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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Nonlinear Observer-Based Feedback for Open-Channel Level Control

This paper is devoted to nonlinear observer and controller design for water level control of open-channel flow in irrigation canals or dam-river systems. A finite-dimensional model, previously developed by orthogonal collocation methods, based on Saint Venant equations and used for control design, is now further used for online flow rate and water infiltration estimation. This is done by a so-called state observer. In particular, the estimates obtained in this way can successfully be used in a controller previously proposed, resulting in a water level control law using only two level measurements along the canal (instead of the four measurements previously needed). The study is restricted to the case of a rectangular wetted section and subcritical flow. The results have been validated by simulations, on an implicit finite difference simulator based on a Preissmann scheme for various scenarios.     

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.     

Nonlinear Control of Open-Channel Water Flow Based on Collocation Control Model

This paper is devoted to the nonlinear control of open-channel water flow dynamics via a one-dimensional collocation control model for irrigation canals or dam-river systems. Open channel dynamics are based on the well-known Saint-Venant nonlinear partial differential equations. In order to obtain a finite-dimensional model an orthogonal collocation method is used, together with functional approximation of the solutions of Saint-Venant equations based on Lagrange polynomials. This method can give a more tractable model than those obtained from classical finite-difference or finite-element methods (from the viewpoint of both state dimension and structure), and is well suited for control purposes. In particular it is shown how such a model can be used to design a nonlinear controller by techniques of dynamic input–output linearization with the goal of controlling water levels along an open-channel reach. Controller performance and robustness are illustrated in simulations, with a simulated model for the canal chosen as more accurate than the one used for control design.     

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.     

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.     

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.     

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.     

无刷直流电机智能控制系统的研究

基于对无刷直流（BLDC）电机的工作和控制原理的分析,提出了无刷直流电机的双闭环自适应模糊PID控制方案。采用模糊控制逻辑实现PID控制器参数的在线自整定,详细说明了自适应模糊PID控制器的设计方法。算法简单有效,易于实现无刷直流电机交流伺服系统的全数字化。用Matlab／Simulink对系统进行了仿真,仿真结果显示系统具有良好的静动态性能,和较快的响应速度。     

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.     

Hydraulic Modeling of a Mixed Water Level Control Hydromechanical Gate

This article describes the hydraulic behavior of a mixed water level control hydromechanical gate present in several irrigation canals. The automatic gate is termed “mixed” because it can hold either the upstream water level or the downstream water level constant according to the flow conditions. Such a complex behavior is obtained through a series of side tanks linked by orifices and weirs. No energy supply is needed in this regulation process. The mixed flow gate is analyzed and a mathematical model for its function is proposed, assuming the system is at equilibrium. The goal of the modeling was to better understand the mixed gate function and to help adjust their characteristics in the field or in a design process. The proposed model is analyzed and evaluated using real data collected on a canal in the south of France. The results show the ability of the model to reproduce the function of this complex hydromechanical system. The mathematical model is also implemented in software dedicated to hydraulic modeling of irrigation canals, which can be used to design and evaluate management strategies.     

Rules for parameter adjustment in a PI controller for metallurgical heaters

The development of a set of rules (a rule base) incorporating operator experience in adjusting the parameters of a PI furnace controller is discussed. Sets of rules for the adjustment of the PI components in furnace heating and cooling are considered separately. The applicability of the rules in specific operating conditions is analyzed. The rules are verified on models of two furnaces with different dynamics. The proposals reduce overshoot due to dynamic changes, with up to 24% savings in the time required to track the settings. Thus, if a parameter-optimization system for a PI controller based on the proposed rules is used to take account of the nonlinearity of the furnace, productivity is increased and production costs fall.