Optimal Design of a Compacted Soil Liner Containing Sorptive Amendments

The design of a compacted soil liner that includes sorptive amendments is presented and evaluated as a combinatorial optimization problem. An objective function based on the materials costs, opportunity costs, and construction costs of the liner was used to evaluate the effect of incorporating four sorptive materials: benzyltriethylammnonium-bentonite, hexadecyltrimethylammonium-bentonite, shale, and granular activated carbon (GAC) into a compacted clay liner in order to mitigate transport of organic solutes through the liner. The results from this study indicate that the inclusion of sorptive amendments as a component in compacted soil liners can effectively retard the transport of organic contaminants through the liner without violating regulatory hydraulic conductivity requirements. In all cases when aqueous transport was considered as a constraint in the objective function formulation, the resulting liner always contained some amount of sorptive amendment. In general, shale and GAC were selected for use in the sorptive liner design for all organic solutes tested. The modeling framework presented in this study is general and could be used to evaluate other types of sorptive materials or additional constraints, and thus represents a flexible new tool for the design of compacted soil liners.     

Optimal Design of Channel Having Horizontal Bottom and Parabolic Sides

The cost of open channels can be minimized by using (1) the optimal design concept; (2) a new geometric shape to substitute for the trapezoidal channels, and/or (3) a composite channel. The channels in which the roughness along the wetted perimeter become distinctly different from part to part of the perimeter are called composite channels. The feasibility of a new cross-sectional shape that has a horizontal bed and two parabolic sides and lined as a composite channel is investigated to substitute for the trapezoidal cross section. The optimal design concept is used to establish the efficacy of the proposed new cross-sectional shape, because it gives the best and unique design of open channels. In optimal design concept, the geometric dimensions of a channel cross section are determined in a manner to minimize the total construction costs. The constraints are the given channel capacity and other imposed restrictions on geometric dimensions. The Lagrange multiplier technique is used to solve the resulting channel optimization models. The developed optimization models are applied to design the proposed and trapezoidal channels to convey a given design flow considering various design scenarios which include unrestricted, flow depth constrained, side slopes constrained, and top width constrained design. Each of these design scenarios again takes into account fixed freeboard, and depth-dependent freeboard cases of design. An analysis of the optimization results establishes the cost-saving capability of the proposed cross-sectional shape in comparison to a trapezoidal cross section.     

Optimal Design of a Stable Trapezoidal Channel Section Using Hybrid Optimization Techniques

A cost effective channel section for a specified flow rate, roughness coefficients, longitudinal slope, and various cost parameters can be determined using an optimization technique. However, the derived optimal channel section may not be feasible for construction because of in situ conditions. The local soil conditions may not support the optimal side slope of the channel and if constructed, the slope may fail. It is therefore necessary to also incorporate the criteria for side slope stability in designing an optimal open channel section. In this paper, a new methodology has been developed to design a stable and optimal channel section using hybrid optimization techniques. A genetic algorithm based optimization model is developed initially to determine the factor of safety of a channel slope for given soil parameters. This optimization model is then externally linked with a separate sequential quadratic programming based optimization model to evaluate the parameters of the stable and optimal channel section. Solution for various example problems incorporating different soil parameters are illustrated to demonstrate the applicability of the developed methodology.     

Design of Minimum Seepage-Loss Nonpolygonal Canal Sections with Drainage Layer at Shallow Depth

Analytical solutions exist for the seepage discharge from polygonal and nonpolygonal canal sections underlain by a drainage layer at a hydraulically infinite depth. These solutions lead to underestimation of the seepage discharge if a drainage layer occurs at a shallow depth. This paper presents solutions for seepage discharge from circular and exponential sections overlying a shallow drainage layer. The discharge has been calculated by a finite-difference-based numerical solution of the differential governing the seepage flow. The phreatic boundaries of the flow domain were described in terms of two parameters that were estimated by a minimization process. Such seepage computations were performed for a large number of independent dimensionless variables of the section geometry. Subjecting the computed seepage to regression analyses, explicit equations for seepage discharge loss have been obtained. Using these seepage loss equations, the design variables for minimum seepage loss have been obtained. The use of the design equations has been illustrated by design examples.     

Performance of Historic Downstream Canal Control Algorithms on ASCE Test Canal 1

Researchers have developed several algorithms to automatically control water levels in irrigation canals. Proportional-integral (PI) control logic has been used for downstream water-level control, but its performance has not always been satisfactory. Heuristic downstream water-level controllers (e.g., canal automation for rapid demand deliveries, or CARDD) have also been proposed but not rigorously tested. The ASCE Task Committee on Canal Automation Algorithms developed a series of test cases to evaluate the performance of canal control algorithms. In this paper, simulation tests were performed on the ASCE Test Canal 1 using three downstream control algorithms: (1) The standard PI control logic; (2) The PI control logic with hydraulic decouplers; and (3) The heuristic CARDD control logic. These controllers were tuned manually using trial-and-error techniques. Performance of the PI control logic improved with the addition of hydraulic decouplers. CARDD did not perform as well as the PI controllers under the conditions imposed on ASCE Test Canal 1. Robustness of these controllers depends on the aggressiveness of the controller as well as the initial flow rate.     

Optimal Design Strategy of Connected Control Method for Two Dynamically Similar Structures

Structural control of adjacent flexible structures has been shown to be effectively accomplished using the connected control method (CCM), which uses an auxiliary structure to provide a reaction force. A perceived constraint of the CCM is the ineffective control of structures with similar dynamics. However, the writers have presented a modified CCM mechanism in which dampers are connected between dynamically similar structures with a difference in connection height using cantilever structures. The research described in this paper extends the CCM to couple two dynamically similar structures and determines optimal stiffness and damping in the connector link. A two-degree-of-freedom building model is developed for the optimal design of the connected control devices. The optimal solutions of the connector stiffness and damping take into account the presence of fixed points in the systems transfer functions. Analytical results confirm the effectiveness of the proposed method and design. Experimental tests then verify the response reduction capabilities of the proposed optimal design.     

Simple Optimal Downstream Feedback Canal Controllers: Theory

A new class of downstream water-level feedback controllers is proposed that can vary from a series of individual proportional-integral (PI) controllers (each gate adjusted based on one water level) to fully centralized controllers (each gate adjusted based on all water levels) that include the effects of lag time. The controller design method uses discrete-time state-feedback control with a quadratic penalty function, physically based states, and no state estimation. A simple, linear model of canal pool response, the integrator-delay model, is used to define the state transitions. All controllers within this class are tuned for the entire canal using optimization techniques. This avoids the tedious task of manually tuning simple controllers. The relative performance of the various controllers within this class can be directly compared without simulation, since the same objective function is used to tune each controller. An example is provided which suggests that the fully centralized controller will perform better than a series of local controllers. However, reasonably good performance can be obtained for some intermediate PI controllers that pass information to one additional check structure upstream and downstream. This should limit some of the difficulties reported for full optimal controllers where all check structures respond to water-level errors in all pools (e.g., saturation of inputs). The results of simulation studies of these controllers are provided in a companion paper.     

Simple Optimal Downstream Feedback Canal Controllers: ASCE Test Case Results

In a companion paper, a class of downstream-water-level feedback canal controllers was described. Within this class, a particular controller is chosen by selecting which controller coefficients to optimize (tune), the remaining coefficients being set to zero. These controllers range from a series of simple proportional-integral (PI) controllers to a single centralized controller that considers lag times. In this paper, several controllers within this class were tuned with the same quadratic performance criteria (i.e., identical penalty functions for optimization). The resulting controllers were then tested through unsteady-flow simulation with the ASCE canal automation test cases for canal 1. Differences between canal and gate properties, as simulated and as assumed for tuning, reduced controller performance in terms of both water-level errors and gate movements. The test case restrictions placed on minimum gate movement caused water levels to oscillate around their set points. This resulted in steady-state errors and much more gate movement (hunting). More centralized controllers handle unscheduled flow changes better than a series of local PI controllers. Controllers that explicitly account for pool wave travel times did not improve control as much as expected. Sending control actions within a given pool to upstream pools improved performance, but caused oscillations in some cases, unless control signals were also sent downstream. A good compromise between controller performance and complexity is provided by controllers that pass feedback from a given water level to the check structure at the upstream end of its pool (i.e., that used for downstream control of an individual pool) and to all upstream and one downstream check structures.     

Optimal Design of Pressurized Irrigation Subunit

A linear programming (LP) model is presented for optimal design of the pressurized irrigation system subunit. The objective function of the LP is to minimize the equivalent annual fixed cost of pipe network of the irrigation system and its annual operating energy cost. The hydraulic characteristics in the irrigation subunit are ensured by using the length, energy conservation, and pressure head constraints. The input data are the system layout, segment-wise cost and hydraulic gradients in all the alternative pipe diameters, and energy cost per unit head of pumping water through the pipeline network. The output data are: segment-wise lengths of different diameters, operating inlet pressure head, and equivalent annual cost of the pipeline network. The explicit optimal design is demonstrated with design examples on lateral and submain or manifold of pressurized irrigation systems. The effect of the equations for friction head loss calculation on optimization procedure is investigated through the design example for microirrigation manifold. The performance evaluation of the proposed model in comparison with the analytical methods, graphical methods, numerical solutions, and dynamic programming optimization model reveals the good performance of the proposed model. The verification of operating inlet pressure head obtained by the proposed model with accurate numerical step-by-step method suggested that it is mostly accurate.     

Optimal Design of Open Channel Section Incorporating Critical Flow Condition

The flow at critical condition of an open channel is unstable. At critical condition, a small change in specific energy will cause abrupt fluctuation in water depth of the channel. This is because the specific energy curve is almost vertical at critical state. Therefore, if the design depth of the channel is near or equal to critical depth of the channel, the shape of the channel must be altered to avoid a large fluctuation in water depth. In the present study, a nonlinear optimization model is presented for designing an optimal channel section incorporating the critical flow condition of the channel. The optimization model derives the optimal channel section at a desirable difference from the critical condition of the channel so that a small change in the specific energy of the channel will not cause an abrupt change in flow depth. The objective of the optimization model is to minimize the total construction costs of the channel. Manning’s equation is used to specify the uniform flow condition in the channel. The developed optimization model is solved by sequential quadratic programming using MATLAB. Applicability of the model is demonstrated for a trapezoidal channel section with composite roughness. However, it also can be extended to other shapes of channel.     

Design of a Single-Pool Downstream Controller Using Quantitative Feedback Control Theory

A downstream controller is designed for an irrigation canal reach using a design technique called quantitative feedback control theory (QFT). The performance of this controller is compared to a proportional, integral, derivative (PID) controller and a linear quadratic regulator (LQR) controller. In this study, the QFT controller is designed for a single canal reach because it best demonstrates how a controller is designed. Previous research for this canal model provided data for comparison. For the operating conditions that are defined in this paper, the QFT controller is shown to have slightly better performance than the PID controller and better performance than the LQR controller. When the canal hydraulic roughness is increased, the QFT controller still performed better than the PID controller.     

Optimal Design of a Special Class of Curvilinear Bottomed Channel Section

Section elements of a new class of curvilinear bottomed channel whose boundary maps along a circle onto the hodograph plane have been investigated in the study. The perimeter of this type of channel always lies between an ellipse and a parabola of the same top width and flow depth. Presented herein are optimal section properties from least area and minimum seepage loss point of view for the curved channel section. The study also addresses the constraints on the channel dimensions and the velocity of flow. A nondimensional parameter approach has been used to simplify the analysis. Design procedures for different cases have been presented to demonstrate the simplicity of the method.     

Real-Time Implementation of Model Predictive Control on Maricopa-Stanfield Irrigation and Drainage District’s WM Canal

Water resources are limited in many agricultural areas. One method to improve the effective use of water is to improve delivery service from irrigation canals. This can be done by applying automatic control methods that control the gates in an irrigation canal. The model predictive control (MPC) is one such advanced control method. In this article, the MPC is used to deliver irrigation water to the WM Canal at the Maricopa-Stanfield Irrigation and Drainage District. The tests show that the water is efficiently delivered to the users and water level deviations at all locations are small. The control is compared to the results from an advanced Linear Quadratic Regulator control method, also tested on the actual canal.     

Salt River Project Canal Automation Pilot Project: Simulation Tests

The feasibility of automatically controlling water levels and deliveries on the Salt River Project (SRP) canal system through computer-based algorithms is being investigated. The proposed control system automates and enhances functions already performed by SRP operators, namely feedforward routing of scheduled demand changes, feedback control of downstream water levels, and flow control at check structures. Performance of the control system was tested with unsteady flow simulation. Test scenarios were defined by the operators for a 30 km, four-pool canal reach. The tests considered the effect of imperfect knowledge of check gate head-discharge relationships. The combined feedback-feedforward controller easily kept water level deviations close to the target when dealing with routine, scheduled flow changes. Those same routine changes, when unscheduled, were handled effectively by the feedback controller alone. The combined system had greater difficulty in dealing with large demand changes, especially if unscheduled. Because feedback flow changes are computed independently of feedforward changes, the feedback controller tends to counteract feedforward control actions. The effect is unimportant when dealing with routine flow changes but is more significant when dealing with large changes, especially in cases where the demand change cannot be fully anticipated.     

Performance of Model Predictive Control on ASCE Test Canal 1

Model predictive control (MPC) is a popular control algorithm in the process control industry that is particularly suited to the automatic control of irrigation water delivery systems because it explicitly accounts for the long delay times encountered in open-channel flow. In addition, a feedforward routine is easy to implement in MPC and many of the constraints that canal operators face can be directly incorporated into the MPC scheme. The ASCE Task Committee on Canal Automation Algorithms developed a series of test cases to evaluate the performance of canal control algorithms. In this paper, simulation tests were performed on ASCE test canal 1 using a remote downstream control configuration of MPC. The MPC algorithm effectively controls ASCE test canal 1, and its performance was similar to that of other proposed controllers. When there were no minimum gate movement constraints, MPC was fairly robust because the controller performance did not significantly degrade under untuned conditions. In the presence of minimum gate movement constraints, the water levels continually oscillate around the water level setpoint. Using the configuration presented in this paper, the feedforward portion of MPC does not perform as well as other proposed feedforward routines. This underperformance is related to the simplifications made by the underlying process model and not to MPC itself.     

Automatic Tuning of PI Controllers for an Irrigation Canal Pool

This paper presents a method to automatically tune decentralized proportional integral (PI) controllers for an irrigation canal pool. The auto tune variation (ATV) method is based on a relay experiment, which generates small amplitude oscillations of the canal pool. The ATV procedure can be used to get the integrator delay model parameters of a canal pool, which in turn can be used to tune a PI controller using classic rules, or other rules such as the ones proposed by Litrico and Fromion. This method does not require advanced automatic control knowledge and is implemented in the SIC software developed by Cemagref, which also incorporates a supervisory control and data acquisition module for real-time control. The ATV method is evaluated by simulations and experiments on a real irrigation canal located in the South of France, for local upstream, local downstream, and distant downstream controller tuning.     

Design of Hydraulically Efficient Power-Law Channels with Freeboard

A power-law channel is a generalized form of the parabolic channel. The exponent of the governing equation is a variable that for certain maximum permissible side slopes can be determined by maximizing the cross-sectional area of flow (or minimizing the wetted perimeter). Using this exponent rather than the constant allows a hydraulically more efficient open channel section to be designed. In earlier work on power-law channels freeboard was neglected to simplify the analysis. However as pointed out by several authors, a channel without freeboard is of academic interest only and not practical. All open channels are in practice designed and constructed with freeboard as a factor of safety. In this paper freeboard has been introduced as an additional parameter to be taken into account when designing a power-law channel. The work from this paper is applied to an earlier example of a parabolic channel to demonstrate a practical design.     

Canal Seepage Reduction by Soil Compaction

Simple in situ vibratory soil compaction of earth lined canals was tested to determine the impact on seepage losses. Commercial equipment was used for vibratory compaction of long sections of five irrigation district earthen canals. Ponding tests were conducted before and after compaction. When the sides and bottoms of the canals were compacted, seepage reductions of about 90% were obtained; reductions of 16–31% were obtained when only sides were compacted.     

Most Hydraulically Efficient Standard Lined Canal Sections

Cross-sectional dimensions of the most hydraulically efficient lined canals are evaluated based on an analysis of a generalized trapezoidal shape that reduces to two standard sections with rounded bottom vertices used in India, as well as to the commonly used trapezoidal section with sharp bottom vertices. The method of Lagrange multipliers is applied to find the dimensions of optimal sections when the only constraint imposed is that of uniform flow and normal depth and, in addition, when values of either channel side slope, bottom width, top width, or supply depth are specified as well. The analytic solutions obtained for the generalized trapezoidal section are shown to match known solutions for limiting cases including those for sections in the shape of sharp-cornered trapezoids, rectangles, triangles, and semicircles. Solutions presented will be useful for evaluating standard cross-sectional shapes used for lined canals in India, as well as other sections that can be obtained from the generalized trapezoid with rounded bottom vertices.