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Predictive PI strategy for hydrographs control in a experimental microscale flume
Proceedings Proceedings of of the the 3rd 3rd IFAC IFAC Conference Conference on on Advances Proceedings of the 3rd IFAC Conference on Control Advances in in Proportional-Integral-Derivative Proportional-Integral-Derivative Proceedings of the 3rd IFAC Conference on Control Ghent, May 9-11, 2018 Available online at www.sciencedirect.com Advances in Proportional-Integral-Derivative Control Ghent, Belgium, Belgium, May 9-11, 2018 Advances in Proportional-Integral-Derivative Proceedings of the 3rd IFAC Conference on Control Ghent, Belgium, May 9-11, 2018 Ghent, Belgium, May 9-11, 2018 Advances in Proportional-Integral-Derivative Control Ghent, Belgium, May 9-11, 2018
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IFAC PapersOnLine 51-4 (2018) 19–24
Predictive PI strategy for hydrographs Predictive PI strategy for hydrographs Predictive PI strategy for hydrographs Predictive PI strategy for hydrographs control in a a experimental experimental microscale flume control in microscale flume Predictive PI strategy for hydrographs control in a experimental microscale flume control in a experimental microscale flume ∗ ∗ ∗∗ control in a experimental microscale flume ∗ Oscar A. Briones ∗ Oscar E. Link ∗∗ Rub´ e n M. Alarc´ o n Rub´ en M. Alarc´ on ∗ Oscar A. Briones ∗ Oscar E. Link ∗∗
Rub´ e o E. Link ∗∗ ∗ Oscar A. Alejandro J.Briones Rojas ∗∗∗ Oscar Rub´ en n M. M. Alarc´ Alarc´ on nAlejandro Oscar A.J. Briones Rojas ∗∗ Oscar E. Link ∗∗ ∗ Alejandro J. Rojas ∗ Rub´ en M. Alarc´ onAlejandro Oscar A.J.Briones Oscar E. Link Rojas ∗ ∗ {rualarcon, obriones, ∗ Electrical Engineering Department, e-mail: Alejandro J. ((Rojas Electrical Engineering Department, e-mail: {rualarcon, obriones, ∗ (( e-mail: {rualarcon, obriones, ∗ Electrical Engineering Department, arojasn}@udec.cl). Electrical Engineering Department, e-mail: {rualarcon, obriones, arojasn}@udec.cl). ∗∗ ∗ arojasn}@udec.cl). ∗∗ Civil Engineering Engineering Department, ( e-mail: olink@ udec.cl). Electrical Department, ( e-mail: {rualarcon, obriones, Department, ( e-mail: olink@ udec.cl). ∗∗ Civil Engineering arojasn}@udec.cl). Engineering Department, e-mail: ∗∗ Civil University Concepci´ o n,Chile Civil University Engineeringof Department, e-mail: o olink@ udec.cl). ofarojasn}@udec.cl). Concepci´ on, n, ((Concepci´ Concepci´ oolink@ n,Chileudec.cl). ∗∗ Concepci´ o n,Chile Civil University Engineeringof e-mail: o University ofDepartment, Concepci´ on, n, (Concepci´ Concepci´ oolink@ n,Chileudec.cl). University of Concepci´ o n, Concepci´ o n,Chile Abstract: Hydraulics, specifically the engineering related to river Abstract: Hydraulics, specifically the engineering related to river infrastructure, infrastructure, has has had had always always Abstract: Hydraulics, specifically the engineering related to river infrastructure, has had to deal with issues as floods, erosion debilitating important civil infrastructure (bridges, etc.). Abstract: specifically thedebilitating engineering important related to river had always always to deal withHydraulics, issues as floods, erosion civil infrastructure, infrastructure has (bridges, etc.). to deal with issues as floods, erosion debilitating important civil infrastructure (bridges, etc.). In recent years it has been shown that there is predictive value for hydraulics in studying and Abstract: Hydraulics, specifically the engineering related to river infrastructure, has had always to with issues as been floods, erosion debilitating important civilfor infrastructure In deal recent years it has shown that there is predictive value hydraulics in(bridges, studyingetc.). and In recent years it has shown that there predictive value hydraulics in studying and analyzing these phenomena at a scale. this the microscale experimental to deal with issues as been floods, debilitating important civil infrastructure etc.). In recent years it has been shown that there isFor predictive value for hydraulics in(bridges, studyingcanal and analyzing these phenomena aterosion a reduced reduced scale.is For this reason reason thefor microscale experimental canal analyzing these phenomena at a scale. this microscale experimental was build at Hydraulics at Universidad of Concepci´ oon, second copy In has been shown that there predictive value for hydraulics inaastudying and analyzing these phenomena atLaboratory a reduced reduced scale. For this reason reason the microscale experimental canal wasrecent build years at the theit Hydraulics Laboratory at the theisFor Universidad ofthe Concepci´ n, with with second canal copy was build at the Hydraulics Laboratory at the Universidad of Concepci´ o n, with a second copy for control purposes at the Control Systems Laboratory (LCS). The partial differential equations analyzing these phenomena at a reduced scale. For this reason the microscale experimental canal was build at the Hydraulics Laboratory at Laboratory the Universidad of The Concepci´ on,differential with a second copy for control purposes at the Control Systems (LCS). partial equations for purposes at Systems Laboratory (LCS). The partial equations that govern the are unnecessarily for Known offers was build at theprocess Hydraulics Laboratory atcomplex the Universidad ofpurposes. Concepci´ on,differential withliterature a second copy for control purposes at the the Control Systems Laboratory (LCS). The partial differential equations thatcontrol govern the process areControl unnecessarily complex for control control purposes. Known literature offers that govern the process are unnecessarily complex for control purposes. Known literature offers the alternative of a third order linear system, capturing the canal standing wave with aa second for at the Control Systems Laboratory (LCS). Thestanding partial differential that governpurposes theofprocess are unnecessarily complex for control purposes. Known offers the control alternative a third order linear system, capturing the canal waveliterature withequations second the alternative of a order linear capturing canal standing wave with order system together with an to account the accumulation. However, such that govern are unnecessarily complex forfor control purposes. Known offers the alternative ofprocess a third third order linear system, system, capturing canal standing waveliterature with aa second second order systemthe together with an integrator integrator to account for the mass mass accumulation. However, such order system together with an integrator to account for the mass accumulation. However, such a proposal, even when slowing the control to discard the standing wave dynamics is only valid the alternative of a third order linear system, capturing the canal standing wave with a second order systemeven together an integrator mass accumulation. However, such a proposal, when with slowing the controltotoaccount discardfor the standing wave dynamics is only valid a even when slowing the control discard the standing wave is valid long canals. The microscale experimental canal does satisfies that assumption, therefore order system together with an integrator for the mass accumulation. However, such afor proposal, even when slowing the controltoto toaccount discard thenot standing wave dynamics is only only valid forproposal, long canals. The microscale experimental canal does not satisfies thatdynamics assumption, therefore for long canals. The microscale experimental canal does not satisfies that assumption, therefore we propose and adjust a first order structure to the process, which proves adequate for any a even when slowing control to canal discard the standing wave dynamics is only for long canals. microscale experimental does not satisfies that assumption, therefore weproposal, propose andThe adjust a first the order structure to the process, which proves adequate forvalid any we propose and adjust a first order structure to the process, which proves adequate for any given operating point selection. Nevertheless, the main three parameters of the plant model for long canals. microscale experimental canal does not satisfies assumption, therefore we propose andThe adjust a first order structure to the process, whichthat proves for any given operating point selection. Nevertheless, the main three parameters of adequate the plant model given operating selection. Nevertheless, main three parameters of the model (gain, time and vary operating aa preliminary control we propose and point adjust a time first delay) order structure tothe the process, which As proves any given operating point selection. Nevertheless, the main three point. parameters of adequate the plant plantfor model (gain, time constant constant and time delay) vary with withthe the operating point. As preliminary control (gain, time time delay) vary operating point. As approach weconstant consider aselection. plant model selection forthe specific operating point aspreliminary the nominal plant given operating pointand Nevertheless, main three parameters ofthe thenominal plant control model (gain, time constant and timemodel delay) vary with with the operating point. As aaas preliminary control approach we consider a plant selection for aathe specific operating point plant approach we consider a selection for specific operating the plant and PI using the reaction curve method of We compare the (gain, time and timemodel delay) vary with operating point.point As aas control approach wea consider a plant plant model selection for aathe specific operating point aspreliminary the nominal plant and adjust adjust aconstant PI control control using the reaction curve method of Ziegler-Nichols. Ziegler-Nichols. Wenominal compare the and adjust a PI control using the reaction curve method of Ziegler-Nichols. We compare the previous PI tuning with a predictive PI λ tuning to achieve robustness, and thus better deal (in approach weatuning consider a plant model selection for atospecific point the nominal plant and adjust PI control the reaction curve method of Ziegler-Nichols. Webetter compare the previous PI with ausing predictive PI λ tuning achieveoperating robustness, andasthus deal (in previous PI tuning with a predictive PI λ tuning to achieve robustness, and thus better deal (in this preliminary control approach) with the inherent variability of the plant model parameters. and adjust a PI control using the reaction curve method of Ziegler-Nichols. We compare the previous PI tuning with approach) a predictivewith PI λthe tuning to achieve robustness, and thus better deal (in this preliminary control inherent variability of the plant model parameters. this preliminary control inherent variability of the model parameters. previous PI tuning with approach) a predictivewith PI λthe tuning to achieve robustness, and thus better deal (in this preliminary control approach) the inherent variability of Elsevier the plant plant parameters. © 2018, IFAC (International Federationwith of Automatic Control) Hosting by Ltd.model All rights reserved. this preliminary control approach) with the inherent variability of the plant model parameters. Keywords: PID controller,PPI ,discrete system, time delay, hydrographs, open channel, Keywords: PID controller,PPI ,discrete system, time delay, hydrographs, open channel, PLC. PLC. Keywords: PID PID controller,PPI controller,PPI ,discrete ,discrete system, system, time time delay, delay, hydrographs, hydrographs, open open channel, channel, PLC. Keywords: PLC. Keywords: PID controller,PPI ,discrete system, time delay, hydrographs, opentheir channel, PLC.(Pachauri and 1. extreme events will increase increase intensity 1. INTRODUCTION INTRODUCTION extreme events will their intensity (Pachauri and 1. INTRODUCTION extreme events will increase their intensity (Pachauri and and Meyer, 2014). 1. INTRODUCTION extreme events will increase their intensity (Pachauri Meyer, 2014). Meyer, 2014). 1. INTRODUCTION extreme events increase their intensity (Pachauri and It It is is aa 2014). fact thatwill when the velocity velocity of It is is aa central central objective objective of of Rivers Rivers Engineering Engineering the the optimal optimal Meyer, It fact that when the of the the water water on on the the Meyer, 2014). It is a central objective of Rivers Engineering the optimal design of fluvial works, such as channeling, river defenses, It is a fact that when the velocity of the water on the bed exceeds a threshold velocity, it occurs movement of It is a central objective of Rivers Engineering thedefenses, optimal It design of fluvial works, such as channeling, river is exceeds a fact that when the velocity of the water on the bed a threshold velocity, it occurs movement of design of fluvial works, such as channeling, river defenses, bridges, potable water and irrigation catchments, hydrobed exceeds a threshold velocity, it occurs movement of the sediment particles. Specifically, the particles around It is a central objective of Rivers Engineering the optimal design of fluvial works, such as channeling, river defenses, bridges, potable water and irrigation catchments, hydro- It issediment a fact that when the velocity of the water on the bed exceeds aparticles. threshold velocity, it the occurs movement of the Specifically, particles around bridges, potable water and and irrigation catchments, hydro- bed electric stations dams, among others; the sediment sediment particles. Specifically, the particles around pillars aathreshold bridge quickly, because the water design fluvial works, suchirrigation as channeling, river defenses, bridges, potable water and irrigation catchments, hydroelectricofpower power stations and irrigation dams, among others; exceedsof velocity, it the occurs movement of the Specifically, particles pillars ofaparticles. bridge move move quickly, because thearound water electric power stations and irrigation dams, among others; thus maximizing its safety against floods and preserving the pillars of particles. bridge move quickly, because thecausing water flow sediment accelerates in the the move vicinity of the the obstacle, causing bridges, potable water andirrigation irrigation catchments, hydro- the electric power stations and dams, among others; thus maximizing its safety against floods and preserving Specifically, thebecause particles around pillars of aa bridge quickly, the water flow accelerates in vicinity of obstacle, thus maximizing its safety safety against floods and preserving the functionality of river where they are flow accelerates in Studies the move vicinity of the thebecause obstacle, causing local undermining. of have done electric power stations and irrigation dams,where among others; thus maximizing its against and preserving the ecological ecological functionality of the the floods river they are the of a bridge quickly, thecausing water flow accelerates in the vicinity of obstacle, localpillars undermining. Studies of undermining undermining have been been done the ecological functionality of the the Engineering river where where theystudare flow located. Since its its inception, Rivers Engineering has studlocal undermining. Studies of undermining have been done in the past, imposing a constant flow (Link et al., 2017; thus maximizing its safety against floods and preserving the ecological functionality of river they are located. Since inception, Rivers has accelerates in Studies thea vicinity offlow the(Link obstacle, causing local undermining. of undermining have been done in the past, imposing constant et al., 2017; located. Since its its inception, Rivers Engineering ied movement of that is, hydraulics, imposing in theundermining. past, imposing constant flow (Link (Link et been al., 2017; 2017; Pizarro et 2017). the ecological functionality of the river where has theystudare local located. Since inception, has studied the the movement of water, water, Rivers that is,Engineering hydraulics, imposing Studies of undermining have done in the past, aa constant flow et al., Pizarro et al., al.,imposing 2017). ied the movement of water, that is, hydraulics, imposing conditions with a constant flow, although in reality the Pizarro et al., 2017). located. Since Rivers Engineering has studied the movement of water, flow, that is, hydraulics, imposing conditions withitsainception, constant although in reality the in the past, imposing a constant flow (Link et al., 2017; Pizarro et al., 2017). In channel flows, conditions with constant flow, although in reality reality the Pizarro imposed by the variable flow floods In open open et channel flows, the the dynamics dynamics is is usually usually represented represented ied the movement water, that is, hydraulics, imposing conditions with aa of constant although in the imposed by the flow, variable flow during during floods al., 2017). In open channel flows, the dynamics is usually represented mathematically by the Saint-Venant equations. This is is aa conditions imposed by the variable flow during floods open channel flows, dynamics isequations. usually represented control most most of the the problems associated withduring the design of In mathematically by thethe Saint-Venant This conditions with a constant although inthe reality the imposed by the flow, variable flow floods control of problems associated with design of mathematically by the the Saint-Venant equations. Thisfrom is aa system of two partial derivative equations that derive In open channel flows, the dynamics is usually represented control most of the problems associated with the design of mathematically by Saint-Venant equations. This is river works. Among them are the overflowing of rivers and system of two partial derivative equations that derive from conditions by the variable flow floods control mostimposed of the problems withduring the design of system river works. Among them are associated the overflowing of rivers and of two twolaws partial derivative equations thatmomentum, derive from the of conservation of and by Saint-Venant equations. Thisfrom is a river works. Among them are associated the overflowing overflowing of rivers rivers and system of partial derivative equations that derive floods, alluviums, orproblems the undermining undermining of with bridges and other the physical physical laws of the conservation of mass mass and momentum, control mostAmong of theor the design of mathematically river works. them are the of and floods, alluviums, the of bridges and other the physical laws of conservation of mass and momentum, which describe the process of one-dimensional flow in free system of two partial derivative equations that derive from floods, alluviums, or the undermining of bridges and other the physical laws of conservation of mass and momentum, structures. This needs to be improved urgently, since, in which describe the process of one-dimensional flow in free river works. Among them are the overflowing of rivers and floods, alluviums, or thetoundermining bridges and other structures. This needs be improvedofurgently, since, in which describe the process of one-dimensional one-dimensional flow in in free free surface (Litrico and Fromion, 2009). These in the physical laws ofprocess conservation of mass and equations momentum, structures. This needs toundermining be improved improved urgently, since, inaa which describe the of flow the context context of fluvial floods surface (Litrico and Fromion, 2009). These equations in floods, alluviums, or thedisasters, ofurgently, bridgesrepresent and other structures. This needs to be since, in the of natural natural disasters, fluvial floods represent surface (Litrico and Fromion, 2009). These equations in their non-conservative formula are nonlinear equations which describe the process of one-dimensional flow in free the context of natural disasters, fluvial floods represent a surface (Litrico and Fromion, 2009). These equations in threat of central importance for people and, on the other their non-conservative formula are nonlinear equations structures. This needs to be for improved since, ina their non-conservative formula are nonlinear equations the context of natural disasters, fluvial urgently, floods threat of central importance people and, onrepresent the other in derivatives, so they have analytical (Litrico and Fromion, 2009). These equations in threat of central central importance for people people and, onrepresent thefailure othera surface their non-conservative are nonlinear equations hand, scour is the most recurrent cause of bridges bridges failure in partial partial derivatives, soformula they usually usually have no no analytical the context of fluvial threat of for and, on the other hand, scour is natural theimportance mostdisasters, recurrent causefloods of in partial derivatives, so they usually have no analytical solution. Because of the complexity of modeling using their non-conservative formula are nonlinear equations hand, scour is the most recurrent cause of bridges failure in partial derivatives, so they usually have no analytical throughout the world. Lamentable examples of this are solution. Because of the complexity of modeling using threat of central importance for people and, on the other hand, scour the is the most Lamentable recurrent cause of bridges failure throughout world. examples of this are solution. Because of the the complexity of modeling using the Saint-Venant equations, in addition to the enormous derivatives, so they have no analytical throughout the world. Lamentable examples of2006, this are in solution. Because of complexity of using the in Biob´ during 2006, the thepartial Saint-Venant equations, in usually addition tomodeling the enormous hand, scoursuffered is the most recurrent cause of bridges failure throughout the world. Lamentable examples of this are the floods floods suffered in the the Biob´ıo ıo Region Region during the the Saint-Venant equations, in addition to the enormous computational cost involved, numerical methods should Because ofinvolved, the complexity of to modeling using the floodsthat suffered in the the Biob´ ıonorthern Region during 2006, the the Saint-Venant equations, innumerical addition the enormous alluvions inBiob´ theıo northern zone of Chile in computational cost methods should throughout theoccurred world. Lamentable examples this the are the floods suffered in Region during alluvions that occurred in the zone of2006, Chile in solution. computational cost involved, numerical methods should usually be used for their resolution. Other efforts to the Saint-Venant equations, in addition to the enormous alluvions that occurred in the northern zone of Chile in computational cost involved, numerical methods should 2015 and 2017, as well as the collapses of the Tadcaster usually be used for their resolution. Other efforts to the suffered theas Region of during 2006, alluvions occurred inBiob´ theıo northern zone Chilethe in usually 2015floods and that 2017, as in well the collapses theofTadcaster be used for their resolution. Other efforts to identify open channel flows and indeed complete river computational cost involved, numerical methods should 2015 and 2017, as well as the collapses of the Tadcaster usually be used for their resolution. Other efforts to bridge, UK, in December 2015, and the Pitrufqu´ e n bridge identify open channel flows and indeed complete river alluvions that occurred in the northern zone of Chile in 2015 and 2017, as well as2015, the collapses of the Tadcaster bridge, UK, in December and the Pitrufqu´ en bridge identify open channel flows and in complete river systems can can be channel found for example inindeed (Li et et al., 2005; Nasir be used for for their resolution. Other efforts to bridge, UK, in December December 2015, and the Moreover, Pitrufqu´ nthe bridge identify open flows and indeed complete river railway on the Tolt´ een 2016. exsystems be found example (Li al., 2005; Nasir 2015 and as well as2015, thein of the Tadcaster bridge, UK, in and the Pitrufqu´ een bridge railway on2017, the Tolt´ n river, river, incollapses 2016. Moreover, the ex- usually systems can be channel found for forflows example inindeed (Li et et al., al., 2005; Nasir Nasir and Weyer, 2016). identify open and complete river railway on the Tolt´ e n river, in 2016. Moreover, the exsystems can be found example in (Li 2005; pected scenarios of climate change indicate that these and Weyer, 2016). bridge, in December 2015, the Pitrufqu´ enthe bridge railway on the Tolt´ n river, inand 2016. Moreover, ex- and Weyer, 2016). pected UK, scenarios of eclimate change indicate that these can 2016). be found for example in (Li et al., 2005; Nasir pected scenarios scenarios of eclimate climate change indicate thatthethese these and Weyer, railway on the Tolt´ n river, change in 2016.indicate Moreover, ex- systems pected of that pected scenarios of climate change indicate that these 19 and Weyer, 2016). Copyright © 2018 IFAC 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2018, 2018 IFAC 19 Hosting by Elsevier Ltd. All rights reserved. Copyright 2018 responsibility IFAC 19 Control. Peer review© of International Federation of Automatic Copyright ©under 2018 IFAC 19 10.1016/j.ifacol.2018.06.011 Copyright © 2018 IFAC 19
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2.2 Experimental setup The microscale canal of 6.38 m long and 14.6 cm wide (see Figure 1) was studied for this work. The channel has several actuators and sensors, of which we use a centrifugal pump that handles the flow manipulation by means of a VFD and also we have a stepper motor at our disposal to adjust the opening of the sluice gate. The sensors used will be an electromagnetic flow meter and an ultrasonic level sensor, the latter being the best for the identification of parameters due to their non-contact characteristics. A Piping & Instrumentation Diagram (P&ID) is provided in Figure 2.
Fig. 1. Experimental setup at the LCS. This work presents a data acquisition (SCADA), identification and control solution for the experimental microscale canal that will allow the generation of controlled growing waves, the measurement of scour around bridge pile models and hysteresis measurement (that is, of the lag between the waves of speed and depth) in a laboratory setup. We propose in this study the use of a Proportional Integral (PI) control strategy and compare it to a Predictive Proportional Integral (PPI) control strategy, Shinskey (2001); Ren et al. (2003); Hassan et al. (2017), to initially manipulate the level reliably and in a repeatable manner. The main contribution of the present work is a model identification exercise for control purposes of the experimental microscale canal which results in a first order with time delay structure with plant parameters dependent on the operation point. The aforementioned contribution has a high impact in various areas related to River Engineering, since it allows to initiate the experimental study of fluvial processes under more realistic conditions, such as tracking of hydrographs from real scaled data.
Fig. 2. Model P&ID. 2.3 Control and data acquisition For the manipulation of the actuator signals and sensing, a graphical interface was developed through the GUI, see Figure 3, where,
The second contribution is a preliminary study on the plant requirements for PI tuning, comparing the use of a standard PI, tuned using the reaction curve method Goodwin et al. (2001), and the necessity of a robust PI design, for which we investigate the use λ tuning of a PPI ˙ om and T.H¨ controller (Astr¨ agglund, 1995). This paper is organized as follows: Section 2 introduces the main assumptions and preliminary information on the models available for water canals. Section 3, based on real data from the experimental microscale canal available at the “Laboratorio de Control de Sistemas”, propose a model structure and identifies the plant model for a range of operating points. Section 4 compares the standard PI control tuning with a PPI control tuning in light of the robustness necessity that arise from the model. Section 5 concludes the present work with final remark and future directions of inquires.
Fig. 3. Graphic interface implementation. (1) Display: visualization of flow, level, frequency and position of the gate. (2) System settings: manual / automatic control for flow and level with their respective set point of independent flow and level. (3) Variable-frequency drive (VFD): Start / Stop of the VFD and performs fault elimination. (4) Sluice Gate: status of the sluice gate, raise, lower, set to zero and relative movement. (5) Hydrogram load: start of the test, elapsed time and end of the test. (6) Acquisition of data: acquisition information and emergency stop. (7) Signal Plots: plot of flow, level, temperature, frequency and gate.
2. PRELIMINARIES 2.1 Assumptions In this work we consider, • There are no leaks in the experimental setup. • Variable flow. • Constant sluice gate opening. 20
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3. MODEL IDENTIFICATION
the observed behavior does not fit an integrator response. Indeed the best structure for such a reduced scale process is a structure defined by Kp −sθ ˜ e U (s) − D(s) , (5) Y (s) = τs + 1 Also, if the gate remains constant, then we can assume ˜ ˜ p , and ignore the terms associated to D(s) as a constant D dynamic, so that equation (5) would look like, Kp −sθ ˜ p, e U (s) − Kp D (6) Y (s) = τs + 1 ˜ p we consider it as a level offset and that we and then Kp D assume it as part of the level, giving as final result a first order model with delay, like the equation in (7), and whose parameters can be estimated with the minimum squares method with data obtained experimentally. Kp −sθ Y (s) = e U (s), (7) τs + 1
In this section we obtain a mathematical model of the experimental microscale canal that will then allow for the simulation of the process and the following up controller tuning. 3.1 Model structure selection We define the following variables of interest: - d: is the height for the sluice gate, measured from the bottom of the microscale canal. - u: the flow of water from the water pump. - θ: the transport delay associated with the water traveling the length of the microscale canal. - y: the water level inside the microscale canal. See Figure 2 for the relative location of d, u and y inside the microscale canal. From (Litrico and Fromion, 2009) the most detailed structure for the physical process at end should be the Saint-Venant structure given by
In this way, we can say that a first-order model is sufficient to capture the most significant information from an experimental canal and then apply a control strategy, which is confirmed by (Weyer, 2000)
∂A(x, t) ∂Q(x, t) + =0 ∂t ∂x
∂ Q2 (x, t) ∂Q(x, t) + ∂t ∂x A(x, t) +gA(x, t)
The logic behind the proposed model structure in (7) lies in the fact that the output mass (and volume) flow is proportional to the square root of the difference of water levels before and after the sluice gate (Litrico and Fromion, 2009, 6.2). If there is a sudden increase in the input flow, the water level before the sluice gate will increase after τ seconds, and therefore the output flow will also start to increase after τ seconds. As result the water level inside the microscale canal will start increasing from the previous level up to a a new greater level, when the output flow will again be equal to the increased input flow. The described behavior is ideally captured by a first order model with delay structure as proposed, and as validated in the following identification exercise.
Y (x, t) + Sf (x, t) − Sb (x) ∂x
=0
21
(1)
where Q(x, t) is the discharge, A(x, t) is the wet area, g the gravitational acceleration, Sb (x) is the bed slope, Sf (x, t) is the friction slope and Y (x, t) is the water level. A nonlinear model also based on the conservation of mass principle, taken from (Li et al., 2005), results in (relatively speaking) simplified candidate structure for the plant model d π y(t) = u(t − θ) − d3/2 (t), (2) dt where π(·) is a polynomial on the derivatives of y and represents the pool dynamics. It is well known that for short pools the polynomial is known to be of order three, the integrator resulting from the mass balance and a second order lightly damped oscillatory mode due to the standing traveling wave that take place inside the pool. Under the consideration of a control solution working below the frequency of the pool’s traveling wave we can replace simplify the model to d (3) a y(t) = u(t − θ) − d3/2 (t), dt where a represents the surface area of pool-i. As stated in Li et al. (2005), a linearization through the change of variable d˜ = d3/2 converts the model in (3) into 1 −sθ ˜ e U (s) − D(s) , (4) Y (s) = sa where in (4) we have moved into the Laplace domain. The problem with the above structure is that the microscale canal does not satisfies the assumption of a long pool and thus, even below the frequency of the pool’s traveling wave,
Fig. 4. Gains of plant (Kp ) We proceed to adjust the structure for different operating points. For this we realized, 3 experimental tests, maintaining a fixed gate opening at 1, 2 and 3 cm respectively and applying steps of rise and fall in between 0% and 100% with amplitude of 10% in each step. In this way, we obtain the values of Kp depicted in Figure 4, τ values in Figure 5 and θ values as reported in Figure 6. 21
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Where: - Gc : controller transfer function . See (8) and (11). - Gp : plant transfer function . - Hs : sensor transfer function . Consider that: - Gp : is represented by equation (5) if the sluice gate position is variable, otherwise, if the gate is at a fixed height, it is better represented by equation (7). - Hs : the sensor block, as the VFD, is characterized together with the process in the structure proposed in (7). That is we assumed Hs = 1, Goodwin et al. (2001). In this section we have proposed and identified the block Gp standing for the real process. In the next section we proceed to discuss the tuning of block Gc as a PI structure.
Fig. 5. Plant time constant (τ )
4. CONTROLLER DESIGN Given the non-linearity of the process, we consider the design of the controllers for an operating point defined by U (s) at 50 % with a sluice gate opening of 2 cm (or 8 %) . With this choice, the plant parameters are Kp = 1.244 , τ = 89.69 y θ = 15.44. 4.1 PI Control The PI controller is determined using the Ziegler-Nichols reaction curve method (Goodwin et al., 2001) where Fig. 6. Transport delay of plant (θ)
U (s) = Kc
Observe that the values for each parameter are variable functions of the operating point, in this case represented by the percentage of water pump flow (the operation point is really defined by a triplet of values given by the input flow, sluice gate height and water level height, but to better report the obtained results we only use the percentage of input flow and three different sluice gate heights).
˜ d e
Gc
u
Gp
E(s),
(8)
The PPI control is a PI controller with a predictive control action component suited for process with long times delay, (Shinskey, 2001). A design method for the PPI controller ˙ om and T.H¨agglund, 1995). is known as λ-tuning (Astr¨ This tuning method assume that the desired closed-loop transfer function between the output and setpoint signal is specified as, e−sθ Y (s) = , (10) R(s) 1 + sλτ where λ is a tuning parameter that allows to modify the time constant. The controller transfer function that satisfy (10) can then be obtained as 1 + sτ E(s). (11) U (s) = Kp (1 + sλτ − e−sθ ) ˙ om and T.H¨ The choice of λ as suggested in Astr¨ agglund (1995) must be between 0.5 and 5. To stress the potential improvement of a PPI controller, over a standard PI controller, when closed-loop robust stability might be a
Finally, the following block diagram represents the proposed closed loop system:
−
4.2 PPI Control
max. value 5 [lt/s] 25 [cm] 50 [Hz] 25 [cm]
As a reference, in Table 1 we show the physical quantities that represent the maximum value of the variables used in the international system that represent 100% in engineering variables, considering that these are valid for Setup.
r
1 1+ Tr s
and Kc is the controller gain and Tr is the integral time. 0.9τ Both can be estimated as Kc = K and Tr = 3θ. pθ The tuned PI controller transfer function for the selected operating point is then (9) 1 U (s) = 4.2026 1 + E(s), (9) 46.32s
Table 1. Variables Variable Flow Level Frequency Sluice Gate
y
ym Hs
Fig. 7. Closed loop block diagram. 22
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two subsections. First, we have that the PI controller in the z-plane is given by z − zc U (z) = Kc E(z), (13) z−1 v where Kc is the same of the continues controller Kc = 4.2026 and zc = 0.9611 for a sampling time of 1.8 seconds. Then we rewrite it as (14) U (z) = U (z)z −1 + Kc E(z) − zc E(z)z −1 , and return to the time domain representation in discrete (15) u(k) = u(k − 1) + Kc e(k) − Kc zc e(k − 1), to obtain the recursive equation that will be programmed in the PLC. The implementation of a PPI control with λ different of 1 is not so evident. We consider using ˙ om and T.H¨agglund, 1995), but the method as in (Astr¨ approaching the plant time delay using a fourth order Pade function approximation. The transfer function for the PPI controller is then 1 GTo , (16) Gc = Gp 1 − T o
necessity we provide in Figures 8 and 9 the gain margin and phase margin of the PPI controller for different values of lambda, blue line, compared to the standard PI, dashed red line. It is necessary to mention that both the gain margin and phase margin consider the approximations made later in section 4.3. We can notice that the PPI controller complies with better characteristics throughout the tested range. Therefore, according to the recommendation, we select a λ value of 0.5 , guaranteeing a response twice as fast than the open loop plant response, which achieves a gain margin of 6.305 and a phase margin of 77.32. After the above analysis we have that the designed transfer function for the PPI controller is then U (s) =
1 + s89.69 E(s). 1.244 (1 + s44.845 − e−s15.44 )
23
(12)
were,
Gp =
Kp L(s), 1 + sτ
(17)
and for design condition L(s) , (18) 1 + sλτ were the L(s) is the fourth order Pade function for delay θ = 15.22, then s4 − 1.295s3 + 0.75s2 − 0.228s + 0.0296 e−sθ ≈ L(s) = 4 . s + 1.295s3 + 0.75s2 + 0.228s + 0.0296 (19) From this we have an approximate PPI controller in continuous time defined as 1.6s5 + 2.1s4 − 1.24s3 + 0.4s2 − 0.05s + 0.0005 U (s) = E(s) s5 + 1.3s4 + 0.8s3 + 0.2s2 + 0.039s (20) and its z equivalent, for a sampling time of 1.8, considering the parameters of the plant at the operating point, defined as 1.6z 5 − 4.76z 4 + 5.69z 3 − 3.47z 2 + 1.06z − 0.12 U (z) = E(z) z 5 − 2.94z 4 + 3.49z 3 − 2.13z 2 + 0.67z − 0.09 (21) Finally the implemented controller follows the next recursive equation, To =
Fig. 8. Gains margin
u(k) = 2.94u(k − 1) − 3.49u(k − 2) + 2.13u(k − 3) − 0.67u(k − 4) + 0.09u(k − 5) + 1.61e(k) − 4.76e(k − 1) +5.69e(k −2)−3.47e(k −3)+1.06e(k −4)−0.12e(k −5). (22) 4.4 Experimental Comparison Fig. 9. Phase margin
For the experimental comparison we perform a water height step change, from 60% to 80% as reported in Figure 10. Observe that at the start, a 60% water height coincides with an input flow of 50% (the state operating point). The requested change also results in an increase of the input flow to 60%, green line. Such as, this setpoint excursion reports from the cyan lines in Figures 4, 5 and 6 (recall that the chosen operating point considers a sluice gate opening of 2cm), changes in the plant model gain Kp
4.3 Experimental Implementation For the experimental implementation we make use of a programmable logic controller (PLC), which works in discrete time. Therefore we now have to find the discretetime counterparts of both controllers from the previous 23
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ACKNOWLEDGEMENTS The authors thankfully acknowledge the support from the Faculty of Engineering, Universidad de Concepci´ on, through Project FIPI 2017 “lnstrumentaci´ on y Control de fIujo, velocidad, nivel y erosi´ on del canal hidr´ aulico con lecho m´ ovil ”. A. J. Rojas thankfully acknowledges the support from the Chilean Research Agency CONICYT, through Basal Project FB0008. Additionally the authors thankfully acknowledge the support from the Technical University Federico Santa Maria through the advanced center for electrical and electronic engineering (AC3E). REFERENCES ˙ om, K. and T.H¨agglund (1995). PID Controllers: TheAstr¨ ory,Design and Tuning. Instrument Society of America. Goodwin, G., Graebe, S., and Salgado, M. (2001). Control System Design. Prentice Hall. Hassan, S., Ibrahim, R., Saad, N., Asirvadam, V., and Chung, T. (2017). Robustness and stability of a predictive PI controller in wirelessHart network characterized by stochastic delay. International Journal of Electrical and Computing Engineering, 7(5), 2605–2613. Li, Y., Cantoni, M., and Weyer, E. (2005). On Water-Level Error Propagation in Controlled Irrigation Channels. In Proceedings of the 44th IEEE Conference on Decison and Control and European Control Conference, 2101– 2106. Seville, Spain. Link, O., Castillo, C., Pizarro, A., Rojas, A., Ettmer, B., Escauriaza, C., and Manfreda, S. (2017). A model of bridge pier scour during flood waves. Journal of Hydraulic Research, 55(3), 310–323. Litrico, X. and Fromion, V. (2009). Modeling and Control of Hydrosystems. Springer. Nasir, H. and Weyer, E. (2016). System identification of the upper part of Murray River. Control Engineering Practice, 52, 70–92. Pachauri, R. and Meyer, L. (2014). Climate change 2014: Synthesis report. contribution of working groups i, ii and iii to the fifth assessment report of the intergovernmental panel on climate change. Technical report, IPCC. Pizarro, A., Ettmer, B., Manfreda, S., Rojas, A., and Link, O. (2017). Dimensionless effective flow for estimation of pier scour caused by flood waves. Journal of Hydraulic Engineering, 143(7), 1–7. Ren, Z., Zhang, H., and Shao, H. (2003). Comparison of pid and ppi control. In Proceeding of the 42and IEEE CDC, 133–138. Shinskey, F. (2001). Pid-deadtime control of distributed processes. Control. Eng. Practice, 9(11), 1177–1183. Weyer, E. (2000). System identification of an open water channel. IFAC Proceedings Volumes, 33(15), 265 – 270. 12th IFAC Symposium on System Identification (SYSID 2000), Santa Barbara, CA, USA, 21-23 June 2000.
Fig. 10. Results of implementation from (approximately) 1.2 to 1.3, time constant from 80 to 100 and time delay from 20 to 10. We clearly have that the above reported plant model parameters excursions, interpreted as modeling errors, were no match for the gain margin (1.6 for the PI and 6.3 for the PPI) and phase margin (27.03 for the PI and 77.3 for the PPI) as clearly the water height closed loop behavior of the PI and PPI controller solutions in Figure 10 are quite similar, red lines. Nevertheless, Figures 8 and 9 suggest that worse variations would result in a better behavior for the PPI controller over the PI controller. Finally, we also observe from Figure 10 the presence of the standing wave as a ripple in the measured real level signal. This motivates and confirms as a future research direction, the inclusion of this feature in the proposed plant model structure. 5. CONCLUSIONS Motivated by the recently tested predictive value of microscale setups for Hydraulics, we have modeled and controlled the microscale experimental canal at the LCS. For control purposes a first order transfer function with time delay was successful in capturing the essentials of the plant dynamics. The drawback was that due to the reduced scale of the canal and the nonlinearities present in it, the three plant model parameters are not constant and vary as functions of the chosen operating point. In a preliminary control approach we compared a standard PI tuning, with a PPI λ tuning that offered a more robust solution, to better deal with the variable nature of the plant model parameters. Future research should aim to include the modeling of the standing wave, on the identification side of the problem, and the application of more advanced control algorithms to achieve either robust performance or directly treat the parameters variability ( as in a gain scheduling approach, nonlinear control, etc.) 24
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Predictive PI strategy for hydrographs Predictive PI strategy for hydrographs Predictive PI strategy for hydrographs Predictive PI strategy for hydrographs control in a a experimental experimental microscale flume control in microscale flume Predictive PI strategy for hydrographs control in a experimental microscale flume control in a experimental microscale flume ∗ ∗ ∗∗ control in a experimental microscale flume ∗ Oscar A. Briones ∗ Oscar E. Link ∗∗ Rub´ e n M. Alarc´ o n Rub´ en M. Alarc´ on ∗ Oscar A. Briones ∗ Oscar E. Link ∗∗
Rub´ e o E. Link ∗∗ ∗ Oscar A. Alejandro J.Briones Rojas ∗∗∗ Oscar Rub´ en n M. M. Alarc´ Alarc´ on nAlejandro Oscar A.J. Briones Rojas ∗∗ Oscar E. Link ∗∗ ∗ Alejandro J. Rojas ∗ Rub´ en M. Alarc´ onAlejandro Oscar A.J.Briones Oscar E. Link Rojas ∗ ∗ {rualarcon, obriones, ∗ Electrical Engineering Department, e-mail: Alejandro J. ((Rojas Electrical Engineering Department, e-mail: {rualarcon, obriones, ∗ (( e-mail: {rualarcon, obriones, ∗ Electrical Engineering Department, arojasn}@udec.cl). Electrical Engineering Department, e-mail: {rualarcon, obriones, arojasn}@udec.cl). ∗∗ ∗ arojasn}@udec.cl). ∗∗ Civil Engineering Engineering Department, ( e-mail: olink@ udec.cl). Electrical Department, ( e-mail: {rualarcon, obriones, Department, ( e-mail: olink@ udec.cl). ∗∗ Civil Engineering arojasn}@udec.cl). Engineering Department, e-mail: ∗∗ Civil University Concepci´ o n,Chile Civil University Engineeringof Department, e-mail: o olink@ udec.cl). ofarojasn}@udec.cl). Concepci´ on, n, ((Concepci´ Concepci´ oolink@ n,Chileudec.cl). ∗∗ Concepci´ o n,Chile Civil University Engineeringof e-mail: o University ofDepartment, Concepci´ on, n, (Concepci´ Concepci´ oolink@ n,Chileudec.cl). University of Concepci´ o n, Concepci´ o n,Chile Abstract: Hydraulics, specifically the engineering related to river Abstract: Hydraulics, specifically the engineering related to river infrastructure, infrastructure, has has had had always always Abstract: Hydraulics, specifically the engineering related to river infrastructure, has had to deal with issues as floods, erosion debilitating important civil infrastructure (bridges, etc.). Abstract: specifically thedebilitating engineering important related to river had always always to deal withHydraulics, issues as floods, erosion civil infrastructure, infrastructure has (bridges, etc.). to deal with issues as floods, erosion debilitating important civil infrastructure (bridges, etc.). In recent years it has been shown that there is predictive value for hydraulics in studying and Abstract: Hydraulics, specifically the engineering related to river infrastructure, has had always to with issues as been floods, erosion debilitating important civilfor infrastructure In deal recent years it has shown that there is predictive value hydraulics in(bridges, studyingetc.). and In recent years it has shown that there predictive value hydraulics in studying and analyzing these phenomena at a scale. this the microscale experimental to deal with issues as been floods, debilitating important civil infrastructure etc.). In recent years it has been shown that there isFor predictive value for hydraulics in(bridges, studyingcanal and analyzing these phenomena aterosion a reduced reduced scale.is For this reason reason thefor microscale experimental canal analyzing these phenomena at a scale. this microscale experimental was build at Hydraulics at Universidad of Concepci´ oon, second copy In has been shown that there predictive value for hydraulics inaastudying and analyzing these phenomena atLaboratory a reduced reduced scale. For this reason reason the microscale experimental canal wasrecent build years at the theit Hydraulics Laboratory at the theisFor Universidad ofthe Concepci´ n, with with second canal copy was build at the Hydraulics Laboratory at the Universidad of Concepci´ o n, with a second copy for control purposes at the Control Systems Laboratory (LCS). The partial differential equations analyzing these phenomena at a reduced scale. For this reason the microscale experimental canal was build at the Hydraulics Laboratory at Laboratory the Universidad of The Concepci´ on,differential with a second copy for control purposes at the Control Systems (LCS). partial equations for purposes at Systems Laboratory (LCS). The partial equations that govern the are unnecessarily for Known offers was build at theprocess Hydraulics Laboratory atcomplex the Universidad ofpurposes. Concepci´ on,differential withliterature a second copy for control purposes at the the Control Systems Laboratory (LCS). The partial differential equations thatcontrol govern the process areControl unnecessarily complex for control control purposes. Known literature offers that govern the process are unnecessarily complex for control purposes. Known literature offers the alternative of a third order linear system, capturing the canal standing wave with aa second for at the Control Systems Laboratory (LCS). Thestanding partial differential that governpurposes theofprocess are unnecessarily complex for control purposes. Known offers the control alternative a third order linear system, capturing the canal waveliterature withequations second the alternative of a order linear capturing canal standing wave with order system together with an to account the accumulation. However, such that govern are unnecessarily complex forfor control purposes. Known offers the alternative ofprocess a third third order linear system, system, capturing canal standing waveliterature with aa second second order systemthe together with an integrator integrator to account for the mass mass accumulation. However, such order system together with an integrator to account for the mass accumulation. However, such a proposal, even when slowing the control to discard the standing wave dynamics is only valid the alternative of a third order linear system, capturing the canal standing wave with a second order systemeven together an integrator mass accumulation. However, such a proposal, when with slowing the controltotoaccount discardfor the standing wave dynamics is only valid a even when slowing the control discard the standing wave is valid long canals. The microscale experimental canal does satisfies that assumption, therefore order system together with an integrator for the mass accumulation. However, such afor proposal, even when slowing the controltoto toaccount discard thenot standing wave dynamics is only only valid forproposal, long canals. The microscale experimental canal does not satisfies thatdynamics assumption, therefore for long canals. The microscale experimental canal does not satisfies that assumption, therefore we propose and adjust a first order structure to the process, which proves adequate for any a even when slowing control to canal discard the standing wave dynamics is only for long canals. microscale experimental does not satisfies that assumption, therefore weproposal, propose andThe adjust a first the order structure to the process, which proves adequate forvalid any we propose and adjust a first order structure to the process, which proves adequate for any given operating point selection. Nevertheless, the main three parameters of the plant model for long canals. microscale experimental canal does not satisfies assumption, therefore we propose andThe adjust a first order structure to the process, whichthat proves for any given operating point selection. Nevertheless, the main three parameters of adequate the plant model given operating selection. Nevertheless, main three parameters of the model (gain, time and vary operating aa preliminary control we propose and point adjust a time first delay) order structure tothe the process, which As proves any given operating point selection. Nevertheless, the main three point. parameters of adequate the plant plantfor model (gain, time constant constant and time delay) vary with withthe the operating point. As preliminary control (gain, time time delay) vary operating point. As approach weconstant consider aselection. plant model selection forthe specific operating point aspreliminary the nominal plant given operating pointand Nevertheless, main three parameters ofthe thenominal plant control model (gain, time constant and timemodel delay) vary with with the operating point. As aaas preliminary control approach we consider a plant selection for aathe specific operating point plant approach we consider a selection for specific operating the plant and PI using the reaction curve method of We compare the (gain, time and timemodel delay) vary with operating point.point As aas control approach wea consider a plant plant model selection for aathe specific operating point aspreliminary the nominal plant and adjust adjust aconstant PI control control using the reaction curve method of Ziegler-Nichols. Ziegler-Nichols. Wenominal compare the and adjust a PI control using the reaction curve method of Ziegler-Nichols. We compare the previous PI tuning with a predictive PI λ tuning to achieve robustness, and thus better deal (in approach weatuning consider a plant model selection for atospecific point the nominal plant and adjust PI control the reaction curve method of Ziegler-Nichols. Webetter compare the previous PI with ausing predictive PI λ tuning achieveoperating robustness, andasthus deal (in previous PI tuning with a predictive PI λ tuning to achieve robustness, and thus better deal (in this preliminary control approach) with the inherent variability of the plant model parameters. and adjust a PI control using the reaction curve method of Ziegler-Nichols. We compare the previous PI tuning with approach) a predictivewith PI λthe tuning to achieve robustness, and thus better deal (in this preliminary control inherent variability of the plant model parameters. this preliminary control inherent variability of the model parameters. previous PI tuning with approach) a predictivewith PI λthe tuning to achieve robustness, and thus better deal (in this preliminary control approach) the inherent variability of Elsevier the plant plant parameters. © 2018, IFAC (International Federationwith of Automatic Control) Hosting by Ltd.model All rights reserved. this preliminary control approach) with the inherent variability of the plant model parameters. Keywords: PID controller,PPI ,discrete system, time delay, hydrographs, open channel, Keywords: PID controller,PPI ,discrete system, time delay, hydrographs, open channel, PLC. PLC. Keywords: PID PID controller,PPI controller,PPI ,discrete ,discrete system, system, time time delay, delay, hydrographs, hydrographs, open open channel, channel, PLC. Keywords: PLC. Keywords: PID controller,PPI ,discrete system, time delay, hydrographs, opentheir channel, PLC.(Pachauri and 1. extreme events will increase increase intensity 1. INTRODUCTION INTRODUCTION extreme events will their intensity (Pachauri and 1. INTRODUCTION extreme events will increase their intensity (Pachauri and and Meyer, 2014). 1. INTRODUCTION extreme events will increase their intensity (Pachauri Meyer, 2014). Meyer, 2014). 1. INTRODUCTION extreme events increase their intensity (Pachauri and It It is is aa 2014). fact thatwill when the velocity velocity of It is is aa central central objective objective of of Rivers Rivers Engineering Engineering the the optimal optimal Meyer, It fact that when the of the the water water on on the the Meyer, 2014). It is a central objective of Rivers Engineering the optimal design of fluvial works, such as channeling, river defenses, It is a fact that when the velocity of the water on the bed exceeds a threshold velocity, it occurs movement of It is a central objective of Rivers Engineering thedefenses, optimal It design of fluvial works, such as channeling, river is exceeds a fact that when the velocity of the water on the bed a threshold velocity, it occurs movement of design of fluvial works, such as channeling, river defenses, bridges, potable water and irrigation catchments, hydrobed exceeds a threshold velocity, it occurs movement of the sediment particles. Specifically, the particles around It is a central objective of Rivers Engineering the optimal design of fluvial works, such as channeling, river defenses, bridges, potable water and irrigation catchments, hydro- It issediment a fact that when the velocity of the water on the bed exceeds aparticles. threshold velocity, it the occurs movement of the Specifically, particles around bridges, potable water and and irrigation catchments, hydro- bed electric stations dams, among others; the sediment sediment particles. Specifically, the particles around pillars aathreshold bridge quickly, because the water design fluvial works, suchirrigation as channeling, river defenses, bridges, potable water and irrigation catchments, hydroelectricofpower power stations and irrigation dams, among others; exceedsof velocity, it the occurs movement of the Specifically, particles pillars ofaparticles. bridge move move quickly, because thearound water electric power stations and irrigation dams, among others; thus maximizing its safety against floods and preserving the pillars of particles. bridge move quickly, because thecausing water flow sediment accelerates in the the move vicinity of the the obstacle, causing bridges, potable water andirrigation irrigation catchments, hydro- the electric power stations and dams, among others; thus maximizing its safety against floods and preserving Specifically, thebecause particles around pillars of aa bridge quickly, the water flow accelerates in vicinity of obstacle, thus maximizing its safety safety against floods and preserving the functionality of river where they are flow accelerates in Studies the move vicinity of the thebecause obstacle, causing local undermining. of have done electric power stations and irrigation dams,where among others; thus maximizing its against and preserving the ecological ecological functionality of the the floods river they are the of a bridge quickly, thecausing water flow accelerates in the vicinity of obstacle, localpillars undermining. Studies of undermining undermining have been been done the ecological functionality of the the Engineering river where where theystudare flow located. Since its its inception, Rivers Engineering has studlocal undermining. Studies of undermining have been done in the past, imposing a constant flow (Link et al., 2017; thus maximizing its safety against floods and preserving the ecological functionality of river they are located. Since inception, Rivers has accelerates in Studies thea vicinity offlow the(Link obstacle, causing local undermining. of undermining have been done in the past, imposing constant et al., 2017; located. Since its its inception, Rivers Engineering ied movement of that is, hydraulics, imposing in theundermining. past, imposing constant flow (Link (Link et been al., 2017; 2017; Pizarro et 2017). the ecological functionality of the river where has theystudare local located. Since inception, has studied the the movement of water, water, Rivers that is,Engineering hydraulics, imposing Studies of undermining have done in the past, aa constant flow et al., Pizarro et al., al.,imposing 2017). ied the movement of water, that is, hydraulics, imposing conditions with a constant flow, although in reality the Pizarro et al., 2017). located. Since Rivers Engineering has studied the movement of water, flow, that is, hydraulics, imposing conditions withitsainception, constant although in reality the in the past, imposing a constant flow (Link et al., 2017; Pizarro et al., 2017). In channel flows, conditions with constant flow, although in reality reality the Pizarro imposed by the variable flow floods In open open et channel flows, the the dynamics dynamics is is usually usually represented represented ied the movement water, that is, hydraulics, imposing conditions with aa of constant although in the imposed by the flow, variable flow during during floods al., 2017). In open channel flows, the dynamics is usually represented mathematically by the Saint-Venant equations. This is is aa conditions imposed by the variable flow during floods open channel flows, dynamics isequations. usually represented control most most of the the problems associated withduring the design of In mathematically by thethe Saint-Venant This conditions with a constant although inthe reality the imposed by the flow, variable flow floods control of problems associated with design of mathematically by the the Saint-Venant equations. Thisfrom is aa system of two partial derivative equations that derive In open channel flows, the dynamics is usually represented control most of the problems associated with the design of mathematically by Saint-Venant equations. This is river works. Among them are the overflowing of rivers and system of two partial derivative equations that derive from conditions by the variable flow floods control mostimposed of the problems withduring the design of system river works. Among them are associated the overflowing of rivers and of two twolaws partial derivative equations thatmomentum, derive from the of conservation of and by Saint-Venant equations. Thisfrom is a river works. Among them are associated the overflowing overflowing of rivers rivers and system of partial derivative equations that derive floods, alluviums, orproblems the undermining undermining of with bridges and other the physical physical laws of the conservation of mass mass and momentum, control mostAmong of theor the design of mathematically river works. them are the of and floods, alluviums, the of bridges and other the physical laws of conservation of mass and momentum, which describe the process of one-dimensional flow in free system of two partial derivative equations that derive from floods, alluviums, or the undermining of bridges and other the physical laws of conservation of mass and momentum, structures. This needs to be improved urgently, since, in which describe the process of one-dimensional flow in free river works. Among them are the overflowing of rivers and floods, alluviums, or thetoundermining bridges and other structures. This needs be improvedofurgently, since, in which describe the process of one-dimensional one-dimensional flow in in free free surface (Litrico and Fromion, 2009). These in the physical laws ofprocess conservation of mass and equations momentum, structures. This needs toundermining be improved improved urgently, since, inaa which describe the of flow the context context of fluvial floods surface (Litrico and Fromion, 2009). These equations in floods, alluviums, or thedisasters, ofurgently, bridgesrepresent and other structures. This needs to be since, in the of natural natural disasters, fluvial floods represent surface (Litrico and Fromion, 2009). These equations in their non-conservative formula are nonlinear equations which describe the process of one-dimensional flow in free the context of natural disasters, fluvial floods represent a surface (Litrico and Fromion, 2009). These equations in threat of central importance for people and, on the other their non-conservative formula are nonlinear equations structures. This needs to be for improved since, ina their non-conservative formula are nonlinear equations the context of natural disasters, fluvial urgently, floods threat of central importance people and, onrepresent the other in derivatives, so they have analytical (Litrico and Fromion, 2009). These equations in threat of central central importance for people people and, onrepresent thefailure othera surface their non-conservative are nonlinear equations hand, scour is the most recurrent cause of bridges bridges failure in partial partial derivatives, soformula they usually usually have no no analytical the context of fluvial threat of for and, on the other hand, scour is natural theimportance mostdisasters, recurrent causefloods of in partial derivatives, so they usually have no analytical solution. Because of the complexity of modeling using their non-conservative formula are nonlinear equations hand, scour is the most recurrent cause of bridges failure in partial derivatives, so they usually have no analytical throughout the world. Lamentable examples of this are solution. Because of the complexity of modeling using threat of central importance for people and, on the other hand, scour the is the most Lamentable recurrent cause of bridges failure throughout world. examples of this are solution. Because of the the complexity of modeling using the Saint-Venant equations, in addition to the enormous derivatives, so they have no analytical throughout the world. Lamentable examples of2006, this are in solution. Because of complexity of using the in Biob´ during 2006, the thepartial Saint-Venant equations, in usually addition tomodeling the enormous hand, scoursuffered is the most recurrent cause of bridges failure throughout the world. Lamentable examples of this are the floods floods suffered in the the Biob´ıo ıo Region Region during the the Saint-Venant equations, in addition to the enormous computational cost involved, numerical methods should Because ofinvolved, the complexity of to modeling using the floodsthat suffered in the the Biob´ ıonorthern Region during 2006, the the Saint-Venant equations, innumerical addition the enormous alluvions inBiob´ theıo northern zone of Chile in computational cost methods should throughout theoccurred world. Lamentable examples this the are the floods suffered in Region during alluvions that occurred in the zone of2006, Chile in solution. computational cost involved, numerical methods should usually be used for their resolution. Other efforts to the Saint-Venant equations, in addition to the enormous alluvions that occurred in the northern zone of Chile in computational cost involved, numerical methods should 2015 and 2017, as well as the collapses of the Tadcaster usually be used for their resolution. Other efforts to the suffered theas Region of during 2006, alluvions occurred inBiob´ theıo northern zone Chilethe in usually 2015floods and that 2017, as in well the collapses theofTadcaster be used for their resolution. Other efforts to identify open channel flows and indeed complete river computational cost involved, numerical methods should 2015 and 2017, as well as the collapses of the Tadcaster usually be used for their resolution. Other efforts to bridge, UK, in December 2015, and the Pitrufqu´ e n bridge identify open channel flows and indeed complete river alluvions that occurred in the northern zone of Chile in 2015 and 2017, as well as2015, the collapses of the Tadcaster bridge, UK, in December and the Pitrufqu´ en bridge identify open channel flows and in complete river systems can can be channel found for example inindeed (Li et et al., 2005; Nasir be used for for their resolution. Other efforts to bridge, UK, in December December 2015, and the Moreover, Pitrufqu´ nthe bridge identify open flows and indeed complete river railway on the Tolt´ een 2016. exsystems be found example (Li al., 2005; Nasir 2015 and as well as2015, thein of the Tadcaster bridge, UK, in and the Pitrufqu´ een bridge railway on2017, the Tolt´ n river, river, incollapses 2016. Moreover, the ex- usually systems can be channel found for forflows example inindeed (Li et et al., al., 2005; Nasir Nasir and Weyer, 2016). identify open and complete river railway on the Tolt´ e n river, in 2016. Moreover, the exsystems can be found example in (Li 2005; pected scenarios of climate change indicate that these and Weyer, 2016). bridge, in December 2015, the Pitrufqu´ enthe bridge railway on the Tolt´ n river, inand 2016. Moreover, ex- and Weyer, 2016). pected UK, scenarios of eclimate change indicate that these can 2016). be found for example in (Li et al., 2005; Nasir pected scenarios scenarios of eclimate climate change indicate thatthethese these and Weyer, railway on the Tolt´ n river, change in 2016.indicate Moreover, ex- systems pected of that pected scenarios of climate change indicate that these 19 and Weyer, 2016). Copyright © 2018 IFAC 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2018, 2018 IFAC 19 Hosting by Elsevier Ltd. All rights reserved. Copyright 2018 responsibility IFAC 19 Control. Peer review© of International Federation of Automatic Copyright ©under 2018 IFAC 19 10.1016/j.ifacol.2018.06.011 Copyright © 2018 IFAC 19
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2.2 Experimental setup The microscale canal of 6.38 m long and 14.6 cm wide (see Figure 1) was studied for this work. The channel has several actuators and sensors, of which we use a centrifugal pump that handles the flow manipulation by means of a VFD and also we have a stepper motor at our disposal to adjust the opening of the sluice gate. The sensors used will be an electromagnetic flow meter and an ultrasonic level sensor, the latter being the best for the identification of parameters due to their non-contact characteristics. A Piping & Instrumentation Diagram (P&ID) is provided in Figure 2.
Fig. 1. Experimental setup at the LCS. This work presents a data acquisition (SCADA), identification and control solution for the experimental microscale canal that will allow the generation of controlled growing waves, the measurement of scour around bridge pile models and hysteresis measurement (that is, of the lag between the waves of speed and depth) in a laboratory setup. We propose in this study the use of a Proportional Integral (PI) control strategy and compare it to a Predictive Proportional Integral (PPI) control strategy, Shinskey (2001); Ren et al. (2003); Hassan et al. (2017), to initially manipulate the level reliably and in a repeatable manner. The main contribution of the present work is a model identification exercise for control purposes of the experimental microscale canal which results in a first order with time delay structure with plant parameters dependent on the operation point. The aforementioned contribution has a high impact in various areas related to River Engineering, since it allows to initiate the experimental study of fluvial processes under more realistic conditions, such as tracking of hydrographs from real scaled data.
Fig. 2. Model P&ID. 2.3 Control and data acquisition For the manipulation of the actuator signals and sensing, a graphical interface was developed through the GUI, see Figure 3, where,
The second contribution is a preliminary study on the plant requirements for PI tuning, comparing the use of a standard PI, tuned using the reaction curve method Goodwin et al. (2001), and the necessity of a robust PI design, for which we investigate the use λ tuning of a PPI ˙ om and T.H¨ controller (Astr¨ agglund, 1995). This paper is organized as follows: Section 2 introduces the main assumptions and preliminary information on the models available for water canals. Section 3, based on real data from the experimental microscale canal available at the “Laboratorio de Control de Sistemas”, propose a model structure and identifies the plant model for a range of operating points. Section 4 compares the standard PI control tuning with a PPI control tuning in light of the robustness necessity that arise from the model. Section 5 concludes the present work with final remark and future directions of inquires.
Fig. 3. Graphic interface implementation. (1) Display: visualization of flow, level, frequency and position of the gate. (2) System settings: manual / automatic control for flow and level with their respective set point of independent flow and level. (3) Variable-frequency drive (VFD): Start / Stop of the VFD and performs fault elimination. (4) Sluice Gate: status of the sluice gate, raise, lower, set to zero and relative movement. (5) Hydrogram load: start of the test, elapsed time and end of the test. (6) Acquisition of data: acquisition information and emergency stop. (7) Signal Plots: plot of flow, level, temperature, frequency and gate.
2. PRELIMINARIES 2.1 Assumptions In this work we consider, • There are no leaks in the experimental setup. • Variable flow. • Constant sluice gate opening. 20
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3. MODEL IDENTIFICATION
the observed behavior does not fit an integrator response. Indeed the best structure for such a reduced scale process is a structure defined by Kp −sθ ˜ e U (s) − D(s) , (5) Y (s) = τs + 1 Also, if the gate remains constant, then we can assume ˜ ˜ p , and ignore the terms associated to D(s) as a constant D dynamic, so that equation (5) would look like, Kp −sθ ˜ p, e U (s) − Kp D (6) Y (s) = τs + 1 ˜ p we consider it as a level offset and that we and then Kp D assume it as part of the level, giving as final result a first order model with delay, like the equation in (7), and whose parameters can be estimated with the minimum squares method with data obtained experimentally. Kp −sθ Y (s) = e U (s), (7) τs + 1
In this section we obtain a mathematical model of the experimental microscale canal that will then allow for the simulation of the process and the following up controller tuning. 3.1 Model structure selection We define the following variables of interest: - d: is the height for the sluice gate, measured from the bottom of the microscale canal. - u: the flow of water from the water pump. - θ: the transport delay associated with the water traveling the length of the microscale canal. - y: the water level inside the microscale canal. See Figure 2 for the relative location of d, u and y inside the microscale canal. From (Litrico and Fromion, 2009) the most detailed structure for the physical process at end should be the Saint-Venant structure given by
In this way, we can say that a first-order model is sufficient to capture the most significant information from an experimental canal and then apply a control strategy, which is confirmed by (Weyer, 2000)
∂A(x, t) ∂Q(x, t) + =0 ∂t ∂x
∂ Q2 (x, t) ∂Q(x, t) + ∂t ∂x A(x, t) +gA(x, t)
The logic behind the proposed model structure in (7) lies in the fact that the output mass (and volume) flow is proportional to the square root of the difference of water levels before and after the sluice gate (Litrico and Fromion, 2009, 6.2). If there is a sudden increase in the input flow, the water level before the sluice gate will increase after τ seconds, and therefore the output flow will also start to increase after τ seconds. As result the water level inside the microscale canal will start increasing from the previous level up to a a new greater level, when the output flow will again be equal to the increased input flow. The described behavior is ideally captured by a first order model with delay structure as proposed, and as validated in the following identification exercise.
Y (x, t) + Sf (x, t) − Sb (x) ∂x
=0
21
(1)
where Q(x, t) is the discharge, A(x, t) is the wet area, g the gravitational acceleration, Sb (x) is the bed slope, Sf (x, t) is the friction slope and Y (x, t) is the water level. A nonlinear model also based on the conservation of mass principle, taken from (Li et al., 2005), results in (relatively speaking) simplified candidate structure for the plant model d π y(t) = u(t − θ) − d3/2 (t), (2) dt where π(·) is a polynomial on the derivatives of y and represents the pool dynamics. It is well known that for short pools the polynomial is known to be of order three, the integrator resulting from the mass balance and a second order lightly damped oscillatory mode due to the standing traveling wave that take place inside the pool. Under the consideration of a control solution working below the frequency of the pool’s traveling wave we can replace simplify the model to d (3) a y(t) = u(t − θ) − d3/2 (t), dt where a represents the surface area of pool-i. As stated in Li et al. (2005), a linearization through the change of variable d˜ = d3/2 converts the model in (3) into 1 −sθ ˜ e U (s) − D(s) , (4) Y (s) = sa where in (4) we have moved into the Laplace domain. The problem with the above structure is that the microscale canal does not satisfies the assumption of a long pool and thus, even below the frequency of the pool’s traveling wave,
Fig. 4. Gains of plant (Kp ) We proceed to adjust the structure for different operating points. For this we realized, 3 experimental tests, maintaining a fixed gate opening at 1, 2 and 3 cm respectively and applying steps of rise and fall in between 0% and 100% with amplitude of 10% in each step. In this way, we obtain the values of Kp depicted in Figure 4, τ values in Figure 5 and θ values as reported in Figure 6. 21
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Where: - Gc : controller transfer function . See (8) and (11). - Gp : plant transfer function . - Hs : sensor transfer function . Consider that: - Gp : is represented by equation (5) if the sluice gate position is variable, otherwise, if the gate is at a fixed height, it is better represented by equation (7). - Hs : the sensor block, as the VFD, is characterized together with the process in the structure proposed in (7). That is we assumed Hs = 1, Goodwin et al. (2001). In this section we have proposed and identified the block Gp standing for the real process. In the next section we proceed to discuss the tuning of block Gc as a PI structure.
Fig. 5. Plant time constant (τ )
4. CONTROLLER DESIGN Given the non-linearity of the process, we consider the design of the controllers for an operating point defined by U (s) at 50 % with a sluice gate opening of 2 cm (or 8 %) . With this choice, the plant parameters are Kp = 1.244 , τ = 89.69 y θ = 15.44. 4.1 PI Control The PI controller is determined using the Ziegler-Nichols reaction curve method (Goodwin et al., 2001) where Fig. 6. Transport delay of plant (θ)
U (s) = Kc
Observe that the values for each parameter are variable functions of the operating point, in this case represented by the percentage of water pump flow (the operation point is really defined by a triplet of values given by the input flow, sluice gate height and water level height, but to better report the obtained results we only use the percentage of input flow and three different sluice gate heights).
˜ d e
Gc
u
Gp
E(s),
(8)
The PPI control is a PI controller with a predictive control action component suited for process with long times delay, (Shinskey, 2001). A design method for the PPI controller ˙ om and T.H¨agglund, 1995). is known as λ-tuning (Astr¨ This tuning method assume that the desired closed-loop transfer function between the output and setpoint signal is specified as, e−sθ Y (s) = , (10) R(s) 1 + sλτ where λ is a tuning parameter that allows to modify the time constant. The controller transfer function that satisfy (10) can then be obtained as 1 + sτ E(s). (11) U (s) = Kp (1 + sλτ − e−sθ ) ˙ om and T.H¨ The choice of λ as suggested in Astr¨ agglund (1995) must be between 0.5 and 5. To stress the potential improvement of a PPI controller, over a standard PI controller, when closed-loop robust stability might be a
Finally, the following block diagram represents the proposed closed loop system:
−
4.2 PPI Control
max. value 5 [lt/s] 25 [cm] 50 [Hz] 25 [cm]
As a reference, in Table 1 we show the physical quantities that represent the maximum value of the variables used in the international system that represent 100% in engineering variables, considering that these are valid for Setup.
r
1 1+ Tr s
and Kc is the controller gain and Tr is the integral time. 0.9τ Both can be estimated as Kc = K and Tr = 3θ. pθ The tuned PI controller transfer function for the selected operating point is then (9) 1 U (s) = 4.2026 1 + E(s), (9) 46.32s
Table 1. Variables Variable Flow Level Frequency Sluice Gate
y
ym Hs
Fig. 7. Closed loop block diagram. 22
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two subsections. First, we have that the PI controller in the z-plane is given by z − zc U (z) = Kc E(z), (13) z−1 v where Kc is the same of the continues controller Kc = 4.2026 and zc = 0.9611 for a sampling time of 1.8 seconds. Then we rewrite it as (14) U (z) = U (z)z −1 + Kc E(z) − zc E(z)z −1 , and return to the time domain representation in discrete (15) u(k) = u(k − 1) + Kc e(k) − Kc zc e(k − 1), to obtain the recursive equation that will be programmed in the PLC. The implementation of a PPI control with λ different of 1 is not so evident. We consider using ˙ om and T.H¨agglund, 1995), but the method as in (Astr¨ approaching the plant time delay using a fourth order Pade function approximation. The transfer function for the PPI controller is then 1 GTo , (16) Gc = Gp 1 − T o
necessity we provide in Figures 8 and 9 the gain margin and phase margin of the PPI controller for different values of lambda, blue line, compared to the standard PI, dashed red line. It is necessary to mention that both the gain margin and phase margin consider the approximations made later in section 4.3. We can notice that the PPI controller complies with better characteristics throughout the tested range. Therefore, according to the recommendation, we select a λ value of 0.5 , guaranteeing a response twice as fast than the open loop plant response, which achieves a gain margin of 6.305 and a phase margin of 77.32. After the above analysis we have that the designed transfer function for the PPI controller is then U (s) =
1 + s89.69 E(s). 1.244 (1 + s44.845 − e−s15.44 )
23
(12)
were,
Gp =
Kp L(s), 1 + sτ
(17)
and for design condition L(s) , (18) 1 + sλτ were the L(s) is the fourth order Pade function for delay θ = 15.22, then s4 − 1.295s3 + 0.75s2 − 0.228s + 0.0296 e−sθ ≈ L(s) = 4 . s + 1.295s3 + 0.75s2 + 0.228s + 0.0296 (19) From this we have an approximate PPI controller in continuous time defined as 1.6s5 + 2.1s4 − 1.24s3 + 0.4s2 − 0.05s + 0.0005 U (s) = E(s) s5 + 1.3s4 + 0.8s3 + 0.2s2 + 0.039s (20) and its z equivalent, for a sampling time of 1.8, considering the parameters of the plant at the operating point, defined as 1.6z 5 − 4.76z 4 + 5.69z 3 − 3.47z 2 + 1.06z − 0.12 U (z) = E(z) z 5 − 2.94z 4 + 3.49z 3 − 2.13z 2 + 0.67z − 0.09 (21) Finally the implemented controller follows the next recursive equation, To =
Fig. 8. Gains margin
u(k) = 2.94u(k − 1) − 3.49u(k − 2) + 2.13u(k − 3) − 0.67u(k − 4) + 0.09u(k − 5) + 1.61e(k) − 4.76e(k − 1) +5.69e(k −2)−3.47e(k −3)+1.06e(k −4)−0.12e(k −5). (22) 4.4 Experimental Comparison Fig. 9. Phase margin
For the experimental comparison we perform a water height step change, from 60% to 80% as reported in Figure 10. Observe that at the start, a 60% water height coincides with an input flow of 50% (the state operating point). The requested change also results in an increase of the input flow to 60%, green line. Such as, this setpoint excursion reports from the cyan lines in Figures 4, 5 and 6 (recall that the chosen operating point considers a sluice gate opening of 2cm), changes in the plant model gain Kp
4.3 Experimental Implementation For the experimental implementation we make use of a programmable logic controller (PLC), which works in discrete time. Therefore we now have to find the discretetime counterparts of both controllers from the previous 23
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ACKNOWLEDGEMENTS The authors thankfully acknowledge the support from the Faculty of Engineering, Universidad de Concepci´ on, through Project FIPI 2017 “lnstrumentaci´ on y Control de fIujo, velocidad, nivel y erosi´ on del canal hidr´ aulico con lecho m´ ovil ”. A. J. Rojas thankfully acknowledges the support from the Chilean Research Agency CONICYT, through Basal Project FB0008. Additionally the authors thankfully acknowledge the support from the Technical University Federico Santa Maria through the advanced center for electrical and electronic engineering (AC3E). REFERENCES ˙ om, K. and T.H¨agglund (1995). PID Controllers: TheAstr¨ ory,Design and Tuning. Instrument Society of America. Goodwin, G., Graebe, S., and Salgado, M. (2001). Control System Design. Prentice Hall. Hassan, S., Ibrahim, R., Saad, N., Asirvadam, V., and Chung, T. (2017). Robustness and stability of a predictive PI controller in wirelessHart network characterized by stochastic delay. International Journal of Electrical and Computing Engineering, 7(5), 2605–2613. Li, Y., Cantoni, M., and Weyer, E. (2005). On Water-Level Error Propagation in Controlled Irrigation Channels. In Proceedings of the 44th IEEE Conference on Decison and Control and European Control Conference, 2101– 2106. Seville, Spain. Link, O., Castillo, C., Pizarro, A., Rojas, A., Ettmer, B., Escauriaza, C., and Manfreda, S. (2017). A model of bridge pier scour during flood waves. Journal of Hydraulic Research, 55(3), 310–323. Litrico, X. and Fromion, V. (2009). Modeling and Control of Hydrosystems. Springer. Nasir, H. and Weyer, E. (2016). System identification of the upper part of Murray River. Control Engineering Practice, 52, 70–92. Pachauri, R. and Meyer, L. (2014). Climate change 2014: Synthesis report. contribution of working groups i, ii and iii to the fifth assessment report of the intergovernmental panel on climate change. Technical report, IPCC. Pizarro, A., Ettmer, B., Manfreda, S., Rojas, A., and Link, O. (2017). Dimensionless effective flow for estimation of pier scour caused by flood waves. Journal of Hydraulic Engineering, 143(7), 1–7. Ren, Z., Zhang, H., and Shao, H. (2003). Comparison of pid and ppi control. In Proceeding of the 42and IEEE CDC, 133–138. Shinskey, F. (2001). Pid-deadtime control of distributed processes. Control. Eng. Practice, 9(11), 1177–1183. Weyer, E. (2000). System identification of an open water channel. IFAC Proceedings Volumes, 33(15), 265 – 270. 12th IFAC Symposium on System Identification (SYSID 2000), Santa Barbara, CA, USA, 21-23 June 2000.
Fig. 10. Results of implementation from (approximately) 1.2 to 1.3, time constant from 80 to 100 and time delay from 20 to 10. We clearly have that the above reported plant model parameters excursions, interpreted as modeling errors, were no match for the gain margin (1.6 for the PI and 6.3 for the PPI) and phase margin (27.03 for the PI and 77.3 for the PPI) as clearly the water height closed loop behavior of the PI and PPI controller solutions in Figure 10 are quite similar, red lines. Nevertheless, Figures 8 and 9 suggest that worse variations would result in a better behavior for the PPI controller over the PI controller. Finally, we also observe from Figure 10 the presence of the standing wave as a ripple in the measured real level signal. This motivates and confirms as a future research direction, the inclusion of this feature in the proposed plant model structure. 5. CONCLUSIONS Motivated by the recently tested predictive value of microscale setups for Hydraulics, we have modeled and controlled the microscale experimental canal at the LCS. For control purposes a first order transfer function with time delay was successful in capturing the essentials of the plant dynamics. The drawback was that due to the reduced scale of the canal and the nonlinearities present in it, the three plant model parameters are not constant and vary as functions of the chosen operating point. In a preliminary control approach we compared a standard PI tuning, with a PPI λ tuning that offered a more robust solution, to better deal with the variable nature of the plant model parameters. Future research should aim to include the modeling of the standing wave, on the identification side of the problem, and the application of more advanced control algorithms to achieve either robust performance or directly treat the parameters variability ( as in a gain scheduling approach, nonlinear control, etc.) 24