSES AND CHALLENGES

Iven Mareels, Erik Weyer, Su Ki OoiMichael Cantoni, Yuping Li, Girish Nair

Department of Electrical and Electronic Engineering,The University of Melbourne,

Vic 3010, Australia,i.mareels@unimelb.edu.au

Abstract: In Australia gravity fed irrigation systems are critical infrastructureessential to agricultural production and export. By supplementing these large scalecivil engineering systems with an appropriate information infrastructure, sensors,actuators and a communication network it is feasible to use systems engineeringideas to improve the exploitation of the irrigation system. This paper reports howclassical ideas from system identification and control can be used to automateirrigation systems to deliver a near on-demand water supply with vastly improvedoverall distribution efficiency. Copyright c©2005 IFAC

Keywords: large scale systems, irrigation systems, system identification, control,SCADA

1. INTRODUCTION

Over the last seven years researchers at the Uni-versity of Melbourne have collaborated with Rubi-con Systems Australia to achieve near on-demandwater supply in open channel irrigation systems.The research and development process startedby considering what appeared to be a case ofhunting of local controllers in an irrigation net-work. The journey went through modeling andcontrol design, including the development of newsensor and actuator hardware and pilot projects

1 Over the last seven years, different aspects of the workreported here have been variously supported by the Co-operative Research Centre for Sensor, Signal and Infor-mation Processing; the Australian Research Council underan industry-linkage grant, and Rubicon Systems Australia,Pty. Ltd. and AusIndustry. Iven Mareels is now also work-ing with the National ICT Australia, Ltd. that will supportongoing research in this general area under its Water In-formation Networks initiative.

culminating in the present industrial scale ongoingproject where based on the developed ideas andtechnology a large irrigation system in Victoria isbeing fully automated. The ongoing project is re-ported as the largest supervisory control and dataacquisition (SCADA) system of its kind in theworld. Upon completion it will be the first entireirrigation system under closed loop control wherewater orders are met in real time on demand in asmuch as this is physically realisable.

This paper reports on some aspects of this jour-ney. A corresponding paper trail can be foundin the bibliography. The patents (Mareels et al.,2000; Mareels et al., 2001) describe the overall sys-tems engineering philosophy in conjunction withthe newly developed hardware for both measuringand controlling water in open channels.

So far the research and development effort hasfocused on controlling water quantity in openchannels, as captured in water flow, volume and

water levels. This paper is solely devoted to thisissue. In future developments it is envisaged thatwater quality will become a major focus for con-trol. Sensors can assess the biological and chemicalcontent of water to determine its quality in realtime. The information infrastructure to be dis-cussed can then be used to advantage to managewater quality as well as water quantity.

In Australia irrigation accounts for 70% of all freshwater usage (The United Nations World WaterDevelopment Report, Executive Summary, 2003;Water and the Australian Economy, 1999; Se-curing our Water Future Together, 2004; WaterSavings in Irrigation Distribution Systems, 2000).This statistic varies much between different coun-tries, and regions, but globally 70% of all fresh wa-ter is used for irrigation. The majority of irrigationis achieved through an extensive civil infrastruc-ture of reservoirs and open canals that suppliesfresh water to farms. The large scale distributionof water is powered purely by gravity. Also onmost farms, a gravity fed system is in use, suchthat the amount of farm land that can be irrigatedthrough the on-farm water outlet is directly lim-ited by the available water level (potential energy)at the canal outlet, the on-farm supply point.

In the reports (The United Nations World WaterDevelopment Report, Executive Summary, 2003;Water and the Australian Economy, 1999; WaterSavings in Irrigation Distribution Systems, 2000)overall water efficiency in irrigation, that is theratio of volume of water used by crops and lifestock to volume of water extracted from theavailable fresh water resource is estimated to beless than 50%. In Australia, the losses are re-portedly evenly split (Water and the AustralianEconomy, 1999; Water Savings in Irrigation Dis-tribution Systems, 2000) between the large scaledistribution losses and on-farm losses. The latterare to a large extent due to poor timing of irri-gation, a consequence of manual water schedul-ing on the supply canals. Furthermore, the on-farm losses if coupled with poor drainage leadto soil degradation (irrigation-drainage imbalanceinduced salination of soils). Most of the largescale distribution losses are due to the naturaltendency to oversupply water, as a lack of waterhas obviously averse effects on the yield. Somelosses are due to evaporation and canal seepage.In Australia, over supplied water simply meansthat water spills out at the downstream end ofthe irrigation system, and is no longer availableto supply irrigation. The water remains of coursepart of the natural hydro cycle.

Policy makers in Australia have recognized that isimportant to re-consider present water practicesin view of long term environmental and sustain-ability issues. Indeed, Australia is a very dry con-

tinent that presumably cannot sustain the presentexploitation levels of its natural water resources.Climate change, population and industrial growthpressures compound the problem.

Here it is argued that irrigation efficiency is anideal objective for closed loop control. Irrigationefficiency can be vastly improved by installingan information technology infrastructure: sensorsand actuators linked through a supervisory con-trol and data acquisition (SCADA) communica-tion network. The data derived from this can beexploited using systems identification and controltechniques to manage the civil infrastructure toachieve superior efficiency and support new poli-cies in support of long term sustainable water use.Besides the improved distribution efficiency, thenear on-demand water delivery that is achievedleads to significant on-farm efficiency improve-ments as well.

The system identification and control ideas to bediscussed are quite classical, and in this way thepaper illustrates the strength of the present stateof the art in control and systems identificationtheory. Nevertheless new questions or perhapsnew emphases appear and a number of interestingopen problems, particular relevant to large scalesystems engineering are identified.

The remainder of the paper is organized as fol-lows. First a particular implementation of an au-tomated, SCADA equipped irrigation system, in-stalled in Victoria, Australia is described. Thephysical constraints in the irrigation infrastruc-ture, which ultimately limit the performance thatcan be achieved, are touched upon. The controland management objectives are briefly outlined.System modeling is discussed next. Models de-rived from the St-Venant equations and grey boxmodels are compared as to their utility/effortin the context of modeling for control and faultdetection. Next model based control ideas arepursued. A variety of distributed control and cen-tralised control strategies are briefly introduced.More importantly the impact of automation andthe diminishing returns of increased control effortand control sophistication are identified. Resultsfrom the field describing the quality of the pro-posed models and controls are discussed.

2. IRRIGATION SYSTEMS

2.1 Canal Infrastructure

Refer to Figure 1. Through a series of opencanals, water is distributed from reservoirs tofarms under the driving force of the availablepotential energy at the reservoir. The routingand scheduling of water is realized through theadjustment of regulator structures (gates) placed

in the canals. These gates restrict the water flowin the canals. A stretch of canal between up- anddown-stream gates is called a pool.

Datum LineGate position

A pool (1 to 10km)

Overshot gate orregulator

Up streamwater level

Down streamwater level

Flow direction

Slope 1:10000

Water level

Gate anglecontrol variable

Fig. 1. Schematic representation of open canalinfrastructure; vertical cross section throughcanal centre

A section of a canal network, is represented inFigure 2. The canal topology can be representedlike a directed graph (nodes are regulators, arcsare pools, the direction is the flow). In mostgravity fed systems the graph is a tree (but thisis not always the case).

Repeater

19.6kb/s

4 Fs

2.4kb/s links F1

2.4kb/s links F2

10km

~100km

Line of sight

To farm

MainRegulator

Canal

Fig. 2. Schematic representation of open canaltopology (actual schematic)

The discussion here focuses on the so-called over-shot gates (FlumeGateTM 2 )that were developedin the course of the project. In these gates waterflows over the top of the gate leaf, the angle ofwhich can be adjusted to change the amount ofwater that flows over it. The gates can operate inthe overflow regime, where the down stream waterlevel is below the gate level (as on the left in Figure1), or drowned condition, where the downstream

2 These gates are manufactured by Rubicon Systems Aus-tralia, Pty. Ltd.

level is above the gate level (as is illustrated on theright in Figure 1). At the gate water levels imme-diately downstream and upstream of the gate aremeasured.

The main farm outlets are found near the down-stream end of a pool. In Australia, the canalsare designed for flow, and are rather shallow andnarrow, with little storage in pools. A typical slopeof the canal floor is 1/10,000. The canals havelittle free board, in most instances water will spillif the water level would reach 0.5m above thedesign level.

The canal and reservoir infrastructure is sub-stantial. The replacement value (for Australia)is in the order of several tens of billion dollarsin investment. To understand the scale, considerthe following data for a medium size irrigationdistrict in Australia that was used in the pilotprojects described here: 500km of main irriga-tion canal; about 500 regulator structures in thecanals; over 600 on-farm outlets; 1.1Gm2 of farmland irrigated; an annual water allocation of about0.6Gm3. The Goulburn-Murray irrigation district,the largest in Australia, is more than 10 timesthis size (7000km of canal; 17,000 regulators and21,000 on-farm outlets, annual average irrigationwater allocation in excess of 2Gm3) and irrigationdistricts in excess of 100 times this size exist inthe USA, Pakistan, India and China.

The quality of the irrigation service, from a farmperspective, is determined by the timing of theirrigation water and in case the on-farm irrigationis also gravity fed, also by the water level at theon-farm outlet.

Clearly using open canals with banks that arenot water tight to effect water distribution im-plies losses through evaporation and seepage. Thecombined effect of these is estimated at around10% to 15% of supply (Water and the AustralianEconomy, 1999). These losses are insufficient towarrant consideration of replacing the canal in-frastructure by a piped water network (which afterall also has its own problems with leaks).

2.2 Automation Infrastructure

Figure 3 illustrates in situ the new hardwarereplacing the manually controlled on-farm outlets.During the course of the project, new sensors andactuators were developed which form the subjectof two patent applications (Mareels et al., 2000;Mareels et al., 2001). The actual locations forthe gates in the canals are as determined by theexisting infrastructure under manual control, andno optimization of gate placement, in view of thenew and automated management regime, has beenconsidered thus far. This is an interesting aspect

Regulator

UserInterface

Solar Panel

Radio antenna

Fig. 3. Automated gates and communication in-frastructure

of the overall system design that is under furtherinvestigation.

For the purpose of distributing water from reser-voir to farm, all the gates both in the main canalsas well as the on-farm outlets, are actuated andequipped with sensors for water levels and actualgate position (the gate angle is measured). Thisenables measurement of actual demand, watersupplied onto farms, on the irrigation system.Actuation and monitoring functions are typicallycollocated, and very few sole purpose actuator ormonitoring sites are in use.

Each gate/site can communicate via a cellularpacket based radio network to any other site inthe network. The communication network enablesboth broadcasting (e.g. for software upgrades) aswell as peer to peer communications on all sites.A typical direct peer group contains up to 10sites (see also Figure 2). For the above describedaverage irrigation district there are just over a1000 sites, the maximum number of router hopsfor site to site communications is 6, whereas adirect communication to the central node requiresat most 3 router hops. For reasons of security andreliability, the network management overhead indata communication is large, and the actual net

data throughput is very low (measured in bits persecond).

The required data rate for control purposes is keptto a minimum by using event driven communica-tion and by using a particular decentralized con-trol structure. Event based communication meansthat measurement data are only communicatedwhen a water level change (a gate movement or aset point change) exceeds a predetermined thresh-old. Even then, the sensor data must compete withother event driven communications such as de-manded by various hardware and software alarms.As a consequence the time required to successfullycomplete a communication cannot be guaranteedwith certainty. Although and this is confirmed byexperience over a few irrigation seasons, the de-sign methods for the communication network aresuch that with very high confidence the maximumcommunication delay for a data packet can bespecified. The other technique used to minimizethe data rate requirements is the particular de-centralized control structure that is implemented.It is such that water demand information only hasto be passed on to the nearest upstream regulator,which only requires a peer to peer session, withoutsupervisory intervention. Moreover, the centralsupervisory control node does not need regularsampling of sensors and/or actuator states andcan use the event driven data to implement globalnetwork policies.

Locally, at the gate level, all data about sensors,actuators and hardware conditions are monitoredon a regularly sampled basis, and a long historyof all variables is maintained in memory.

At the central node, a global data base of all re-ported and requested events is maintained. In thisdata base, the topology of both the informationnetwork and the irrigation network is also stored.This topology is further enhanced by descriptorsfor all models for pools, regulators and sensors,and the corresponding control algorithms.

2.3 Objectives

From a real-time control point of view the mainobjectives are

• optimization of distribution efficiency, i.e.minimize the total amount of water suppliedby matching supply to demand. Maximaldistribution efficiency is attained when thereis a zero outflow at the bottom end of thecanal tree.

• real-time on-demand water supply of the re-quested water volumes to all irrigation out-lets and;

• water level regulation at the on-farm outletto a given set point (within an agreed dead-band limit);

The supervisory control has to ensure that thephysical flow capacities are not exceeded, thatthe water set points are as agreed by the stakeholders and that the distributed water remainswithin the allocations set by the regulating bodies(as modified by water trade). Clearly, the super-visory control task is in itself a dynamic object.The supervisory control system receives demandrequests by the farmers through an automatedordering system. These orders are verified, if thewater order is legitimate and if there is the phys-ical capacity to supply before the water orderis processed. If rejected, the water order can berescheduled to an agreed time. The supervisorycontrol system can suggest alternative time slotsfor the water order. These aspects are not dis-cussed further. That some form of reschedulingis in general unavoidable is clear from the his-togram in Figure 4. It shows the distribution ofregulator sizes (in flow m3/s) for one section ofthe above irrigation system. The total on-farminstalled outflow capacity in this section is closeto 25m3/s, which is a little more than 4 times theinflow capacity (the in flow capacity at the topregulator is 6.1m3/s). This is typical across theentire irrigation system.

0.5 1.5 2.5 3.5 4.5 5.5 6.50

10

20

30

40

50

60

Flow capacity in m /s3

Nu

mb

ero

fre

gu

lato

rs

Fig. 4. Histogram of regulator sizes in m3/s atthe downstream end in a typical irrigationdistrict

Equally important from a management perspec-tive is to keep track of water flow and watervolumes, as well as the general condition of theirrigation canals (e.g. leakage detection, evapora-tion losses, hardware failures).

3. MODELS FOR IRRIGATION SYSTEMS

Understanding the behaviour of the irrigationsystem is key to arriving at an acceptable closedloop control solution. The natural subsystemsin irrigation systems are a single pool and theregulator structures. Given the topology of theirrigation system, an entire model is then butthe concatenation of pool and regulator modelsas dictated by the system topology (see Figure2).

3.1 St-Venant Equation Based Models

Traditionally, open channel dynamics are de-scribed using the shallow water equations, or theso called St-Venant equations (Brutsaert, 1971;Chaudhry, 1993; Cunge et al., 1980). One partic-ular representation is given by

∂Ai

∂t+

∂Qi

∂x= −qi,off (x, t), (1)

which models the mass balance along the lengthof the pool, and

∂Qi

∂x+

(gAi

Bi− Q2

i

A2i

)∂Ai

∂x+

2Qi

Ai

∂Qi

∂x

+gAi(Sf (Qi, Ai, x, t) − Si(x)) = 0,

(2)

which models the momentum balance along thelength of the pool. Here t ≥ 0 is time, and0 ≤ x ≤ Li is a position along the centre lineof the pool, where Li is the length of the ith pool.

In (1) and (2) Ai(x, t) is the water cross sectionat position x along the center line of pool i attime t (it equals the local depth of water times thewidth of the canal). Bi(x) is the width of the poolat position x, it is assumed that the cross sectionof the canal is rectangular. The width informa-tion can be obtained either from design drawings,or perhaps more interestingly from satellite im-ages. Qi(x, t) is the total flow in m3s−1 throughthe cross section Ai(x, t). qi,off (x, t) representsthe flow off-take per meter canal (in m2s−1) atposition x. This term models not only a farmoutlet, or an off-take into another pool/canal butalso accounts for seepage and evaporation (hencethe potential dependence on time, as seepage issubject to seasonal variation and evaporation ex-periences seasonal and diurnal variations). TheSf (Qi, Ai, x, t) represents the momentum loss permeter canal, due to friction but also water off-takes, seepage and evaporation. Si(x) representsthe slope of the bottom of pool i. The latter rep-resents essentially the available potential energyper meter canal. The constant g = 9.81ms−2

represents gravitational acceleration. The friction

term Sf is a nonlinear function of flow and area,for which various empirical formulas exist. Heremodeled as time-invariant, although slow timevariations can be expected due to effects such asbank erosion and plant growth.

The boundary conditions are the inflow into thetop-end of the pool Qi(0, t) and the outflowQi(L, t) at the bottom-end of the pool. These areto be derived from the hydraulic characteristicsof the regulating structures at the up- and down-stream end of the pools. For Q1(0, t) this will typi-cally be a discharge from a reservoir, or major feedcanal. Q.(L., t) for each of the end pools is to beminimised, ideally zero outflow is to be achieved.For the other boundary conditions Qi(L, t) =Qi+1(0, t) = fi(Ai(L, t), Ai+1(0, t), uj(t)), wherefi is the hydraulic characteristic for that regula-tor, and uj is the control variable, which enablesthe variation of the flow through this regulator.Hydraulic characteristics can be determined fromexperimental data. Hydraulic characteristics es-sentially relate geometry of the regulator, as cap-tured by the down and up-stream water conditionsand the gate position to flow over the regulator.

To complete the model for the purpose of pre-diction an initial condition has to be provided,a suitable starting point is a steady state flowcondition (zero flow for example).

The models (1) and (2) are nonlinear partial dif-ferential equations, which can be solved using anumerical integration scheme. Typically, a Preis-mann scheme, which involves using a discretisa-tion in both space and time domain (Chaudhry,1993; Cunge et al., 1980) is advocated.

Despite the obvious physical interpretation thatis associated with the variables, and the clearvalidity of the principles on which the St-Venantequations are constructed, these equations repre-sent a considerable modeling cost when they areto be applied to a particular canal. In order for themodel to become relevant to a particular canal, orpool it is necessary to fit functions like Bi, Sf ,qi,off and Si. Typically this involves providinga parametric representation for these functions,and then estimating the parameters, using saynon-linear least squares techniques, from a historyof measurements. The mapping from the discretevalues of flow Qi and cross sections Ai at certainpositions along the canal, and at certain timeinstances to the parameters is not trivial. Onesuch approach is discussed in some detail in (Ooiet al., 2003b). It is shown there that the St-Venantequations are indeed adequate for the purpose ofmodeling of open channel behaviour. This studyuses data from Australian irrigation canals. Anearlier study (Brutsaert, 1971) also shows the ade-quacy of the St-Venant equation using a similaritystudy under laboratory conditions.

Despite this, it is not clear that the cost of es-tablishing an accurate quantitative model usingthis route is actually justified in the context ofirrigation systems. Moreover, it is also not obvi-ous that the St-Venant equations represent themost appropriate starting point for managementand/or control of irrigation systems.

In a nutshell the advantage of the St-Venantequations, with the corresponding boundary andinitial conditions, are:

• familiar and physically relevant variables aremodeled;

• parameters have an obvious physical inter-pretation;

• interpolation across all time and space (sim-ulation information not limited to discretesample points);

• an expectation to be reliable across a broadrange of operating conditions.

These have to be weighted against the obviousdisadvantages

• significant cost in achieving quantitativelyreliable models from discrete data;

• significant cost, perhaps prohibitive cost tosimulate an entire canal or irrigation system;

• relevance beyond the operational regimes re-mains questionable as it cannot be verifiedagainst real data.

There is a more philosophical and more funda-mental objection rooted in the way the St-Venantequations are actually used. As the St-Venantequations do not permit analytic solutions theyare by necessity numerically integrated using somediscretisation scheme. One could therefore arguethat for all practical purposes the St-Venant equa-tions are merely an abstraction (and perhaps apoor one). Clearly only the finite dimensional nu-merical approximation, a computer algorithm, isthe real model. It is this computer algorithm thatis tuned against the data and that forms the ac-tual model and that predicts the actual behaviour.This begs a number of natural questions

• Can this finite dimensional and discretetime/space model not be considered as thebasis for control design?

• Which discretisation scheme is the most ap-propriate for control design? After all only asmall portion of the open-loop behaviour istargeted in closed-loop operation and theremay be better schemes than the Preismannscheme.

• Perhaps the model may be further simplifiedusing model order reduction techniques torepresent only adequately the smaller closedloop behaviour (Litrico et al., 2003; Litricoand Fromion, 2004).

Rather than pursuing these questions from a St-Venant equation perspective, which leads to sev-eral interesting open problems in the study ofinfinite dimensional systems, they are pursued di-rectly from a data-to-model system identificationperspective.

3.2 Grey box models

The above motivates the consideration of a greybox, lumped model approach to construct a modelfor a pool adequate for control design in anirrigation system (Ooi, 2003; Ooi et al., 2005; Ooiet al., 2003a; Ooi et al., 2003b; Weyer, 2001;Euren and Weyer, 2005). It should be observedthat significant simplifications as compared to thefull complexity of the St-Venant equations maybe expected as the management regime in anirrigation system requires tight control over thewater levels, despite significant variations in flow.Hence the model does not have to explain thebehaviour over all possible water levels.

What is minimally required is a model that linksthe control input ui which is the gate position atregulator i (a regulator may have several gatesin parallel, but this issue is ignored to simplifythe presentation) to water levels and flows at thecritical points along the canals, typically the up-(yi,u) and down-stream (yi,d) water levels at theregulators. With reference to Figure 5 consider acanal where all pools are simply in line. To furthersimplify the exposition, assume that the regula-tors are overshot gates in free-flow conditions. Inthis situation, the downstream water levels at theregulators are largely irrelevant. The ideas can beapplied mutatis mutandis to other situations aswell, including the more complicated situationswith under shot regulators and drowned overshotgates (Euren and Weyer, 2005).

Fromsupply

Todrain

RegulatorPool

1 2 3 N-1 N

1u

,1dy ,2dy

,2uy,3uy

2u 3u1Nu - Nu

. . .

Fig. 5. In-line canal system, a series of regulatorsand pools

The flow Qi over the regulator i is a static functiondetermined by the geometry of the regulator,which is varied by the gate position ui and thesupply water level yu,i at the regulator site. Thisrelationship is the hydraulic characteristic Hi forthe regulator,

Qi = Hi(ui, yu,i). (3)

Besides the hydraulic characteristic, a model forthe dynamics of the pool is required. This modelis in its simplest form a mass balance, the volumeof water in the pool is increased by the flow overthe up-stream regulator and decreased by the flowover the down-stream regulator. In (Weyer, 2001;Mareels et al., 2000; Mareels et al., 2001) a modelis proposed that captures conservation of mass,and the first mode of standing waves in a pool:

pi(d

dt)yu,i+1(t) = −

∑j

qi,jνi,j(t)

+ ciHi(ui(t − τi), yu,i(t − τi))

− ci+1Hi+1(ui+1(t), yu,i+1(t)).

(4)

A continuous time model is used, as in generalregular sampling is not available. This is thereforethe preferred embodiment of the model. Althoughfor identification purposes it is clear that theabove model only requires local information atthe upstream and downstream gate of the pool.In this situation it is possible to obtain regularlysampled and synchronized data series of the waterlevels and gate positions for any particular pool.In (4) yi,u is the water level upstream of regulatori; τi is a time-delay. It is associated with thefastest wave phenomena in the pool between gatesi and i + 1 (which can be linked to the criticalvelocity in the pool (Chaudhry, 1993)). An actionon the upstream end of the pool is observed at thedownstream end of the pool after τi time units.

The model dynamics are captured via the poly-nomial pi(ξ). For short pools, up to a few kmin length, a polynomial of degree 3 suffices toachieve a high fidelity model. For such pools,the roots of pi(ξ) consist of an integrator and aweakly damped oscillatory pair. The integratorcaptures the idea of water storage in the pool. Theoscillatory roots capture the dynamics associatedwith the dominant standing wave(s) in the pool.The terms νi,j represent water off-takes betweenregulator i and i + 1 and the qi,j are static gains.(Most off-takes are placed near the down-streamend of the pool, which simplifies the model, andensures better quality of service for the farmer,as the down stream water level can be regulatedmore easily than the up stream water level.)

Typical order of magnitudes for the various pa-rameters in the Australian irrigation districtswhere field trials have been conducted thus farare:

• time delay is approximately 3 min per km• dominant wave period is approximately 9

min per km• achievable (closed loop) dominant time con-

stant is approximately 10 to 15 min per km

The parameters appearing in (4) are readily ob-tained via standard linear system identificationtechniques. This can be done both from openloop experiments as well as from closed loop data(Ooi et al., 2005; Ooi and Weyer, 2001; Ooi etal., 2003a; Ooi et al., 2003b; Weyer, 2001). Thelatter is critically important when considering alarge scale irrigation system.

The grey box model (4) compares favourably withthe St-Venant model (1) and (2) in that it hasmuch lower complexity and yet similar or betterprediction accuracy (see below and Figure 6).

Validation tests across both low and high flowregimes have been completed. In Figure 6, adaptedfrom (Ooi et al., 2003b), a comparison is madebetween the St-Venant based models and the greybox models. The Figure 6 represents a set of open-loop simulated model responses compared againstthe actual field measurements. The inputs to thesimulation are the regulator positions over time(using the measured positions), and the initialwater level condition. The data set for the mod-eling and validation are from different irrigationseasons.

The least accurate model, which is still very use-ful, is the St-Venant model where the model pa-rameters are not tuned to the actual pool butguestimated based on a rule of thumb. The re-sponse is the dashed line in Figure 6. This modelis by no means disgraced. The other St-Venantmodel has its parameters (a model for the frictionwas adjusted) optimally selected based on fieldobservations. Its response is dash-dot line in Fig-ure 6. These models are compared against a greybox model that uses a third order model, (leaky)integrator and standing waves and a first ordergrey box model that only captures the (leaky)integrator trends. The grey box models have beenidentified from open-loop experiments. All mod-els are reasonably accurate. From a simulationperspective, the best model, based on quality foreffort, is the third order grey box model. Forcontrol purposes the first order grey box modelwill suffice, when the wave phenomena are ap-propriately considered in the closed loop design(Weyer, 2003a).

3.3 Automated Model Building

Given the size of a typical irrigation system auto-mated model building and model maintenance isessential. Model maintenance must be performedwithin the constraints imposed by normal man-agement conditions. As demonstrated in (Ooi andWeyer, 2001) the grey box models (4) allow forsimple calibration of the parameters under closedloop conditions. A few hours of data, using per-mitted changes in the water level reference set

Fig. 6. Experimental validation of grey box andSt-Venant based models

points, exploiting the available dead band, sufficesto tune the model parameters. Such variation isallowed under normal operating conditions as thetypical dead band for the set point regulation is ofthe order of 10cm (under manual operation, waterlevels were deemed acceptably regulated when lessthan 30cm away from set points).

Figure 7 taken from (Ooi and Weyer, 2001) com-pares a validation data set (black solid line) with asimulation (dotted line) based on a model derivedfrom closed loop data. Only 90 minutes of closedloop data with minimal set point variations wereused to derive the relevant parameters of a firstorder grey box model (4) that sufficed for controldesign purposes.

0 50 100 150 200 250 300 350 400 450 50023.6

23.65

23.7

23.75

23.8

23.85

23.9

23.95

24

24.05

Wat

er L

evel

(m

AH

D)

Time (min.)

Fig. 7. Validating closed loop system identifica-tion, using grey box models

It is important to notice that the tuning of themodel for a particular pool is inherently a decen-tralized task. It involves only data gathered fromthe up-stream and down-stream regulators. Giventhe available compute engines at the various mon-itoring sites a model update can be performedlocally using peer-to-peer communications. Once

the modeling or model maintenance is completed,the new model parameters can be communicatedto the central node, which requires very littlecommunication resources, as it only involves a fewcoefficients to be updated.

In case of hardware failures (Choy and Weyer,2005), like a regulator break-down, or sensor fail-ure, an alarm is raised that also triggers a modelupdate (and if necessary a control law update) toreflect the new dynamics.

A model for an entire irrigation system is con-structed from the logical interconnection of theindividual pool models.

3.4 An Open Modeling Issue

The apparent data-based validation of both a St-Venant partial differential equation model anda low order grey box model within the presentcontext poses an interesting and open question inmodel order reduction (Litrico et al., 2003; Litricoand Fromion, 2004). Under what conditions andin what sense can the grey box model (4) beconsidered as an approximation for the coupledpartial differential equation model (1) and (2).

This question is not only of academic interest.The basic parameters in the grey box model havea physical meaning, the dominant time constant,the wave period and time-delay are all related tothe behaviour of the St-Venant equations. If therelationship between the St-Venant equations andthe grey box model is better understood it may bepossible to derive a simple map, a rule of thumb,linking physical parameters like pool length, crit-ical velocity, manning coefficient (an importantparameter describing the friction losses in openchannel flow) to a reasonably first guess for thecoefficients in the grey box model. At presentsuch a map is essentially being constructed fromexperience. An answer to the above open problemwould provide a sound theoretical basis for such arule of thumb.

The question is not trivial in that even takinginto account that the water levels are reasonablytightly controlled the St-Venant equations (2)remain highly nonlinear due to their nonlineardependence on the flow. Hence classical modelorder reduction techniques do not apply.

The situation is a nonlinear version of the classi-cal lumped parameter Pi and T-section approx-imations used in electrical power engineering torepresent a transmission line. Transmission lineequations are linear St-Venant equations.

3.5 On-line Model Uses

The need for a low complexity model structure likethe grey box model cannot be argued solely on thebasis of simulation or control design requirements.Indeed simulation and most control design tech-niques only use the model in an off-line capacityin which complexity plays a lesser role. (The useof model predictive control methods has not asyet been pursued, but a low complexity model isdefinitely an advantage in this case.)

The model is used in the supervisory controlto determine the limits of physical capability ofthe irrigation system to meet demand. Off-linean approximate table can be constructed thatindicates which demand can be met in real time,but it is simpler and more accurate to actuallycalculate from the present state of the modelforward to verify that the physical constraints canbe satisfied (the present scheduling policy workson a first come first served basis).

The model has however far more important on-line uses, which justify a low order complexitymodel. The main on-line use of the model is infault detection and fault isolation. The single mostvaluable use of the model in this respect is theidentification in real-time of leaks, which are iden-tified and localized, as a (significant) differencebetween water levels predicted by the model andactually achieved water levels as measured by thesensors.

The development of fault detection methods thatexploit the full capabilities of the model andsensory data is ongoing.

4. CONTROL FOR IRRIGATION SYSTEMS

In the following discussion, consider a series ofin-line pools (see Figure 5), and assume overshotgates at the regulators. . Other approaches, notdiscussed here, for control of canals can be foundin (Halleux et al., 2003; Schuurmans et al., 1999;Malaterre and Baume, 1998).

From a control perspective, and to simplify thediscussion, the predictive models discussed abovecan be further simplified. Indeed, as the wavedynamics of the pools are not to be excited,because the free space in the canals above thewater level is not designed to cope with standingwaves, this part of the model may be ignoredfor control design as long as the design ensuresthat the waves are not going to be excited. Themain wave frequency from the model is thus animportant input into the control design process,determining the cut-off frequency of a low passfilter applied to the control input.

With this simplification, and introducing appro-priate scaling and some abuse of notation, thepool dynamics, represented in continuous time,are given by

yu,i+1(t) = ui(t − τi) − ui+1(t) − di(t). (5)

The index i refers to the regulator i, i = 1, · · · , N .The ui are the input variables, which are actuallynonlinear functions of the gate positions and thewater levels at the regulator. This representationglobally linearises the non-linear behaviour of thecanal; although the inputs are constrained in thatumax,i ≥ ui ≥ 0. The disturbance di(t) ≥ 0 isthe total water off-take from pool i (upstream ofregulator i+1 and downstream from regulator i).As discussed above, it is (almost) a measurabledisturbance, although some aspects of the off-taketerm cannot be measured directly. Evaporation,seepage and unscheduled off-takes caused by bankerosion or bank collapse are clearly difficult tomeasure directly. The evaporation and seepage areonly a small fraction of the total off-take, and theunscheduled off-takes can be identified from themodel.

The control design is to ensure that uN = 0 (nooutflow at the bottom regulator) and that all yu,i

i = 2, · · · , N are regulated to their reference valuesyref

u,i , i = 2, · · ·N (within a deadband). In this casesetpoint regulation automatically delivers wateron demand, provided that in steady state demandis within the capacity constraint, that is di(t) +ui+1(t) < umax,i for all i = 1, · · ·N − 1.

4.1 Decentralised Control

A decentralized control design is discussed indetail in (Weyer, 2002) see also (Li et al., 2005).The main features are that the upstream regulatorinput ui i = 1, · · · , N − 1 is used to regulatethe water level yu,i+1 i = 1, · · ·N − 1 based oninformation that is available at the down streamregulator i + 1 and the local regulator i as well asthe measured off-take on the pool i. The controllercan thus be implemented using a peer-to-peercommunication session. uN is set to zero.

Assuming the off-take is measurable, the decen-tralized control law takes the form:

ui = Tff,i(s) (di + ui+1)+ Tf,i(s)

(yref

u,i+1 − yu,i+1

) (6)

Here uN = 0 and i = 1, · · · , N−1. Tff,i is the feedforward control part and Tf,i implements localfeedback.

This leads to the closed loop being described by

ui =sTff,i(s) + Tf,i(s)s + Tf,i(s)e−sτi

(di + ui+1) (7)

with uN = 0 and i = N − 1, N − 2, · · · , 1 and

yu,i+1 − yrefu,i+1 =

Tff,i(s)e−sτi − 1s + Tf,i(s)e−sτi

(di + ui+1) .(8)

This representation shows clearly how distur-bances propagate upstream; di affects all yu,k −yref

u,k for k = 1, · · · , i + 1. The decentralised designis by necessity a trade-off between how much thelocal disturbance di is rejected from the waterlevel yu,i+1 and how these disturbances propagateupstream, the effect on yu,k for k = 1, · · · , i. Thetransfer function governing the upstream propa-gation of disturbances is

Pi(s) =sTff,i(s) + Tf,i(s)s + Tf,i(s)e−sτi

, (9)

the local rejection is governed by

Ri(s) =Tff,i(s)e−sτi − 1s + Tf,i(s)e−sτi

. (10)

The critical element in these transfer functions isthe delay.

A similar argument can be developed for when theoff-take is not measurable. In this case, the controllaw takes the form

ui = Tff,i(s)ui+1 + Tf,i(s)(yref

u,i+1 − yu,i+1

),(11)

starting with uN = 0. The corresponding closedloop is described by the iteration (i = N−1, · · · , 1)

ui = Pi(s)ui+1 + Ti(s)di, (12)

which describes the regulator inputs and

yu,i − yrefu,i = Ri(s)ui+1 + Si(s)di, (13)

which describes the error-propagation. Here

Ti(s) =Tf,i(s)

s + Tf,i(s)e−sτi, (14)

and

Si(s) =−1

s + Tf,i(s)e−sτi. (15)

4.2 Decentralised control, without off-take measurements

When the off-takes may not be measured, thefeedback Tf,i(s) = Hi(s)/s must include an inte-grator in order to reject the off-take disturbancesdi. This makes the control design much more chal-lenging as the plant also contains an integrator.

In the presence of a double integrator and havingto contend with the unavoidable delay in Pi,Ri, Si and Ti, it can be shown that is now

impossible to avoid that water levels errors areamplified as they propagate upstream along thecanal. In (Li et al., 2005) it is demonstratedthat for any linear (stable) design ‖Pi(s)‖∞ >1. The way to arrive at a good design is toachieve strong disturbance rejection by way ofensuring that ‖Ri−1(s)Pi(s)‖∞ << 1. In this way,even very long chains of pools can be adequatelycontrolled. 3

The design proceeds in two phases, first stabil-ity/robustness is guaranteed for the local pooldynamics (design emphasis on Si); a phase marginof about 40 degrees and a gain margin of about-10dB is considered adequate. A feedback consist-ing of a PI controller, with low pass filter as toavoid the excitation of the wave dynamics, i.e.Tf = KP s+KI

s(Tws+1) , can achieve this goal. The feedforward term is essentially a low pass filter, againto ensure that waves are not excited. Moreover,the feed forward term must be designed with careto avoid the amplification of disturbances alongthe canal. To complete the design, it must beverified against the entire system dynamics, thisboils down to the non-trivial verification of thetransfer functions Ri−1ΠkPk.

0 200 400 600 800 1000 1200 1400 160021.12

21.13

21.14

21.15

21.16

21.17

21.18

21.19

21.2Response in pool 10

mA

HD

Minutes

Fig. 8. Decentralised control in action, PI withfeedforward

Figures 8 and 10 illustrate the response of the de-centralized controller (PI+filter) under a controltest scenario. These graphs display field data fromthe Haughton Main Canal. The set point is thedash-dot line and the solid line is the recordedwater level realized by the controller. Several setpoint changes and disturbances occur over theperiod of time (a bit more than a day’s worth of

3 Worst case scenario is when all pools are identical, asin this situation the consecutive amplifications are re-enforcing each other. This is a rather unusual situation inpractice, and one that can always be avoided by adjustingthe location of regulators, or better by adding a regulatorstructure.

data is displayed). The controller maintains thewater level to better than 5cm.

0 200 400 600 800 1000 1200 1400 160023.74

23.75

23.76

23.77

23.78

23.79

23.8

23.81

23.82

mA

HD

Minutes

Response in pool 9

Fig. 9. Decentralised control in action, PI withfeedforward

4.3 Decentralised control with off-take measurements

Assuming that the off-takes are measured, it ispossible to use a simple lead-lag controller in thefeedback path (Tf,i) and a simple low pass filterin the feed forward path. The design is somewhatsimplified in this situation as compared to thedesign based on the integrator in the feedbackpath. The only relevant transfer functions are Ri

and Pi, which makes it indeed somewhat easierto achieve acceptable gain and phase margins aswell as disturbance rejection. The main designproblem concerns the feed forward action, as thisdominates the error propagation along the canals.As the design is only marginally easier than thePI based design, the PI based design, which hasgreater robustness with respect to off-takes, is tobe preferred.

4.4 Centralised Control

Based on the model (5) linear quadratic methodsas well as H∞ design methods may be pursued todeliver a global controller see (Weyer, 2003c; Liet al., 2004; Li et al., 2005). These serve asbenchmarks for the decentralized controllers.

The information infrastructure briefly discussedabove does not enable one to implement a centralcontrol strategy across an entire irrigation district.Linear quadratic, centralised controllers have beenfield tested in smallish irrigation systems. Besidesserving as a benchmark for the decentralized con-trollers, a centralized control law can be usedto derive an acceptable decentralized controller,through pruning the weaker input-output connec-tions.

To complete an adequate linear quadratic designit is essential to augment the state of the system(water levels yi) with the integrals of the regula-tion errors (

∫ t

0(yref

i − yi)) and states to describehigh pass filtered input variables (emphasizingthe frequency content above the standing wavefrequency of the pool that can be effected by theparticular input variable). The latter are essentialto avoid excitation of standing waves in the pools.A linear quadratic design completed along theselines provides an overall responsiveness betterthan what can be achieved using the above de-centralized controller, with acceptable robustnessproperties. The design process is however muchmore demanding. In particular the selection of thequadratic weights so as to achieve an intuitivelyacceptable response is a time-consuming task.

The intuition derived from the decentralized con-troller can be used to better advantage in an H∞design. The decentralized controller can be usedto deliver the loop shaping that is required toachieve a high gain in the low frequency band(to reject the load disturbances), a 20dB/dec rolloff around the cross over frequency (which islimited by the wave frequency) to achieve suf-ficient phase margin, and faster roll-off aroundand beyond the wave frequencies. Using the de-centralized controller to guide the selection of theloop shaping frequency dependent weights, allowsthe H∞ design method to deliver a very robustand high performing controller that satisfies allcontrol requirements. The resulting controller isa global controller, with a performance similar toa well designed linear quadratic controller. Theadvantage is that the design effort is much smallerthan what is required for the linear quadraticcontroller, and entirely comparable to the decen-tralized controller. Field tests are planned for thenear future.

0 200 400 600 800 1000 1200 1400 160026.34

26.36

26.38

26.4

26.42

26.44

26.46

26.48

Minutes

mA

HD

Response in pool 8

Fig. 10. Decentralised control in action, PI withfeedforward

4.5 A law of diminishing returns

In order to appreciate the benefit that may bederived from the various control scenarios, a com-parison is made between

• manual control, the present situation, wherewater orders are averaged, and water regula-tion is effected once every 24h by manuallyadjusting the regulator structures.

• decentralized control, without feed forward;PI+filter design using a simple anti-windupscheme.

• decentralized control, with feed forward;PI+filter design using a simple anti-windupscheme.

• global, centralized control (using a linearquadratic regulator).

The comparison is based on a 3-pool simula-tion, where the scenarios have been implementedon an equal footing. All control implementationsencounter identical circumstances. The scenariostretches over a nine day period. It involves:

• A water order cancellation. Half-way throughthe simulation, a water order (45h long orderof 37500 m3) is cancelled. Farmers can orderwater, typically 4 days in advance, but areallowed to cancel the order with only onehour notice. This is a very demanding sce-nario from a manual regulation point of view,but realistic.

• A 2.5cm rain event that last for 10h. Underrain conditions, farmers are allowed to stopirrigation. This leads to an emergency stopof the irrigation system, which is virtuallyimpossible to control well under manual op-erations.

• Ten normal water orders, of various lengthand magnitude. The water orders are orga-nized as per typical manual operations, so asto create a situation advantageous for manualoperations.

The scenario is illustrated in Figure 11, in whichthe head over the most upstream regulator isindicated. This illustrates the water supply intothe canal, which is the main control action to im-plement the down stream requested water orders.

The results are that any of the automated meth-ods achieve all the water orders as requestedand avoid spilling water during the rain condi-tion. The decentralized control strategies achieve100% water efficiency in that no water is spilledover the most down stream regulator. The LinearQuadratic Regulator controller achieves quickerand better water level regulation (barely notice-able) and an overall efficiency of 99%. (The LQregulator sacrifices a minimal amount of water infavour of achieving a better water level regula-

2000 4000 6000 8000 10000 120000

0.1

0.2

0.3TCC with Feedforward

met

er

2000 4000 6000 8000 10000 120000

0.1

0.2

0.3

met

er TCC no Feedforward

2000 4000 6000 8000 10000 120000

0.1

0.2

0.3

met

er

LQ

2000 4000 6000 8000 10000 120000

0.1

0.2

met

er

Open loop

Time (min)

Rain starts Rain stops

refuse of offtake

Head of water over supply regulator

Fig. 11. Water supply over a 9 day period into anirrigation canal

tion.) There is clearly no real incentive to imple-ment centralized control action.

The corresponding water level response in themost down stream pool is illustrated in Figure12. In this pool it is most difficult to manageacceptable water regulation under manual con-trol. Typically the bottom end of the irrigationsystem experiences poor quality of service undermanual operations. Using the decentralized con-trollers there is saturation during the rain event(regulators are closed) and at the end of the ir-rigation period, small excess of water supply, butno outflow. This water is stored in the most downstream pool.

2000 4000 6000 8000 10000 1200021.28

21.3

21.32

TCC with FeedforwardmA

HD

2000 4000 6000 8000 10000 1200021.28

21.3

21.32

TCC without Feedforward

mA

HD

2000 4000 6000 8000 10000 1200021.28

21.3

21.32

Central Control LQmA

HD

2000 4000 6000 8000 10000 12000

21.4

21.6

Open loop

Time (min)

mA

HD Rain starts

Rain stops

Saturation

Saturation

Refuse of offtake

Upper critical point Flood

Fig. 12. Waterlevel response in the most down-stream pool

Under manual operations, the overall efficiencywas 80% (which is very good compared to his-torical averages, typical best practice manual op-eration achieves an efficiency of about 70%). Thequality of service is however poor, despite the factthat the water orders were placed as to be advan-tageous to manual control. Only 90% of the waterorders is met. The water levels dropped below

the minimum required to satisfy the requesteddemand over about 10% of the total duration.Moreover, during the rain period, the most downstream pool flooded its banks for about a day. Therain period only lasted for 10h, but there was asignificant water flow imbalance at the beginningof the rain period, which together with the slowresponse of manual control, aggravated the raineffect to cause significant flooding.

To observe substantial differences between thedifferent forms of automated, real-time, irrigationmanagement, larger canal systems must be com-pared. Various scenarios have been simulated, andit quickly becomes clear that decentralized controlwith feed forward (and anti-windup) achieves nearglobal optimal performance. In most scenarios itsperformance cannot be distinguished from cen-tralized control (which cannot be implemented)and it is substantially better than the decentral-ized control without feed forward. The latter suf-fers from a larger variation in water levels, andcannot always supply water orders as requestedbecause water levels fall below the agreed mini-mum supply point.

4.6 Implementation Issues

There are two main implementation issues tocontend with: sampling and saturation.

As pointed out, the information infrastructuredoes not allow for regular sampling. Globally sam-pling is performed on an event basis (e.g. onlythe time that a water level changes by 2cm up ordown is reported), although locally, at each siteregular sampling is performed. The decentralizedcontroller does not suffer, as it only uses localinformation. A global controller must be designedas to cope with rather varying information ratesand delays across the range of variables it requiresto compute the control inputs. Substantial furtherresearch work is necessary. This issue is at theheart of so called network control. An alterna-tive approach to communication limited control isexposed in for example (Nair et al., 2004) wherean information theoretic point of view is pursued.The latter identifies the minimum data rates re-quired to achieve stability. It turns out that inthe case at hand, as the instability in the plant islimited to a chain of integrators that any non-zerocommunication rate suffices to achieve stability.Of course, this does not imply good performance,but it indicates that the required communicationcannot be demanding. This is in-line with thepresent engineering solution and experience.

Saturation issues can be addressed using anti-windup control ideas. The design can be com-pleted, and consequently adapted as to ensure

smooth feedback without integrator saturation(Zaccarian et al., 2004a; Zaccarian et al., 2004b).Simple anti-windup control is implemented.

4.7 Open Issues

There are a number of interesting open aspectsfrom a theoretical point of view that have receivedlittle attention in the control literature. Eventbased sampling and a better understanding of thedisturbance propagation in the irrigation system.The latter is made difficult because of the combi-nation of marginally stable open loop dynamicscombined with delays. Although no single pooldynamics is dominated by delay effects, the con-catenation of many similar systems in a tree likestructure makes this an interesting and difficultproblem, see (Li et al., 2004; Li et al., 2005) forfirst results in the case of a string of identicalpools. This work addresses the worst case sce-nario. What is important is to understand theaverage case, where there is a certain (natural)distribution of delays and pool dynamics. Thekey ingredient in understanding the propagationof disturbances through the system is to under-stand the role of the feed forward control in bal-ancing the requirement for providing informationto speed up the response, and yet limiting thisinformation so as not to amplify the disturbances.

Another interesting open problem that has re-ceived not enough attention in the control litera-ture is to determine an appropriate structure for adecentralized controller. This is a problem of de-termining the appropriate information structurefor control design, or which inputs/outputs arebest paired with each other. As, the number of dif-ferent decentralized controller structures is com-binatorially large, exhaustive evaluation is sim-ply not feasible, hence relevant heuristics shouldbe developed. One ad-hoc solution method is touse sequential minimum variance (Weyer, 2003b),based on a particular ordering of the variables tobe regulated. Another is to start from a globalcentralized control design, and to prune the input-output connections based on an appropriate sin-gular value decomposition. In the present applica-tion, both approaches lead rather quickly to theproposed solution method. In sequential minimumvariance, the ordering of the variables that leadsto the above decentralized controller structure isto place the highest priority on the outflow (uN ,next the most down stream water level yN−1, thenthe next water level yN−2 and so on.

5. DISCUSSION

Systems engineering principles as discussed herehave been implemented in support of irrigation

system management in a number of pilot projectsin Victoria, Australia, with excellent outcomesin terms of achieved overall water savings andquality of service: water distribution efficiency ofbetter than 90% (essentially only the unremovablelosses due to evaporation and seepage remain),compared to 70% achieved under manual opera-tions; combined with an ability to meet water re-quests on-demand in better than 90% of all waterorders. All of this is achieved together with muchbetter regulation accuracy, which improves thequality of service to the customers in a significantway. On the basis of these outcomes, Rubicon Sys-tems Australia Pty. Ltd. has been commissionedto start large scale industrial implementation inVictoria.

The white paper on water released by the StateGovernment of Victoria identified that the im-plementation of advanced control, along the linesexpounded here, will save about 400Mm3 of waterper year when completed across all of the irriga-tion districts in Victoria. This volume of savingsnearly equals the total annual water consumptionfor all domestic and industrial use in the Stateof Victoria. This figure is based on a conserva-tive extrapolation of the actually achieved watersavings in the pilot projects to date (only needto achieve half the success achieved in the pilotprojects thus far). Similar studies conducted ina New South Wales report even greater savingpotentials (The Business of Saving Water - theReport of the Murrumbidgee Valley Water Effi-ciency Project, n.d.). The economic benefits thatcan be derived from such water savings initiativesare immense. The (The Business of Saving Water- the Report of the Murrumbidgee Valley WaterEfficiency Project, n.d.) report indicates economicbenefits in the order of $500M when a water savingtarget of 1Gm3 would be realised.

An important outcome of the information infras-tructure is that management, and indeed the com-munity at large, can be much better informedabout the capabilities of the irrigation system;how much water was used, when and where itwas used. Already, changes in the way irrigatorsuse water can be observed, as a more responsivedistribution system enables them to use more wa-ter efficient on-farm practices. This results in evenmore water savings or better economic returns forthe farmers.

The present positive results encourage the expan-sion of the research and development ideas toconsider other aspects of water distribution, on-farm as well as urban. The outcomes realized area small step towards the goal set forth in the(UNESCO Water Report 2003) that fresh watermanagement must happen on the scale of entirewater catchments.

REFERENCES

Brutsaert, W. (1971). The Saint-Venant equationsexperimentally verified. 97, 1387 – 1401.

Chaudhry, M. H. (1993). Open-channel flow.Prentice-Hall.

Choy, S. and E. Weyer (2005). Reconfigurationscheme to mitigate faults in automated irri-gation channels. In: 44th IEEE Conference onDecision and Control. Seville, Spain. submit-ted.

Cunge, J.A., F.M. Holly and A. Verwey (1980).Practical Aspects of Computational River Hy-draulics. Pitman Advanced Pub. Program.

Euren, K. and E. Weyer (2005). System iden-tification of irrigation channels with under-shot and overshot gates. In: 16th IFAC WorldCongress. Prague, Czech Republic. to appear.

Halleux, J., C. Prieur, J.-M. Coron, B. d’AndreaNovel and G. Bastin (2003). Boundary feed-back control in networks of open channels.Automatica 39(8), 1365 – 1376.

Li, Y., M. Cantoni and E. Weyer (2004). Designof a centralized controller for an irrigationchannel using loop-shaping. In: Proc UKACCControl conference. University of Bath, UK.

Li, Y., M. Cantoni and E. Weyer (2005). Onwater-level error propagation in controlled ir-rigation networks. submitted for publication.

Litrico, X. and V. Fromion (2004). Analyticalapproximation of open-channel flow for con-troller design. Applied Mathematical Mod-elling 28(7), 677 – 695.

Litrico, X., V. Fromion, J.-P. Baume and M. Rijo(2003). Modelling and pi control of an irriga-tion channel. In: Proceedings of the EuropeanControl Conference ECC03. Cambridge, UK.

Malaterre, P.O. and B.P. Baume (1998). Modelingand regulation of irrigation canals: existingapplications and ongoing researches. In: Pro-ceedings of IEEE Conference on System, Manand Cybernetics. San Diego, USA. pp. 3850 –3855.

Mareels, I., E. Weyer and D. Aughton (2000).Rubicon research pty ltd, control gates.WIPO Number WO02/16698, PCT NumberPCT/AU01/01036 priority date for Australia21 Aug 2000.

Mareels, I., E. Weyer and D. Aughton (2001).Rubicon systems australia pty ltd, fluid reg-ulation. WIPO Number 02/071163, Aus-tralian Application Number 2002233060,PCT/AU02/00230, priority date for Aus-tralia 2 March 2001.

Nair, G., R. Evans, I. Mareels and B. Moran(2004). Topological feedback entropy andnonlinear controllability. IEEE Trans AutControl, Special Issue on Networked ControlSystems 49(9), 1585 – 1597.

Ooi, S. K., E. Weyer and M. C. Campi (2003a).Finite sample quality assessment of system

identification models of irrigation channels.In: Proceedings of the IEEE Conference onControl Applications. Istanbul, Turkey.

Ooi, S. K., M.P.M. Krutzen and E. Weyer (2003b).On physical and data driven modelling ofirrigation channels. In: Proceedings of the13th IFAC Symposium of System Identifica-tion. Rotterdam, The Netherlands. pp. 1975– 1980.

Ooi, Su Ki (2003). Modelling and control design ofirrigation channels. PhD thesis. Departmentof Electrical and Electronic Engineering, TheUniversity of Melbourne.

Ooi, Su Ki and E. Weyer (2001). Closed loop iden-tification of an irrigation channel. In: Proceed-ings of the 40th IEEE Conference on Decisionand Control. Orlando, USA. pp. 4338 – 4343.

Ooi, Su Ki, M.P.P. Krutzen and E. Weyer (2005).On phyiscal and data driven modeling of ir-rigation channels. Control Engineering Prac-tice 13(4), 461 – 471.

Schuurmans, J., A. Hof, S. Dijkstra, O.H. Bosgraand R. Brouwer (1999). Simple water levelcontroller for irrigation and drainage canals.Journal of Irrigation and Drainage Engineer-ing 125(4), 189 – 195.

Securing our Water Future Together (2004).//www.dse.vic.gov.au/dse. report preparedon behalf of the Department of Victoria Landand Water Management Policy.

The Business of Saving Water - the Report ofthe Murrumbidgee Valley Water EfficiencyProject (n.d.).http://www.napswq.gov.au/publications/pratt-water.html. report prepared by Pratt WaterPty Ltd.

The United Nations World Water Develop-ment Report, Executive Summary (2003).http://www.unesco.org/water/wwap/.

Water and the Australian Economy(1999). http://www.atse.org.au/publications/reports/water9.htm. report prepared on be-half of the Australian Academy of Technolog-ical Sciences and Engineering.

Water Savings in Irrigation Distribution Systems(2000). report prepared by Sinclair Knight &Merz.

Weyer, E. (2001). System identification of an openwater channel. Control Engineering Practise9, 1289 – 1299. based on a prior paper inIFAC Symposium on System Identification,2000.

Weyer, E. (2002). Decentralised pi controller of anopen water channel. In: Proceedings of the 15IFAC World Congress. Barcelona, Spain.

Weyer, E. (2003a). Control of open water chan-nels. IEE Trans on Control Systems Technol-ogy. submitted.

Weyer, E. (2003b). Controller configurations forirrigation channels derived from sequential

minimum variance control. In: In Proceedingsof IEEE Conference on Control Applications.Istanbul, Turkey.

Weyer, E. (2003c). Linear quadratic control of anirrigation channel. In: Proceedings of the 42ndIEEE Conference on Decision and Control.Hawaii, USA. pp. 750 – 755.

Zaccarian, L., E. Weyer, A. Teel, Y. Liand M. Cantoni (2004a). Anti-windup formarginally stable plants applied to open wa-ter channels. In: Proceedings of the 5th AsianControl Conference. Melbourne, Australia.pp. 1702 – 1710.

Zaccarian, L., Y. Li, E. Weyer, M. Cantoni andA. Teel (2004b). Anti-windup for marginallystable plants applied to open water channels.Control Engineering Practice. submitted.