ℒ/Sub 1/ Controller Design for a High-Order 5-POOL Irrigation Canal System (original) (raw)
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L1 Controller Design for a High-Order 5-POOL Irrigation Canal System
IEEE CONFERENCE ON DECISION …, 2000
The aim of this work is to present an application of recent methods for solving the 1 design problem, based on the Scaled-Q approach, on a high-order, non-minimum phase system. We start by describing the system which is an open-channel hydraulic system (e.g.: an irrigation canal). From the discretization and linearization of the set of two partial-derivative equations, a state-space model of the system is generated. This model is a high-order MIMO system (five external perturbations w, five control inputs u, ten controlled outputs z, five measured outputs y, 65 states x) and is non-minimum phase. A controller is then designed by minimizing the 1 norm of the impulse response of the transfer matrix between the perturbations w and the outputs z. Time-domain constraints are added into the minimization problem in order to force integrators into the controller. The numerical resolution of the problem proved to be efficient, despite of the characteristics of the system. The obtained results are compared in the timedomain to classical P ID and LQG controllers on the non-linear system. The results are good in terms of performance and robustness, in particular for the rejection of the worst-case perturbation.
Design of PI Controllers for Irrigation Canals Based on Linear Matrix Inequalities
Water, 2020
A new Proportional-Integral (PI) tuning method based on Linear Matrix Inequalities (LMIs) is presented. In particular, an LMI-based optimal control problem is solved to obtain a sparse feedback that provides the PI tuning. The ASCE Test Canal 1 is used as a case study. Using a linearised model of the canal, different tunings for the design of the PI controller are developed and tested using the software Sobek. Furthermore, the proposed method is also compared with other tunings proposed for the same canal available in the literature. Our results show that the proposed method reduces by half the maximum errors with respect to other assessed alternatives and minimizes undesired mutual interactions between canal pools. Also, our method improves the optimality degree of the PI tuning by 30%. Therefore, it is concluded that the LMI based PI controllers lead to satisfactory performance in regulating water levels and canal flows/structure outflows, outperforming other tested alternatives, ...
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.
LMI & BMI technics for the design of a PI control for irrigation channels
2013 European Control Conference (ECC), 2013
This paper considers the problem of control design for a nonlinear distributed parameter system in infinite dimension which is described by hyperbolic Partial Differential Equations (PDEs) of de Saint-Venant. For describing the dynamic of this nonlinear system over a wide operating range, the Multi-Models approach, which takes into account Linear Time Invariant (LTI) models defined around a set of operating points, has been used. By means of an Internal Model Boundary Control (IMBC), a new design of Proportional Integral (PI) feedback is performed through Bilinear Matrix Inequality (BMI) and Linear Matrix Inequality (LMI) technics. The new results have been simulated and also compared to the previous results, illustrating the new theoretical contribution.
This paper presents an application of a multivariable optimal (LQR) and a multivariable predictive (MPC) controllers. These controllers are applied to a 2-pool irrigation canals. The linear state space model used to design both controllers is derived from Saint-Venant's equations discretized through the Preissmann implicit scheme. The LQR closed-loop controller is obtained from the steady-state solution of the Riccati equation (infinite time horizon). The MPC closed-loop controller is obtained from the same minimization problem, but over a finite time horizon λ. For both controllers, a Kalman Filter is used to reconstruct the state variables and the unknown perturbations from a reduced number of observed variables, which are water levels at the upstream and downstream end of each pool. Although only perturbation rejection is tested and presented in this paper, tracking aspects can also be handled by both controllers. For the LQR controller, known offtake withdrawals and future ...
Design of PI Controllers for Hydraulic Control Systems
Mathematical Problems in Engineering, 2013
The paper proposes a procedure for design of PI controllers for hydraulic systems with long transmission lines which are described by models of high order. Design is based on the combination of the IE criterion and engineering specifications (settling time and relative stability) as well as on the application ofD-decomposition. In comparison with some known results, the method is of graphical character, and it is very simple (solving nonlinear algebraic equations is eliminated). The paper presents the algorithm of software procedure for design of the controller. The method is compared with other methods at the level of simulation, and its superiority is shown. By applying the Nyquist criterion, it is shown that the method possesses robustness in relation to non modelled dynamics.
Mathematical model for robust control of an irrigation main canal pool
Environmental Modelling & Software, 2014
This paper describes the formulation and development of a mathematical model for high-performance robust controller design techniques, based on a complete identification for control procedure, of an irrigation main canal pool (true plant), which is characterized by the exhibition of large variations in its dynamic parameters when the discharge regime changes in the operating range [Qmin, Qmax]. Real-time field data has been used. Four basic steps of the proposed procedure have been defined in which all the stages, from the design of the experiments to the model validation, are considered. This procedure not only delivers a nominal model of the true plant, but also a reliable estimate of its model uncertainty region bounded by the true plant models under minimum and maximum operating discharge regimes (limit operating models). The model uncertainty set, defined by the nominal model and its uncertainty region, is characterized by its being as tight as possible to the true irrigation main canal pool. The obtained results are very promising since this kind of models facilitates the design of robust controllers, which allow improving the operability of irrigation main canal pools and also substantially reduce water losses.
Modelling of irrigation channel dynamics for controller design
SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218), 1998
Irrigation canals are complex hydraulic systems difficult to control. Design methods have been developed using linear control theory. To use this tool, a linear model of the dynamic IS needed.This paper presents a simple model for canal reach dynamics. A reach transfer matrix is obtained by linearisation of Samt Venant equations near a steady flow regime.The accuracy of this transfer matrix is evaluated, in frequency and time domam.
Control-Oriented Model of a Complex Irrigation Main Canal Pool
Proceedings of the 18th IFAC World Congress, 2011
A control-oriented model of a complex irrigation main canal pool (plant), which is characterized by the exhibition of large variations in their dynamic parameters when the discharge regime changes in the operating range [Q min , Q max ], has been developed using system identification for control procedure and also using real-time data. The control-oriented model is comprised by the nominal model of the true plant and for its uncertainty region bounded by the true plant models under low and high operating discharge regimes (limit operating models). The model is obtained from the use of both experimental data, which correspond to main operating discharge regimes of the true plant, and the Prediction Error framework. The results are very encouraging since control-oriented models facilitate the design of high-performance robust controllers, which allow the operability and efficiency of irrigation main canal pools to be increased and service to the users to be improved.
Multiple-Model Optimization of Proportional Integral Controllers on Canals
Journal of Irrigation and Drainage Engineering, 2005
Canals or open channels that convey water often consist of pools in series separated by control structures. Successful implementation of water-level control with these structures using decentralized proportional integral (PI) controllers depends heavily on the tuning of the control parameters. These parameters are hard to determine due to the interactions between the pools and the varying flow conditions in the canal. This paper presents a procedure for tuning any linear controller (including decentralized PI controllers) that guarantees stability of the controlled canal. It minimizes a cost function that weights the water-level deviations from the target level against control efforts at both low-and high-flow conditions. The procedure is tested on a model of the Umatilla Stanfield Branch Furnish Canal in Oregon. The tests show the capability of the procedure to deal with the pool interactions. The results of a realistic turnout schedule applied to the controlled canal show the high performance of the controllers (small water-level deviations in all pools) over varying flow conditions.