Identification and Control of an Open-flow Canal using LPV Models (original) (raw)
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Environmental Modelling & Software, 2014
Irrigation canals are open-flow water hydraulic systems, whose objective is mainly to convey water from its source down to its final users. They are large distributed systems characterized by non-linearity and dynamic behavior that depends on the operating point. Moreover, in canals with multiple reaches dynamic behavior is highly affected by the coupling among them. The physical model for those systems leads to a distributed-parameter model whose description usually requires partial differential equations (PDEs). However, the solution and parameter estimation of those PDE equations can only be obtained numerically and imply quite time-consuming computations that make them not suitable for real-time control purposes. Alternatively, in this paper, it will be shown that open-flow canal systems can be suitably represented for control purposes by using linear parameter-varying (LPV) models. The advantage of this approach compared to the use of PDE equation is that allows simpler models which are suitable for control design and whose parameters can be easily identified from input-output data by means of classical identification techniques. In this paper, the well known control-oriented, model named integral delay zero (IDZ), that is able to represent the canal dynamics around a given operating point by means of a linear time-invariant (LTI) model is extended to multiple operating points by means of an LPV model. The derivation of this LPV model for single-reach open-flow canal systems as well as its extension to multiple-reach open-flow canals is proposed. In particular, the proposed methodology allows deriving the model structure and estimating model parameters using data by means of identification techniques. Thus, a gray-box control model is obtained whose validation is carried out using single-pool and two-pool test canals obtaining satisfactory results.
LPV VS multi-model PI(D) gain-scheduling applied to canal control
Proceedings of the 16th IFAC World Congress, 2005, 2005
This paper compares the multi-model gain scheduling (GS) control versus the linear parameter varying (LPV) gain scheduling control. The results of this comparative study is carried out exclusively with PI controllers. Although the simplicity and easiness of the former approach for controlling non-linear industrial plants, its main drawback relies on the impossibility to assure stability and performance for slow parameter variation. On the other hand, the later approach rigorously ensures stability and performance of the control system for any variation (smooth as well as abrupt) of the plant parameters. Finally, both methodologies are tested on a test bench canal.
Gain-scheduled Smith PID controllers for LPV systems with time varying delay: Application to an open
IFAC Proceedings Volumes (IFAC-PapersOnline), 2008
In this paper, a new approach to design gain scheduled robust linear parameter varying (LPV) PID controllers with pole placement constraints (through LMI regions) is proposed for LPV systems with second order structure and time-varying delay. The controller structure includes a Smith predictor, real time estimated parameters that schedule the controller (including the known part of the delay) and unstructured dynamic uncertainty which covers the unknown portion of the delay. Finally, the proposed control technique is validated in a real case study based on real a single reach canal: the Lunax Gallery at Gascogne (France).
Modelling and PI control of an irrigation canal
The main goal of this paper is to expose and validate a methodology to design efficient automatic controllers for irrigation canals, based on the Saint-Venant model. This model-based methodology enables to design controllers at the design stage (when the canal is not already built). The methodology is applied on an experimental canal located in Portugal. First the full nonlinear PDE model is calibrated, using a single steady-state experiment. The model is then linearized around a functioning point, in order to design linear PI controllers. Two classical control strategies are tested (local upstream control and distant downstream control) and compared on the canal. The experimental results shows the effectiveness of the method.
A delayed feedback control for network of open canals
International Journal of Dynamics and Control, 2013
This paper proposes an algebraic method to design time-delay boundary feedback controllers to regulate the water flow and level in a network of open canals. The network is modeled as n canals with one junction where all canals come together. The Saint-Venant equations are linearized around a prescribed steady state. We consider steady subcritical flow condition and an energy estimate, to build feedback boundary conditions. These boundary conditions depend on data at earlier times and ensure the exponential decrease in L 2-norm of the solution of the linearized model. A single canal is first treated and afterward the analysis is extended to the network. Finally, the controllers are applied numerically to the nonlinear Saint-Venant equations.
Modeling, control and field tests on an experimental irrigation canal
2002
Irrigation canals are complex hydraulic systems difficult to control. Many models and control strategies have already been developed using linear control theory. In the present study, a PI controller is developed and implemented in a brand new prototype canal and its features evaluated experimentally. The base model relies on the linearized Saint-Venant equations which is compared with a reservoir model to check its accuracy. This technique will prove its capability and versatility in tuning properly a controller for this kind of systems
A New Nonlinear Control Methodology for Irrigation Canals Based on a Delayed Input Model
2008
This paper is devoted to nonlinear feedback design for irrigation canals. Such systems are classically described by Saint-Venant nonlinear partial differential equations. Here instead, an ordinary differential equation model (still nonlinear) with a state-dependent input delay is used, on the basis of a model previously proposed in Litrico et al [2003]. The control design approach is based on a state prediction computation and the state predictor is constructed from a dynamic inversion in the same spirit as in Georges et al [2007]. The proposed methodology is analyzed and tested in simulation, first on the basis of the control model, and then using some "more accurate" model.
Irrigation canal models for automatic control purposes
2011
volumes during normal canal operation. In order to develop control algorithms for irrigation canals there is a need for simple linear models to be used in the algorithms. The following simple linear models are approximating the canal in order to give a base to develop control algorithms. The PAC-UPC laboratory canal (Prueba de Algoritmos de Control - Universitat Politecnica de Catalunya) is modelled (input and output discharge) using the following three models: Muskingum, Hayami and Integrator Delay Zero (IDZ) and the results are compared to measurements. All three models are able to describe the irrigation canal in an acceptable way. However, only the IDZ model can capture all the important characteristics. These tested models can be applied to represent real canals for control purposes where it is especially important to obtain good models without extensive measurements. Test campaigns are developped now in cooperation with the CHE (Confederacion Hidrografica del Ebro) in order to...
Tuning of PI controllers for an irrigation canal using optimization tools
Proc. of the …, 1999
Existing methods for the automatic control of water levels in irrigation canals are based on single input, single output linear feedback PI type controllers. Examples of such control systems are EL-FLO and BIVAL, where local PI controllers are used in series to adjust the position of upstream/downstream control gates.
Identification and Adaptive Control for Open Channel Water Flow Systems
Computer-Aided Civil and Infrastructure Engineering, 2011
Despite the continuous advances in the control design for water flow systems such as irrigation and sewer systems, the design and deployment of efficient water flow control systems requires a careful and efficient fine-tuning of their parameters prior and during the actual system operation. In the majority of water flow control applications, the controller design is based on simplified models (e.g., linear models assuming a fixed time-delay) for the water flow dynamics and as a result the initial controller design calls for a major finetuning at the initial deployment of the control system; moreover, the frequent changes in water management commands/needs as well as the severe exogenous disturbances call for a continuous update of the controller parameters. Conventional controller tuning approaches cannot be used for the efficient tuning of the controller parameters in water flow control systems, mainly due to the highly nonlinear dependence of the time-delay with respect to the water flow. In this article, we first introduce and analyze both by means of mathematical analysis and simulation experiments, a computationally sim-