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.     

Tuning of Robust Distant Downstream PI Controllers for an Irrigation Canal Pool. II: Implementation Issues

Based on the companion paper results, this paper presents a robust tuning method to tune a proportional integral (PI) controller that fulfills the design requirements for a single pool with different hydraulic conditions. The robust PI controller parameters are obtained analytically as a function of the physical parameters of the canal pool. Important implementation issues are also considered. Rules are provided for the sampling time selection in order to recover the continuous-time performance. When the sampling time is imposed, it has to be included in the controller design, by modifying the delay of the system. A simple way is proposed to take account of the gate opening as control action variable, instead of the upstream discharge. This robust PI tuning method is evaluated by simulation on a full nonlinear model of two different canal pools for different flow conditions and different implementations: continuous-time control, discrete-time control, using the discharge or the gate opening as control action variable. Simulation results show that the method leads to efficient realistic PI controllers for a canal pool.     

Downstream-Water-Level Control Test Results on the WM Lateral Canal

On steep canals, distant downstream-water-level control can be challenging. The Software for Automated Canal Management was developed, in part, to test various distant downstream water-level controllers. It was implemented on the WM canal of the Maricopa Stanfield Irrigation and Drainage District, Stanfield, Ariz. to compare the performance of various controllers. In 2004, Clemmens and Schuurmans used optimization to determine the coefficients for a variety of controllers. These controllers vary in their complexity from a series of simple, single-input-single-output, proportional-integral controllers to a fully centralized, multiple-input-multiple-output, optimal controller. The controller design also varies regarding which pools are under downstream, or upstream, control and according to the conditions (e.g., flow rate) assumed for controller design. These controllers were tested under actual operating conditions and with unscheduled disturbances. The results of these tests are presented in this paper.     

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.     

Tuning of Robust Distant Downstream PI Controllers for an Irrigation Canal Pool. I: Theory

The paper proposes a new method to tune robust distant downstream proportional integral (PI) controllers for an irrigation canal pool. The method emphasizes the role of gain and phase margins in the controller design, by linking the selection of these robustness indicators to the time domain specifications. This leads to link the frequency domain approach used by automatic control engineers to the time domain approach used by hydraulic engineers. The maximum error corresponding to an unpredicted perturbation is shown to be directly linked to the gain margin and the settling time to the phase margin of the controlled system. The tuning method gives analytical expressions for the controller parameters as function of physical parameters of the canal pool in order to satisfy desired performance requirements. The model is first expressed in terms of dimensionless variables, in order to get generic tuning formulas. The dimensionless PI coefficients are then expressed as functions of time-domain performance requirements. The PI tuning method is evaluated by simulation on a full nonlinear model for a canal pool taken from the ASCE test cases.     

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.     

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.     

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.     

Automatic Downstream Water-Level Feedback Control of Branching Canal Networks: Simulation Results

Previous research on canal automation has dealt with the control of single, in-line canals, while canal operators typically have to control an entire network of canals. Because the branches in a network are hydraulically coupled with each other, control of a branching canal network based on separate controllers for each branch may not be the most effective control strategy. A methodology by which existing automatic control systems could be modified to control branching canal networks is provided in a companion paper. This paper presents results of hydraulic simulations of the new methodology to estimate the controllability of a large portion of the branching canal network operated by the Salt River Project (SRP). Two types of controllers were used for this study: (1) linear quadratic regulator (LQR) and (2) model predictive control (MPC). Both controllers used the same underlying process model [integrator-delay (ID) model], and both controllers were capable of feedback and feedforward control. Under feedback control alone, both controllers gave similar performance, but were unable to effectively control the overall system because of the long delay times. When feedforward control was added to the feedback controller, both of these control systems were able to effectively control the branching canal network operated by SRP. For the LQR controller, the volume compensation method for routing known demand change was used as the feedforward controller. For the MPC controller, the ID model was used as the feedforward controller. Slight differences were noted between the performance of the two feedforward controllers.     

Multiple-Model Optimization of Proportional Integral Controllers on Canals

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.     

Automatic Downstream Water-Level Feedback Control of Branching Canal Networks: Theory

Most of the research on the design of feedback controllers for irrigation canals has been concentrated on single, in-line canals with no branches. Because the branches in a network are hydraulically coupled with each other, it may be difficult to automatically control a branching canal network by designing separate feedback controllers for each branch and then letting them run simultaneously. Thus feedback control of an entire branching canal system may be more efficient if the branching flow dynamics are explicitly taken into account during the feedback controller design process. This paper develops two different feedback controllers for branching canal networks. The first feedback controller was developed using linear quadratic regulator theory and the second using model predictive control. Both algorithms were able to effectively control a simple branching canal network example with relatively small flow changes.     

Robust Fractional-Order PI Controller Implemented on a Laboratory Hydraulic Canal

This paper deals with the development of a new robust fractional-order PI controller for hydraulic canals whose parameters can vary in a wide range. Robustness to gain changes has particularly been increased. A method to design these controllers through the use of frequency specifications is proposed. Analysis of the frequency response of the closed-loop canal shows that the general robustness was also enhanced. Two of these fractional controllers have been experimentally implemented in a laboratory hydraulic canal characterized by time-varying dynamical parameters. A comparison between the real-time responses of the fractional-order control system and those of the standard PI demonstrates the effectiveness of the proposed fractional-order control strategy in terms of performance and robustness.     

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.     

Simple Water Level Controller for Irrigation and Drainage Canals

A simple water level controller for irrigation and drainage canals is proposed; the proposed controller has a master-slave structure where the slaves control the flow rates through the control structures. The master controller consists of PI-based controllers for feedback, and a decoupler and feedforward controller that are based on the inversion of a simple dynamic model of the canal system. The applicability of the controller is demonstrated in field experiments.     

Control of Suspension Bridge Nonlinear Vibrations due to Moving Loads

The flexibility and low damping of the long-span suspended cables in the suspension bridges make them prone to vibrations due to wind and moving loads, which affect the dynamic response of the suspended cables and the bridge deck. This paper shows the design of two control schemes to control the nonlinear vibrations in the suspended cable and the bridge deck due to a vertical load moving on the bridge deck with a constant speed. The first control scheme is an optimal state feedback controller. The second control scheme is a robust state feedback controller, whose design is based on the design of optimal controllers. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. A vertical cable between the bridge deck and the suspended cable is used to install a hydraulic actuator able to generate the active control force on the bridge deck. The MATLAB software is used to simulate the performance of the system with the designed controllers. The simulation results indicate that the proposed controllers are capable of significantly reducing the nonlinear oscillations of the system. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller. It is found that the system with the proposed controllers can provide better performance than the system with the velocity feedback controller.     

Closed-Form Expression of the Response Time of an Open Channel

Computing accurately the response time of an open channel is of extreme importance for management operations on canal networks, such as feed-forward control problems. The methods proposed in the literature to approximate the response time do not always account for the influence of a cross structure at the downstream end of a canal pool, which may have a significant impact on the response time. This paper proposes a new approach to compute the response time, accounting explicitly for the backwater and the feedback effects due to the downstream cross structure. The method provides a distributed analytical expression of the response time as a function of the characteristics of the canal (geometry, roughness) and of the downstream cross structure. A test canal with a weir or a gate at the downstream end is used to compare the new method with some of the others. Results show that the proposed expression accurately reproduces the response time for various backwater and downstream boundary conditions.     

Integrated Auto-Tuning PID Control of Continuous Casting Process

Accuratemouldlevelcontrolisveryimportantincontinuouscastingprocess(seeFig.1)anditisbelievedtobeakeyfactorinimprovingfinalproductquality.Althoughmanymethodshavebeendevelopedformouldlevelcontrol[1,2],theyarenotperfectbecauseonlypartofthefactorssuchasdisturbanceofcastingspeedandnonlinearityofthemouldlevelcontrolsystemareconsidered[3—5].Infact,theperformanceofthehydraulicservosystemofslidinggateanddeviationoftundishweightaretwomajorfactorsaffectingmouldlevelcontrol.Allthesetwoloopsshouldbeconside…     

Response of ASCE Task Committee Test Cases to Open-Loop Control Measures

Automated open- and closed-loop control systems can enhance the performance of irrigation delivery systems. This paper examines the response of the canal test cases developed by the ASCE task committee on canal automation algorithms to a particular anticipatory open-loop control technique, gate stroking. The performance of the ideal gate-stroking solution is compared with the performance of an approximate gate-stroking schedule that was generated by imposing practical constraints on the frequency and magnitude of the gate adjustments. Also analyzed were the performance of a nonanticipatory open-loop control scheme and the effect of model parameter uncertainties on the effectiveness of the control. For the test cases, the approximate gate-stroking schedules performed similarly to the ideal schedules. For two of the test cases, delivery performance was similar with and without anticipation, but was substantially different for the other two tests. The quality of the control degraded as a result of errors in model parameters, particularly in cases with incorrect check gate calibrations and submerged gate flows. Results point out the importance of combining open- and closed-loop control measures to improve the overall effectiveness of the control.     

Scheduled Controllers for Buildings under Seismic Excitation with Limited Actuator Capacity

A new class of scheduled controllers is presented for improving the response of seismic-excited buildings under actuators with limited capacity. The controller is scheduled based on the response of the system on-line, to take full advantage of the inevitably limited actuation. While the controller is nonlinear, the overall approach relies on a variety of techniques from linear designs, which makes it possible to generalize the approach to a variety of systems and control objectives. For example, sufficient conditions for feasibility of a feedback controller are expressed in terms of linear matrix inequalities, thus solvable with standard software. Both state feedback and observer-based controllers are discussed. Performance of the proposed technique is illustrated through simulations of a six-story building subject to earthquake ground motion.     

High-Resolution Method for Modeling Hydraulic Regime Changes at Canal Gate Structures

A method for modeling flow regime changes at gate structures in canal reaches is presented. The methodology consists of using an approximate Riemann solver at the internal computational nodes, along with the simultaneous solution of the characteristic equations with a gate structure equation at the upstream and downstream boundaries of each reach. The conservative form of the unsteady shallow-water equations is solved in the one-dimensional form using an explicit second-order weighted-average—flux upwind total variation diminishing (TVD) method and a Preissmann implicit scheme method. Four types of TVD limiters are integrated into the explicit solution of the governing hydraulic equations, and the results of the different schemes were compared. Twelve possible cases of flow regime change in a two-reach canal with a gate downstream of the first reach and a weir downstream of the second reach, were considered. While the implicit method gave smoother results, the high-resolution scheme—characteristic method coupling approach at the gate structure was found to be robust in terms of minimizing oscillations generated during changing flow regimes. The complete method developed in this study was able to successfully resolve numerical instabilities due to intersecting shock waves.