Design of a Centralized Controller for an Irrigation Channel Using H Loop-shaping

Transcription

1 Control 24, Univerity of Bath, UK, September 24 ID-7 Deign of a Centralized Controller for an Irrigation Channel Uing H Loop-haping Yuping Li, Michael Cantoni and Erik Weyer Abtract Thi paper decribe the deign of a multivariable H loophaping controller for water level regulation on the Haughton Main Channel, Queenland Autralia. A one-degree-of-freedom controller tructure i applied to three ucceive pool. Analyi of robut performance i preented in term of the tructured ingular value. Cloed-loop performance i alo evaluated through imulation with high fidelity model of the channel. The controller how better performance than decentralized PI control, and attain imilar performance to a multivariable LQ controller. The H loop-haping controller i, however, much eaier to tune than an LQ controller. Thi become important when the number of pool to be controlled i increaed. A uch, it i an appealing deign paradigm when high performance control of an irrigation channel i required. I. INTRODUCTION An irrigation channel mut be able to deliver water to farmer on demand, whilt minimizing water loe. Currently, water loe are typically large, and ince water i a carce reource in many part of the world, thi i becoming an increaingly important iue. Continued invetment in the intrumentation and automation of irrigation network, will give rie to a great potential for atifying water demand whilt reducing water loe. Indeed, in recent year thi area ha received ignificant attention, ee e.g. [ ]. In the literature, two approache are commonly employed for controlling irrigation channel, namely, decentralized PI control ([8], [9], []), and multivariable (centralized) LQ or predictive control ([3], [7], []). Naturally we attain better norminal performance with a multivariable LQ controller than with decentralized PI control, but an LQ controller i much more difficult to tune, particularly for large ytem. Decentralized PI control, on the other hand, i advantageou in term of eae of deign and implementation. The channel we conider in thi work i the Haughton Main Channel (HMC), ituated in Queenland Autralia. Very accurate imulation model exit for thi ytem (ee [2] and [3]). Both decentralized PI controller ([], [4], [22]) and a centralized LQ controller ([], [5]) have been deigned for the HMC and teted in the field with promiing reult. In thi paper we employ H loop-haping to deign a multivariable controller for the ame part of the HMC. The controller obtained yield performance comparable to the LQ controller of [,5]. However, it i much eaier to deign, which i a ignificant advantage from the perpective of deigning controller for imilar irrigation ytem on a larger cale. The paper i organized a follow. In ection II, a decription of the HMC and the model ued for control deign are preented. We then decribe the deign of the H loop-haping controller in ection III. Section IV i devoted to a dicuion of the robutne and performance of the reulting control ytem in term of the tructured ingular value. By imulating the controller in cloed-loop with high fidelity model of the HMC, a comparion with decentralized PI control and multivariable LQ control i given in Section V. Finally ome concluion are given in ection VI. II. MODELS OF THE HMC A top view of an irrigation channel i hown in Fig. The tretch of a channel between two gate i referred to a a pool. Along the Reearch funded in part by the Commonwealth of Autralia through the Co-operative Reearch Centre for Senor, Signal and Information Proceing (CSSIP). Yuping Li and Erik Weyer are with CSSIP, Department of Electrical and Electronic Engineering, Univerity of Melbourne, Parkville VIC 3, Autralia {yuping,e.weyer}@ee.mu.oz.au Michael Cantoni i with the Department of Electrical and Electronic Engineering, Univerity of Melbourne, Parkville VIC 3, Autralia m.cantoni@ee.mu.oz.au channel there are offtake to farm and econdary channel feeding off the main channel. In mot cae we do not have meaurement of the offtake, and a uch they are uually treated a diturbance. Gate8 Farm Fig.. Gate Pool8 Gate9 Farm Branch Channel Gate Gate Gate Topview of an irrigation channel Main Channel The water level in the channel are controlled by over-hot gate located along the channel a ketched in Fig 2. The meaurement available for control are the water level uptream of each gate and the gate poition. All water level are given in mahd (meter Autralian Height Datum), relative to a reference level. The height of water above the gate i called the head over the gate. Fig. 2. h 8 y 8 h 9 p 8 y 9 Pool8 p 9 Sideview of an irrigation channel A the offtake are gravity fed, the water level in each pool mut be regulated in order to atify the demand for water from farmer. To the end of formulating model for the water level, a baic volume balance give dv (t) = Q in(t) Q out(t), () dt where V i the volume of one pool, and Q in and Q out are the inflow and outflow repectively. For an overhot gate, Q in and Q out are uually approximated (ee [6]) by: Q(t) = ch 3/2 (t), (2) where Q i the flow, h the head over the gate and c an unknown parameter. Note that thi approximation aume that the gate i in free flow, which mean that the top of the gate i above the immediate downtream water level. At the HMC, there i a drop in bed elevation after each gate, o all gate are in free flow. Auming that the volume in a pool i proportional to the water level, we arrive at ẏ 9(t) = c 8,2h 3/2 8 (t τ 8) c 9,h 3/2 9 (t) d 8(t), (3) where y 9(t) i the water level of the pool to be controlled, h 8(t) i the head over the uptream gate of that pool, and h 9(t) i the head over the downtream gate ee Fig 2. d 8(t) repreent the offtake of water and τ 8 i the time delay in pool 8 i.e. the time it take for the water to flow from the uptream gate to the downtream gate. The unknown parameter c 8,2 and c 9, have been determined from ytem identification experiment ee [2] and [3].

2 Control 24, Univerity of Bath, UK, September 24 ID-7 TABLE I PARAMETERS OF THE PLANT MODEL Pool Length Wave Freq Time Delay c i,2 c i+, i (meter) (rad/min) τ Setting u 8 (t) = h 3/2 8 (t) and u 9 (t) = h 3/2 9 (t), and taking the Laplace tranform, the plant model for pool 8 can be expreed a: y 9 () = c 8,2e τ u 8 () c 9, u 9() d 8(). (4) Modelling pool 9 and the ame way, yield the following plant model: y() = P()u() P d ()d() (5) where y = (y 9, y, y ), u = (u 8, u 9, u ) = (h 3/2 8, h 3/2 9, h 3/2 ) and d = (d 8, d 9, d, h 3/2 ) (h i the head over the downtream gate of pool ). P() i a 3 3 tranfer matrix: P() = c 8,2 e τ 8 c 9, c 9,2 e τ 9 c, c,2 e τ and P d () i a 3 4 tranfer matrix: P d () = c, (6) (7) The parameter c i,2, c i+, for i = 8, 9,, the length, the frequency of the dominant wave and the time delay for each pool are given in Table I. III. DESIGNING THE LOOP-SHAPING CONTROLLER In thi ection we firt dicu the control objective, before pecifying a control ytem configuration. A multivariable controller i then deigned via the H loop-haping technique of McFarlane and Glover [7]. A. Control Objective A the offtake to the farm are gravity fed, i.e. there i no pumping, the water level of each pool hould be maintained at certain level. Offtake by farmer can be treated a load diturbance that mut be rejected by the control ytem. When thee diturbance occur, the water level for each pool hould be controlled to remain at the repective etpoint value through the movement of gate. Since gate movement can induce wave motion, gate movement around the wave frequencie hould be avoided. Therefore, the main control objective include: High loop gain at low frequencie for rejection of load diturbance due to offtake; Roll-off rate of approximately 2dB/dec at the deired bandwidth (limited by wave frequencie) to yield ufficient phae margin for the loop gain and hence tability of the cloed-loop ytem; High roll-off rate at frequencie beyond the deired bandwidth, to give low loop gain at wave frequencie in order to uppre effect of the wave and mitigate uncertainty in the plant model at high frequency. Water i uually lot when it pae the lat gate without being ued. In irrigation channel where only the upper part i automated we hould therefore enure that the flow into the lower non-automated part i regulated according to the downtream demand. The flow over the lat gate i proportional to the head over the lat gate to the power of 3/2 (ee (2)), and the head i given by: h = y p (8) where p i the poition of gate. If gate were the firt nonautomated gate, p would be adjuted manually about once a day in order to meet the demand for water further downtream. When calculating the daily poition for gate one aume that the water level y i on etpoint, o water level control i alo important for delivering the right flow to the downtream plant of the ytem. B. Control Sytem Configuration Since any water level etpoint change or load diturbance due to offtake i reflected in the error between the etpoint and the meaured value of the water level in the pool, we et thee error a the input ignal to the controller. By chooing the head over the uptream gate of each pool a the output ignal of the controller, we get a control ytem configuration a hown in Fig 3, where r and y repreent the etpoint and meaured value of the water level of pool 8 to repectively, d repreent the offtake from pool 8 to and any change in the head over gate. In deigning the controller K r Fig. 3. K() u d P() Cloed loop Control Sytem P d () we aim to minimize the effect of the diturbance d on the output y. C. Deign of Centralized Controller Uing H Loop-Shaping Toward achieving the control objective jut identified, we can deign weight (which will ultimately appear a a part of the controller ) to hape the (open) loop gain according to the pecification decribed above. A robut tabilization problem i then formulated, and olved, for the weighted plant. Indeed, thi i preciely the H loop-haping procedure of McFarlane and Glover [7 9]. Two tep are involved in the H loop-haping procedure. Firt, the ingular value of the nominal plant, P, are haped, uing W and W 2, to give a deired (open) loop gain hape W 2 PW. A tabilizing controller K i then yntheied to achieve a bound on a meaure of cloed-loop robutne. The final feedback controller i contructed by combining K and the weight a W K W 2. Step. Loop Shaping The nominal plant P and the haping function W, W 2 are combined to form the haped plant P = W 2 PW. The weight W and W 2 are deigned to enure that the haped plant ha the following propertie: σ(p ) in the low-frequency range, which correpond to the control objective of high loop gain at low frequencie for offtake load diturbance rejection; σ(p ) in the high-frequency range, which correpond to the control objective of low loop gain at high frequencie to uppre wave reonance and to mitigate under-modelled high frequency dynamic. For the plant model (6) of pool 8 to, we elect the pot-compenator W 2 = I and the pre-compenator W a a diagonal 3 3 matrix: W () = diag [ ki ( + T ci ) ( + T fi ) ˆd ], i = 8, 9, (9) In order to enure complete diturbance rejection (aymptotically), we include an integrator in the weight function W (). To uppre the wave reonance, a low-pa filter +T f i included to enure a low loop gain at the wave frequencie. We alo enure that the roll-off rate of σ(p ) be around 2dB/dec around the deired bandwidth, o that y

3 Control 24, Univerity of Bath, UK, September 24 ID-7 in the ubequent H optimization tep, which yield a tabilizing controller for the weighted plant, an acceptable level of robut tability i achieved. Thi i achieved by including the term (+T c) in W (), which eentially provide ome phae lead around cro-over. We ee that ince the plant model P in (6) i nearly diagonal and each term in P i rather imple, the weight function W ha a imple tructure. A plot of the ingular value of the nominal plant P and the haped plant P i hown in Fig 4. We ee that compared with P, P ha higher gain at low frequencie and lower gain at the wave frequencie. In contrat to claical loop-haping, the haping of the 6 4 Singular Value of The Shaped Plant magnitude 6 Singular Value of The Open Loop Gain Singular Value of The Shaped Plant rad/min Fig. 5. Singular value of the open loop gain magnitude Singular Value of The Nominal Plant Note that the main deign work i done in the firt tep, in which we elect the weight function to hape the nominal plant to reflect performance and robutne objective. In the econd tep, the tabilizing controller K i yntheized and the tability margin ɛ i calculated. Thi i alo ued to check whether the weight function choen in tep are appropriate rad/min Fig. 4. Singular value of the haped plant loop gain i carried out without explicit regard for the phae of the nominal plant model and hence, without explicit regard for cloed-loop tability (although completely ignoring the phae typically reult in a poor robut tability margin in the econd tep, which yield a robutly tabiliing controller [8,9]). Step 2. Controller Synthei In thi tep of the deign procedure we conider the robut tabilization of a left coprime factorization M Ñ = P, with [ M Ñ ][ M Ñ ] = I (i.e. the factoriation i normalied). In particular, K i yntheied to enure that [ ] K (I + P I K ) M /ɛ () for ome ɛ e max := [ Ñ M ] 2 H <, where H i the Hankel norm. Thi guarante cloed-loop tability for any perturbation P = ( M + M) (Ñ + N), of the haped plat, that atifie [ N M ] < ɛ. Note that the number ɛ max give an indication of the compatibility between nominal performance objective and the cloed-loop tability requirement. In particular, ɛ max hould not be too mall (typically.25). If ɛ max, the weight W and W 2 mut be adjuted. Baed on the haped plant we get by combining W () and the nominal plant P() for pool 8 to, the H optimization problem decriped in tep 2, i olved uing the matlab function ncfyn (ee [2]), to obtain K. In order to ue thi it i neceary to have finitedimenional model of the weighted plant, and a uch, the time delay in (6) are replaced by firt order Pade approximation (note that the loop-gain at the correponding non-minimum phae zero i low). A lightly uboptimal controller achieving ɛ =.3 i obtained, which guarantee tability in the face of up to 3% uncertainty in the coprime factor. A decribed above, the final feedback controller K = W K W 2 i formed by combining the weight and K. The ingular value of PK (the final open loop-gain) are hown in Fig 5. Compared with the ingular value of the haped plant P, we ee that becaue ɛ =.3 i ufficiently large, the loop gain obtained with the controller K = W K and the original plant P doe not change much with repect to the loop-hape deigned in tep (a Theorem 8.9 and 8. in [9] predict). IV. ASSESSING ROBUST PERFORMANCE WITH µ Conider, the cloed-loop interconnection tructure of a perturbed model of the nominal plant and loop-haping controller hown in Fig 6. The dahed box labelled P p repreent the nominal plant P p u w W del Fig. 6. G K z + + P dit + + y W p The cloed-loop interconnection tructure model with multiplicative uncertaintie. Inide the box W del and G parameterize the uncertainty. W del i deigned to reflect the amount of uncertainty in the model, o that we may aume that G < (i.e. σ( G(jω)) < for all ω). Good performance i taken to mean that the tranfer function from dit to e be mall, in the ene. Indeed we want thi to be true for all poible uncertainty G, i.e. W p(i + P(I + GW del )K) < () for all table G with G <. The weight W p allow u to normalie the right hand ide of the inequality o that when () i atified, the ize of the perturbed enitivity function (I + P(I + GW del )K) i guaranteed to be maller than the ize of the invere of the weight W p, at any frequency. Finally, note the input ignal dit here can be interpreted a the reference ignal r or diturbance ignal ˆd (when P d i aborbed into W p) in Fig 3. The problem of determining whether the cloed-loop remain table and whether () i atified for all table G with G < can be formulated a a µ-analyi problem [9], [2]. Central to thi analyi i) the LFT configuration hown in Fig 7. Here, G = i a generalized plant contructed from a nominal ( G G 2 G 3 G 2 G 22 G 23 G 3 G 32 G 33 model and appropriate weight, o that: (( ) F G G 3 ) ) u G 3 G 33, G := G33 + G 3 G(I G G) G 3 decribe the uncertain plant et a G varie over ome tructured et i.e. within the context of the robut performance e

4 Control 24, Univerity of Bath, UK, September 24 ID-7 (( problem jut decribed F G G 3 ) ) u G 3 G 33, G mut correpond to the tranfer function from u to(( y in Fig 6; and 2) For a given controller K, F G22 G 23 ) ) L G 32 G 33, K := G22 + G 23K(I G 33K) G 32 correpond to all nominal cloedloop tranfer function by which performance i to be gauged in term of the H norm i.e. within the context of our robut performance problem the tranfer function from dit to e. 2 p e w y G G K z u dit Fig. 9. The Invere of the Performance Weight Function at low frequency (i.e. good et-point tracking and load diturbance rejection). Uing the matlab function mu (ee [2]) we calculate the upper and lower bound for the tructured ingular value to obtain the µ-curve hown in Fig. Since the value of µ i le than, we conclude, Fig. 7. Robut performance tet loop The total uncertainty block in Fig 6 ha the following tructure: TOT = diag[ G, p], where G can be tructured, and the untructured p i ued to convert the correponding the robut performance problem characteried by the inequality () into a tructured robut tability analyi problem. Indeed, including p in the uncertainty block, we have the following ufficient and neceary condition for robut performance of the ytem: Theorem : The loop hown above i well-poed, internally table, and F u(f l (G, K), G) for all table G() with G <, if and only if up µ T OT (F l (G, K)(jω)), ω R where µ denote the tructured ingular value. For proof of Theorem and detail about µ-analyi for robut performance, ee [9] and [2]. For the robut performance problem at hand (ee (), we ue a tructured G to repreent plant uncertainty and elect a diagonal uncertainty weight W del to reflect that at low frequency, there i potentially a 2% modelling error, and at the wave frequencie for pool 8 to, the uncertaintie in the model are up to % at.2rad/min, 58% at.42rad/min, 8% at.74rad/min, and get even larger at higher frequencie ee Fig 8 For the performance weight Fig.. The tructured ingular value upper bound lower bound according to Theorem, that the cloed-loop ytem achieve robut performance with repect to the uncertainty weight function W del and performance weight function W p. Alo note from Fig, that the value of µ i about.2 at low frequencie and.3 at high frequencie. Two poible interpretation can be given for thi: In order to atify the ame performance requirement (a reflected by the weight W p), the ytem could include more uncertainty over thee frequency range. In order to achieve robut performance for the uncertainty characteried by W del, the ytem could achieve more demanding performance requirement (a characteried by W p) over thi frequency range. To ee thi, conider for example, the robut performance problem correponding to the ame W p a ued above, but for which the uncertainty i now characteried in term of the weight hown in Fig. We ee that the new µ-curve are till le than at all frequencie and hence robut performance i achieved. Similarly, conider the robut new uncertainty weight old uncertainty weight Fig. 8. Multiplicative Uncertainty Weight Function W p, we ue a 3 3 diagonal function W p() = (e 4) I3. The ingular value of the invere of thi are hown in Fig 9. A uch, when the µ tet correponding to Thm i atified, we can ay that all perturbed cloed-loop enitivity function will be mall new upper bound for mu. new lower bound for mu old upper bound for mu old lower bound for mu Fig.. Change of µ for more uncertainty performance problem correponding to the uncertainty weight hown

5 Control 24, Univerity of Bath, UK, September 24 ID-7 in Fig 9, but for which the performance weight W p i taken to be the one hown in Fig 2 (which correpond to a more demanding performance requirement). Again we ee that µ i till le than over all frequency pool etpoint with H infinity control with PI control with LQ control pool 9 etpoint with H infinity control with PI control with LQ control new upper bound for mu. new lower bound for mu invere of performance weight (old) old upper bound for mu invere of performance weight (new) 4 old lower bound for mu Fig. 2. Change of µ for more demanding performance requirement V. SIMULATION RESULTS A. Comparion with Decentralized PI Control And Centralized LQ Control We imulate the centralized H loop-haping control cheme uing accurate higher order ytem identification model of the plant (ee [2], [3] for detail) and compare the reult with thoe for decentralized PI control and centralized LQ control. The PI controller operate in ditant downtream mode, where a gate i controlling the water level immediately uptream of the next downtream gate, and feedforward action from the downtream gate i alo ued. For gate 8 the head over gate i calculated a follow ũ 8() = C 8()(y 9,etpoint() y 9()) h 3/2 8 () = ũ 8() + K ff F() K g h 3/2 9 () and imilarly for the other head. K ff i the feedforward gain, and it i equal to.75. F() i a econd order Butterworth filter with cut off frequency around half the wave frequency in the pool (ee Table I). K g i the ratio c 8,2 c 9, for pool 8. C() i a PI controller augmented with a firt order lowpa filter, which ha the ame tructure a the diagonal element in the weight function W () for the H loophaping controller. Detail are given in [4] and [22]. The input-output tructure of the LQ centralized controller i imilar to that of the H loop-haping centralized controller. Further detail are given in [5]. The following cenario wa imulated. At time minute all water level were in teady tate at etpoint of 26.5, 23.85, 2.5mAHD for pool 8, 9 and repectively. An offtake in pool tarted at time 2 min and finihed at min. At time 6 min the poition of gate wa moved from 2 to 3mm, which caued a change of the head over gate. At time 2 min the etpoint for the water level in pool 9 wa reduced from 2.85 to 2.8 mahd. The imulation reult for pool 8, 9 and are hown in Fig 3. We ee that all the three method give acceptable repone. The water level recover moothly from diturbance without large deviation from etpoint and without inducing exceive wave motion. The LQ controller i lightly different in that it alo control h through manipulation of gate. The tep in gate at time 6 min wa ubtituted with a tep in the etpoint for h in the LQ control uch that the teady tate gate poition were 2 and 3mm before and after the tep. The imulation reult how that in all the three pool, better performance i achieved by the centralized controller compared to the decentralized controller. In pool 8 and, when the offtake happen in pool, the LQ controller how a better performance than the H loop-haping controller and the PI controller, epecially with the water level going back fater to etpoint. The centralized H loophaping controller achieve a maller deviation from the water level etpoint, compared to the decentralized PI controller. In pool 9, the pool etpoint with H infinity control with PI control with LQ control Fig. 3. Water level change of pool 8, 9 and H loop-haping controller how a better performance than both the LQ controller and the PI controller. On the other hand, the imulation how that when there i a etpoint change in pool 9 at 2 min, there are water level fluctuation in pool uing the centralized controller while there are no water level fluctuation in pool uing the decentralized PI controller. It would appear that centralized control ditribute the effect of a diturbance over all the three pool, while decentralized control localize the effect of diturbance to the uptream pool. In practice due to dead zone on gate poition, a etpoint error of le than a couple of centimeter i regarded a being on etpoint. With thi in mind we oberve that there i little difference in the performance achieved by the LQ and H loop-haping controller. It i noted however, that by virtue of the almot diagonal tructure of the plant model for the irrigation channel the deign of the H loophaping controller, via weight that hape the loop gain, wa impler than the deign of the LQ controller. Indeed, ignificantly more time wa pent deigning the LQ controller in order to achieve the ame level of performance. Furthermore, the almot diagonal tructure of the plant allow u to ue a diagonal weighting function W, in the deign tep of the H loop-haping procedure. Importantly, thi tructure for the weighting function can be maintained when additional pool are added to the plant model. It i not a clear, on the other hand, how the deign parameter in a LQ framework hould be modified a the number of pool i increaed. B. Robutne of The H Loop-haping Controller In the lat imulation we applied a higher order ytem identification model which i expected to captured the high frequency output uncertainty. In the real irrigation control ytem, there are input

6 Control 24, Univerity of Bath, UK, September 24 ID-7 uncertaintie in addition to the high frequency output uncertainty. There are two main ource for input uncertaintie: Due to error in the look up table for the gate, the actual gate poition may be different from the calculated one. Gate poition error of ±% are often left unattended. Due to the traffic on the radio network, there i time delay between the calculation of the gate poition and when the gate tart moving. There i alo time delay between the water level meaurement being taken and when they were ued for calculation. The uncertainty in time delay from one relay tation to the next one i expected to be le than 2 econd. In the imulation, we include an error of % for each gate poition, i.e. the actual gate poition are % more open than the calculated one. For time delay in ignal tranmiion, we include a time delay of minute for the ignal from the field to the central computer and minute from the central computer to the field. The cenario i the ame a in the lat imulation. The reult are hown in Fig 4. The repone get a bit more ocillatory but they are till acceptable. The time delay could in fact have been 5 minute return without much change in the repone etpoint with uncertainty without uncertainty pool etpoint with uncertainty without uncertainty pool pool etpoint with uncertainty without uncertainty Fig. 4. Water level change of pool 8, 9 and how that the H loop-haping control alo achieve a good level of robut performance. The advantage of uing H loop-haping, compared to LQ baed control, i clear in term of eae of deign/tuning. Indeed, the required weight function are imple and eay to adjut, and to deign a H loop-haping controller for more pool, we need imply augment the weight with imilar diagonal term adjuted appropriately to account for difference in the dynamic of any additional pool. REFERENCES [] Journal of Irrigation and Drainage Engineering, Vol. 24, No., 998, pp [2] Proceeding of IEEE Conference on Sytem, Man and Cybernetic, San Diego, 998, pp [3] Garcia A., M. Hubbard, and J.J. de Vrie (992), Open Channel Tranient Flow Control by Dicrete Time LQR Method, Automatica, Vol. 28, no. 2, pp [4] de Halleux, J., C. Prieur, J.-M. Coro, B. d Andrèa-Novel and G. Batin (23), Boundary feedback control in network of open channel, Automatica, Bol. 39, no. 8, pp [5] Litrico, X. (22), Robut IMC Flow Control of SIMO Dam-River Open-Channel Sytem, IEEE Tran. on Control Sytem Technology, Vol., no. 3, pp [6] Litrico, X., V. Fromion, J.-P. Baume, and M. Rijo, Modelling and PI control of an irrigation channel, Proceeding of European Control Conference ECC3, Cambridge, UK, September 23. [7] Malaterre, P.O., PILOTE: Linear Quadratic Optimal Controller for irrigation Canal, Journal of Irrigation and Drainage Engineering, Vol. 24, no. 4, pp [8] Malaterre, P.O. and B.P. Baume, Modeling and regulation of irrigation canal: exiting application an ongoing reearche, Proceeding of IEEE Conference on Sytem, Man and Cybernetic, San Diego, 998, pp [9] Schuurmann J., A. Hof, S. Dijktra, O.H. Bogra and R. Brouwer, Simple water level controller for irrigation and drainage canal, Journal of Irrigation and Drainage Engineering, Vol. 25. no. 4, pp [] Weyer E., Control of open water channel. Part I: Decentralied control, Submitted for publication, 23. [] Weyer E., Control of open water channel. Part II: Centralied LQ control, Submitted to for publication, 23. [2] Ooi S.K. and Weyer E., Cloed loop identification of an irrigation channel, Proceding of the 4th IEEE CDC, Orlando, USA, pp , 2. [3] E. Weyer, Sytem identification of an open water channel, Control Engineering Practice, Vol. 9, pp , 22. [4] Ooi S.K. and Weyer E., Control deign for an irrigation channel from phyical data, Proceding of European Control Conference ECC3, Cambridge, UK, 23. [5] E. 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In Proceeding of IFAC 5th World Congre, Barcelona, Spain, July 22. VI. CONCLUSIONS In thi paper we have ued H loop-haping to deign a multivariable (centralized) controller for an irrigation channel with overhot gate. From the imulation reult, we ee that the reulting centralized H loop-haping control ytem achieve better performance than decentralized PI control and comparable nominal performance to multivariable LQ control. Both µ analyi and the imulation reult