Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Control of the

Su Ki Ooi ∗ Mathias Foo ∗∗ Erik Weyer ∗

∗ Department of Electrical and Electronic Engineering, The University of , Parkville, VIC 3010, (e-mail: [email protected], [email protected]). ∗∗ National ICT Australia, Research Lab, Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC 3010, Australia (e-mail: [email protected])

Abstract: In this paper, a control system design is proposed for the Broken River in Victoria, Australia. The control scheme is decentralised, and consists of a number of local PI and P controllers. The controllers are designed using frequency response techniques based on simple models obtained using system identification methods. In a simulation example, the control system compared very favorably with current manual operation demonstrating a significant potential for substantial water savings.

Keywords: Control systems, River systems, Environmental systems, System Identification.

1. INTRODUCTION Most likely there will be a change in farming practices due to less available water in the future which again will change The increase in world population and the growth of farming the demand patterns for irrigation water. On the legislative have created an increased demand for water. Agricultural ac- side, higher priorities have been given to environmental water counts for about 70% of the world’s freshwater use (Water demands in the Water Act 2007 (Water in our environment Report 2 (2006)), and the operational losses in the delivery of (2010)) in order to ensure water supply to protect and restore water to farms are large. After more than a decade of drought environmental assets such as and streams. Part of the in Southern Australia, it has become increasingly important to FRM project is to investigate what constitute desirable flows explore new farming practices and strategies for management and water levels from the environmental and ecological point of water in order to prepare for a drier future. Such a com- of view, and this will have an impact on the control objectives. plex resource management issue calls for an interdisciplinary There will also be a number of constraints on the operation of approach including agricultural science, engineering, ecology, the river that the control system must make sure are satisfied. hydrology, economics, social sciences, etc. The research de- For example maximum and minimum allowable flow rates, scribed in this paper is part of the project ”Farms, Rivers, maximum allowable rates of change in flows at key points in the and Markets” (FRM), which was initiated by Uniwater, a joint river, rules and water quality issues associated with “re-starting research initiative by The University of Melbourne and Monash the river” after periods of low or no flow, maintenance of slack University in response to the above challenges. water in specific reaches at defined times, etc. As the name suggests, the project consists of three key inte- In the Broken River it takes about four to six days for the grated components: Farms, Rivers and Markets. The aim of water released from Lake Nillahcootie to reach downstream the Farms project is to explore how the various sources of locations where most of the demand is, i.e. there are long time water can be used in flexible combinations to make farming delays between the point of supply and the point of demand. operations more resilient. The Rivers project is concerned with Furthermore the delays do vary with flow. The control problem the development of systems for managing the water capable is challenging since presently the flow in the river can only be of handling the needs of irrigators and the environment in a regulated at a limited number of locations. Furthermore, there cooperative way. The Markets project aims at developing new are currently only limited opportunities to store water in-stream water products and services better suited to future demands along the Broken River. However, a large off-stream storage from consumers and the environment. in the upper part of the river is planned and the outflow from this storage can be regulated. Moreover, as part of the control Modelling and control system have important parts to play in subproject, the benefit of having extra gates along the river and the Rivers project since well designed control systems for river small storages where in and out flows can be regulated close to flows and levels will allow for a more efficient distribution of the points of demand will be evaluated. The presence of these water leading to reduced operational water losses. In addition, storages add an extra dimension to the original control problem. it will allow for a more accurate and timely delivery of water to farmers while ensuring that the environmental and ecological In this paper, it is assumed that flows along the river can be water needs are satisfied. regulated at a few extra locations, and that off-stream storages are available. Decentralised control of the river is considered, Broadly speaking, the aim of the control system is to improve and a simulation study based on recent historical water orders water resource management and operation for the benefit of adjusted for anticipated future trends shows that large water consumptive users and the environment. However, what the savings can be obtained using the proposed control strategy. specific control objectives should be is not yet fully understood.

Copyright by the 627 International Federation of Automatic Control (IFAC) Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Similar works on modelling and control of irrigation channels, Weir (HS4) is about 76km 1 . The two major streams that see e.g. Cantoni et al. (2007); Litrico et al. (2005); Mareels contribute flow into the Broken River are Lima and Hollands et al. (2005); Ooi and Weyer (2008); Schuurmans et al. (1999); Creeks as shown in Fig. 1. Weyer (2001, 2008), have demonstrated that control systems can yield significant improvements in the quality of service and 2.2 Location where flow can be regulated and storages water distribution efficiency. However, unlike a river, there are no environmental constraints in an irrigation channel. Further- One main objective is to satisfy the demand for water from more, there are more storage and control points in an irrigation irrigators. It is therefore an advantage to be able to regulate channel compared to a river. Hence, there are much shorter flows at points close to the demand such that the time delays can time delays between the points of supply and the points of be reduced. Thus, in this paper it is assumed that the flow can demand in an irrigation channel. These are all factors which be regulated at the following locations (see the map in Fig. 1): make the control problem more difficult for a river. There (I) Lake Nillahcootie, (II) Broken Weir, (III) Outlet of Lake are a number of works on control of rivers with focus on and (IV) Casey’s Weir. The flow cannot be manipulated optimisation of the operation of hydro-electric power plants, at Gowangardie Weir. As most of the irrigation demands are minimising energy cost of pumping and ensuring that the river downstream of Casey’s Weir, having control at this point will is navigable, see e.g. Linke (2010), van Overloop et al. (2010), reduce the delay in the water supply. (III) and (IV) are new Setz et al. (2008), Soncini-Sessa et al. (2007), Castelletti and locations which would require an upgrade in the infrastructure Soncini-Sessa (2007), Glanzmann et al. (2005), Litrico and if the control system were to be implemented. As the control Pomet (2003), Litrico (2002), Sohlberg and Sernf¨alt (2002) and actions will at times reduce the flow below the natural unregu- Papageorgiou (1989). lated flow, water will be backed up behind these proposed new The rest of the paper is organised as follows. A description of control structures, so there must be storage capacity (free board) the Broken River together with the assumptions of where the behind them. In order to increase the storage capacity along the flows can be regulated are presented in the following section river, the following off-stream storages are also considered together with the control objectives and the control configu- (V) Storage 1. Off-stream storage in the former inlet channel ration. The models used for control design are discussed in to , see Fig. 1. Section 3 followed by the design of the controllers in Section 4. (VI) Storage 2. A small off-stream storage between Casey’s In Section 5 a simulation example of an initial control design is and Gowangardie Weirs. presented and the results are evaluated in Section 6. Storage 1 is currently under construction, and Storage 2 is used in the ecological research carried out under the FRM project. 2. THE BROKEN RIVER AND THE CONTROL OBJECTIVES 2.3 Control Objectives

2.1 The Broken River The following control objectives are considered. These are pre- liminary control objectives and in particular the environmental objectives will be modified as the research progresses. a) Satisfy the demand for water from the irrigators and the environment, b) Release as little water from Lake Nillahcootie as possible, c) Maintain the volume of Storage 1 and 2 at 50% and 80% of full capacity respectively, d) Maintain the flow over Broken Weir at desired flow setpoints to satisfy environmental (minimum) flow requirement, see Section 5.1, e) Maintain the water levels at Broken Weir, Lake Benalla and Casey’s Weir at the setpoints of 2.15m, 2.25m and 2.0m respectively. f) Maintain the flow over Gowangardie Weir at a desired flow setpoint in order to satisfy downstream demands and the en- vironmental (minimum) flow requirement, see Section 5.1. Furthermore, as irrigators pump water out of the river there will be restrictions on how far down the water levels in the river can be drawn. In this paper it is assumed that 15cm below the setpoint is within the limits. In addition, Lake Benalla is used for recreational purposes and it is necessary to maintain the water level within a range which the authors have assumed to Fig. 1. Map of the Broken River (not to scale). be ±20cm from the setpoint.

Fig. 1 shows a map of the Broken River in Victoria, Australia. Following current practice it will be assumed that once a water The Broken basin covers 7,724km2 of catchment area. The river order has been approved by the water authority it will be originates from Lake Nillahcootie which stores 40GL of water. 1 Obtained by approximating the rivers by straight lines between the hydraulic The length of the river from Lake Nillahcootie to Gowangardie structures (HS) on the map

628 Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011 delivered regardless of the water level and flow conditions A single reach without storage This is similar to the reach in the river (assuming the levels are high enough so that the with storage but the upstream gate i will be positioned to release pumps can be operated). A failure to release sufficient water the flow Q(t) instead of Qi(t). will therefore manifest itself through decreasing water levels in the in-stream storages associated with the regulation points, Multiple reaches with storage The remaining reaches are potentially violating critical lower limits on the water levels. controlled as in Fig. 3. The release from Lake Nillahcootie is used to control the volume in Storage 1 while the inlet to 2.4 Control Configuration Storage 1 is in upstream level control configuration. In this configuration, the water level upstream of a gate is controlled Below we describe the control configurations considered. Due by the gate itself. Hence, with the upstream level control at the to the long time delays from the point of supply to where the inlet to Storage 1 the water released from Lake Nillahcootie water is required, feedforward of the known future orders of will be passed into Storage 1 while maintaining the water level water is necessary. Under current practise, farmers are required at Broken Weir at the desired level by manipulating the flow to place an order of water four days in advance. into Storage 1.

A single reach with storage For a reach with storage, e.g. the Broken Weir is in flow mode where the measurement of the reach between Casey’s Weir and Gowangardie Weir, the control water level yB is used to compute the required gate position configuration shown in Fig. 2 is used. The reach is assumed pB in order to maintain a desired flow over the weir. In this configuration, Storage 1 rather than Broken Weir is used to control the water level in Lake Benalla since there is limited storage in the weir pool upstream of Broken Weir. Putting everything together, the control configuration shown in Fig. 3 is obtained. PI1 to PI3 and I4 are distant downstream

PI and I-only controller configurations. eVS1 , eyLB , eyC and eQG are the difference between the volume in Storage 1, the water levels at Lake Benalla and Casey’s Weir and flow over Gowangardie Weir and their desired setpoints respectively. QLN, QSout, QLB and QC are the flows at Lake Nillahcootie, out of Storage 1, out of Lake Benalla and Casey’s Weir respectively. 3. MODELLING FORCONTROL DESIGN

Traditionally, the dynamics of a river are modelled using the Saint Venant equations. However, they are difficult to use for control design since they are partial differential equations. Hence, simpler models using system identification methods which capture the relevant dynamics for control have been developed and validated against measured data from the Broken River, see Foo et al. (2010b, 2011) for details. The flow over the weirs and overshot gates can be approximated Fig. 2. Distant downstream control configuration with feedfor- by ward and storage. Q(t) = ch(t)3/2 = c[y(t) − p(t)]3/2 (1) automated with overshot gates where y and y are the upstream where c is a constant. The following model structure are used i j for control design, see Foo et al. (2010b, 2011) for details. water level of gate i and j respectively, pi and pj are the Note that flows from Lima and Hollands creeks are treated position of gates i and j, and hi and hj are the head over gates which are the height of water above the gates. The feedforward as disturbances on the system, and are not considered in the will, due to the time delay, release the flow corresponding to fu- models. ture orders from farmers and the environment τimin before the Reach Lake Nillahcootie to outlet of Storage 1 (LNSout): water is required, and the feedback controller C (s) will adjust i V˙ t Q t − τ − Q t − Q t for any discrepancy in the flow e.g. due to model mismatch or 1( ) = LN ( LNS1) Sout( ) B( ) (2) errors in the rating curve based on the difference between the where V1 and QSout are the volume and outflow of Storage 1 respectively. Q and Q are the flow out of Lake Nillahcootie downstream flow Qj and the desired flow setpoint Qj,setpoint. LN B and the flow over Broken Weir respectively. τ is the time Ci(s) is usually a PI controller. The feedforward and the feed- LNS1 back are added together to produce the required flow in the river delay from Lake Nillahcootie to outlet of Storage 1. Here we ≈ − at the storage, Q. The flow released at Gate i is Q plus the flow have approximated the inflow to Storage 1 QSin(t) QLN (t τ )−Q (t) which is a reasonable approximation since the required by the storage level controller CS(s). The storage level LNS1 B inlet flow to the storage is controlled by a fast acting upstream feedback controller, CS (s) is a Proportional controller, which is level controller. used to maintain the water level in the storage, yS at a setpoint yS;setpoint. The flow out of or into the storage is determined by Reach Outlet of Storage 1 to Lake Benalla (SoutLB): the difference between the flow required in the river, Q and the ′ y˙LB(t) = c1,LBQSout(t − τSout) delayed version Qi(t − τ ) which is the flow expected to arrive ′ ′ 3/2 at the storage after τ min when the flow Q(t) is required. τ is − c2,LB (yLB(t) − pLB(t)) + c3,LBQB(t − τBLB) the travel time between Gate i and the storage. (3)

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Fig. 3. Control configuration for the Broken River. where yLB and pLB are the water level and gate position at 4. CONTROL DESIGN Lake Benalla respectively, while τSout is the time delay from outlet of Storage 1 to Lake Benalla. τBLB is the time delay The controllers are tuned using classical frequency response from Broken Weir to Lake Benalla. methods based on the models in Section 3. Due to the vari- ation in the time delay with the flow, the controller is tuned Reach Lake Benalla to Casey’s Weir (LBC): rather conservatively to ensure robustness. The phase margins 3/2 ◦ ◦ y˙C(t) = c1,C QLB(t − τLBC ) − c2,C (yC (t) − pC(t)) (4) obtained range from 51 to 68 and the gain margins are be- where yC and pC are the water level and gate position at tween 10dB and 23dB. For the Reach CG the range of delays in Table 1 gives a maximum phase change of 48◦ at the crossover Casey’s Weir respectively. QLB is the flow at Lake Benalla and ◦ τLBC is the time delay from Lake Benalla to Casey’s Weir. frequency, which is well within the phase margin of 63 . For the other reaches the variations in the time delays give a maximum Reach Casey’s Weir to Gowangardie Weir (CG): phase change of 30◦ or less at the crossover frequency. QG(t) = QC (t − τCG) (5) where QC and QG are the flow over Casey’s Weir and Gowan- 5. SIMULATION EXAMPLE gardie Weir respectively and τCG is the delay from Casey’s Weir to Gowangardie Weir. Note that this is just a time delay In this section the performance of the control system is illus- model. The reason is that Gowangardie Weir is a fixed free trated in a realistic year long simulation example. Even though overfall weir so it just passes the flow coming from Casey’s the controllers are designed based upon system identification Weir. models, the Broken River with the controllers is simulated using the Saint Venant equations which have been validated Storage 2: against data (Foo et al. (2010a,b, 2011)). As the geographical V˙S (t) = QS(t) (6) area we consider ends at Gowangardie Weir, all demand for where VS is the volume of Storage 2 and QS is the flow into or water (including environmental water) downstream of Gowan- out of Storage 2. gardie Weir will be aggregated into a desired flow over Gowan- gardie Weir. As for inflows from creeks we will only consider The parameters in the models are estimated using prediction error methods based on measured data and data simulated using Table 1. Models parameters the Saint Venant equations which have been validated against real data, see Foo et al. (2010b, 2011) for details. The time Reach c1 c2 c3 Delay (min) Length [Variation] delays are obtained based on simulated step test (under low LNSout --- 2250 22km flow condition, i.e. around 30ML/D) using the Saint Venant [465-2550] equations However, as shown in Foo et al. (2010b, 2011) these SoutLB 0.0102 0.1119 0.0149 375 7km time delays vary with flow, and it will affect the robustness [120-600] margins of a control system. The varying time delay are taken LBC 0.0062 0.1201 - 975 12km into account in the robustness specification of the controllers [165-1035] (see Section 4). The parameters are given in Table 1 together CG --- 1875 27km with the length of each reach and the variation in delay. [825-3375]

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Reach Casey’s to Gowangardie orders Lake Nillahcootie Releases

160 50 Manual Control A 45 140 Control B

40 120 35

30 100 ML/D

25 ML/D 80 20

15 60

10 40 5

0 20 01−Jan−2007 08−Jan−2007 16−Jan−2007 24−Jan−2007 01−Feb−2007 01−Jan−2007 08−Jan−2007 16−Jan−2007 24−Jan−2007 01−Feb−2007 Time Time

Fig. 4. Order of water between Casey’s and Gowangardie Weirs Fig. 5. Releases from Lake Nillahcootie in January 2007. in January 2007. Lima and Hollands Creek and assume that all inflows can be Table 2. Volume of water. aggregated into these two flows. It is assumed that Lake Nillah- Manual Control A Control B cootie is always able to supply the flow required. Total water released from LN 28551ML 19348ML 20302ML Total water required downstream 9640ML 9640ML 9640ML 5.1 External Inputs of Gowangardie Total irrigation order 11475ML 11475ML 11475ML Flow from Hollands Creek 594ML 594ML 594ML The external inputs to the simulation are: Flow from Lima Creek 1203ML 1203ML 1203ML i) Orders of water from irrigators are based on historical Excess water 9233ML 30ML 984ML data adjusted for future trends. Fig. 4 shows the order of water pattern between Casey’s and Gowangardie Weirs in the three different management options in January 2007. As January 2007. expected the release under the Manual operation is higher than ii) For environmental water demand, the minimal flow values those with control. One can also observe that the release is from the Bulk Entitlement (2010) with small weekly ran- slightly higher under Control B than Control A due to the extra dom perturbations are used. 10% added to the flow setpoints and hence the excess flows over iii)Inflow from creeks are based on the historical measured Gowangardie Weir are larger. With control the amount of water flows. released from Lake Nillahcootie is reduced by about 30%. The environmental objective is to satisfy the environmental 5.2 Management options minimum flow requirements. The percentage of time the flows were below the minimum flow requirements are computed. In Three different management methods are considered in the addition, the duration for which these flows were more than simulation study. 20%, 40% and 60% below the minimum flow requirements are also calculated showing how severe the breaches were. The Control System A. The control configuration in Fig. 3 is used. results are shown in Table 3. Note that the flow setpoint of The flow setpoints are equal to the demand from irrigators and Gowangardie Weir includes orders from irrigators while QG,min the environment. is based on environmental demand only. Control System B. Same as Control System A, but an extra Compared to manual operations the flows are below minimum 10% is added to the flow setpoints in order to improve the levels more often with control. However, it is relatively rare satisfactions of demands. that the flows are more than 20% below minimum flows, and Manual operation. Manual regulation of the release from Lake such deviations may be acceptable depending on the purpose Nillahcootie. The flow is adjusted daily according to the known of the minimum flow. If the flow is to maintain habitat, these future demands and an extra 20ML/D is added to account for breaches would not be significant. If however they are designed uncertainty in the actual flow released and transmission losses. to avoid stratification in pools, then the duration of the breach This is similar to current manual operations (Bailey (2010)). will become serious especially in summer, Gawne (2010). Exactly how serious the breaches are will be evaluated in the 6. EVALUATION OF THE CONTROL SYSTEM future collaboration with the ecologist in the FRM project. With Control B, Gowangardie Weir is the only point where the environmental flow requirements are sometimes violated. As As one of the objectives is to keep the amount of water released expected there are fewer breaches when an extra 10% is added from Lake Nillahcootie as small as possible, the amount of to the flow setpoints. excess water which leaves the study area is evaluated. Excess is understood as water not needed for environmental purposes nor Under both manual operation and automatic control we have ordered by irrigators. This volume of water is given in Table 2 100% satisfaction of water orders from irrigators. If insufficient together with the total amount of water released from Lake water is released this will lead to low water levels in the in- Nillahcootie (LN), total volume of water diverted for irrigation stream storages (the weir pools at Gowangardie, Casey’s and and total inflows from Lima and Hollands Creeks for the whole Broken Weir and Lake Benalla), but this only happens relatively year. Fig. 5 shows the releases from Lake Nillahcootie for rarely. The water level is 15cm or more below the setpoint under

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Table 3. Performance measure. Gawne, B. (2010). Private communication with Ben Gawne (FRM Rivers subproject) of The Murray-Darling Freshwater Criteria % of time in season 2006/2007 Research Centre, Latrobe University. Manual Control A Control B Gowangardie Weir Glanzmann, G., von Siebenthal, M., Geyer, T., Papafotiou, G., and Morari, M. (2005). Supervisory water level control for QG ≥5ML/D below setpoint 1.7% 13.6% 7.3% QG < QG,min 3.3% 52.0% 16.5% cascaded river power plants. Proceedings of the 6th Interna- QG 20% < QG,min 1.4% 10.6% 5.7% tional Conference on Hydropower, Stavanger, Norway. QG 40% < QG,min 0.6% 3.8% 1.9% Linke, H. (2010). A model-predictive controller for optimal QG 60% < QG,min 0.2% 1.1% 0.4% hydro-power utilization of river reservoirs. Proceedings of automatic control only 0.1% of the time compared to 0% under IEEE Multiconference on Systems and Control, Yokohama, Japan manual operation. , pages 1868–1873. Litrico, X. (2002). Robust IMC Flow Control of SIMODam- 7. CONCLUSION River Open-Channel Systems. IEEE Trans. on Control Systems Technology, 10(3), pages 432–437. Decentralised control with feedforward of known future orders Litrico, X., Fromion, V., Baume, J.P., Arranja, C., and Rijo, M. is considered for the Broken River. A realistic year long simula- (2005). Experimental validation of a methodology to control tion using historical orders of water from irrigators showed that irrigation canals based on Saint-Venant equations. Control the proposed control system is able to satisfy demands of water Engineering Practice, Vol. 13, pages 1425–1437. from both the irrigators and the environment, and that signifi- Litrico, X. and Pomet, J.B. (2003). Nonlinear modelling and cant water savings can be achieved with only minor degradation control of a long river stretch. Proceedings of the 2003 in the satisfaction of the environmental flow requirements and European Control Conference, Cambridge, UK. deviations from setpoints. The control design example is only Mareels, I., Weyer, E., Ooi, S.K., Cantoni, M., Li, Y., and an initial design, but it gives a good picture of what can be Nair, G. (2005). Systems engineering for irrigation systems: achieved with a control system in place. Successes and challenges. Annual Reviews in Control, Vol. 29, pages 191–204. ACKNOWLEDGEMENTS Ooi, S.K. and Weyer, E. (2008). Control design for an irrigation channel from physical data. Control Engineering Practice, This work was supported by The Farms Rivers and Markets Vol. 16, pages 1132–1150. Project, an initiative of Uniwater and funded by the National Papageorgiou, M. and Messmer, A. (1989). Flow control of a Water Commission, the Victorian Water Trust, The Dookie long river stretch. Automatica, Vol. 25 (2), pp. 177-183. Farms 2000 Trust (Tallis Trust) and the University of Mel- Schuurmans, J., Hof, A., Dijkstra, S., Bosgra, O., and Brouwer, bourne and supported by the Departments of Sustainability R. (1999). 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