Integrator Delay Model Research Articles

The multi-point hydraulic control method for advanced controller design of the open canal irrigation systems

Abstract Most studies about the automatic control of open canal irrigation systems only focus on the distant downstream water level, which ignores the fact that the offtakes may be located anywhere along the canal. Such a simplified control strategy is likely to result in uncontrollable and inefficient water delivery. Therefore, a multi-point hydraulic control method is proposed, in which a simplified Saint-Venant model is formulated to describe the hydraulic states of multiple controlled points. Then, it is underlined that the controlled points with and without the offtakes may have different control objectives. It is suggested to implement soft constraints to the downstream end when there is no offtake, meaning that moderate water level fluctuations are acceptable. By comparing with the common model predictive control (MPC) controller, where the Integrator Delay model and hard constraint are used for distant downstream water level control, the proposed MPC controller successfully improved the water level control stability before the offtakes and the water supply reliability by 91 and 69.5% under the conventional condition and by 54.9 and 27.1% under the water-deficient condition. Accordingly, the proposed multi-point hydraulic control method shows great potential for the precision irrigation of large irrigation districts.

The Integrator Dual-Delay model for advanced controller design of the open canal irrigation systems with multiple offtakes

The Integrator Delay (ID) model is widely used for advanced controller design in canal automation projects, assuming that all offtakes are aggregated into one at the most downstream end for each canal pool. However, such an unrealistic assumption differs greatly from the actual location distribution of the offtakes in most open canal irrigation systems (OCIS), leading to increased uncertainties and inaccurate canal operations. For this reason, this study introduced the Integrator Dual-Delay (IDD) model, capable of innovatively considering the lag-effect of the offtake flow changes alongside the irrigation canal. To investigate the effectiveness of the modified control-oriented model in upgrading the canal automatic operating systems, two centralized model predictive controllers were designed with the ID model and the IDD model, respectively. Then the simulation tests were carried out on the Third Main Canal of the Zhanghe Irrigation System in Southern China. Two performance indicators of Non-dimensional Integrated Square of Error (NISE) and Non-dimensional Integrated Square of Discharge Change (NISQ) were adopted to measure the water level control stability and flow control stability. The results show that with the IDD model, the NISE is reduced from 3.53 × 10-5 to 1.88 × 10-5 and the NISQ is reduced from 3.23 × 10-6 to 2.88 × 10-6, indicating that the proposed IDD model can help the control stabilities of water level and flow to be improved by 46.7 % and 10.8 %, respectively. The IDD model constructs a more accurate state-space prediction process for advanced controller design and contributes to more efficient canal automatic operations, showing great potential in precision irrigation for various OCIS.

An Adaptive Predictive Control Algorithm for Comprehensive Dendritic Canal Systems

Automatic canal control is essential to improve water utilization efficiency in irrigation districts. Water level error in the model used by the control algorithm significantly impacts performance. The integrator delay model, which has a linear structure, is widely used in multi-input/multioutput control algorithms, including linear-quadratic control and model predictive control. However, the integrator delay model is suboptimal for large irrigation districts; the canals are long, the flows are large, there are many scattered offtakes, and the operating conditions vary. We developed an adaptive predictive control mode for the Qinhan Canal in Ningxia Province, China. We used a segment integrator delay model for this large irrigation district and employed a differential evolution algorithm for online system identification; this minimizes error. We analyzed and controlled for various uncertainties (i.e., flow observation noise, geometric and hydraulic parameter errors, and accidental interference with the automatic control system). Simulations indicated that the water level fitting errors were significantly reduced compared with the original model, and water level regulation was significantly improved, especially in terms of the maximum absolute error. Adaptive predictive control was better than linear-quadratic control and model predictive control approach for water level. Adaptive predictive control coped well with several uncertainties. The main factors affecting water level control were the flow observation and gate opening control accuracy, and the extent of real-time data coverage. These features require careful attention when automating and modernizing irrigation districts.

Decentralized ellipsoidal state estimation for linear model predictive control of an irrigation canal

AbstractA centralized linear MPC is used to stabilize an irrigation system whose operation is represented by an integrator-delay model. Since not all the state variables can be measured, a decentralized ellipsoidal estimation strategy is proposed. This approach keeps the quality of a centralized estimation and reduces significantly the computation time for the systems considered. An adaptation of Test Canal 1, developed by the ASCE Task Committee on Canal Automation Algorithms, is used as a case study to show the performance of the proposed methodology.

Experimental comparison of canal models for control purposes using simulation and laboratory experiments

Considerable amounts of water can be saved by automating irrigation canals. The design of most of the practical automatic controllers rely on a simplified model of the irrigation canal. This model can be obtained from measured data (identification) or can be formulated (white box models) assuming simplifications in the physical concepts and using the canal geometry. Several models of this kind are presently available. Moreover, short canals reveal a resonance problem, due to the back and forth of waves. This paper is focused on how to choose a suitable model for short canal pools with the purpose of control design. Four simple models are applied to two different types (resonant and non-resonant) of short canals: First order transfer function based on the Hayami model, Muskingum model, Integrator Delay (ID), and Integrator Delay plus Zero (IDZ). Model predictive controllers are developed based on these models and they are tested numerically and experimentally in order to evaluate their contribution to the control effectiveness. The controllers based on the ID and IDZ model showed the best performance.

Estimating Canal Pool Resonance with Auto Tune Variation

The integrator-delay (ID) model is commonly used to model canal pools that do not exhibit resonance behavior. Simple step tests are often used to estimate ID model parameters; namely, delay time and backwater surface area. These step tests change the canal inflow at the upstream end of the pool and observe water depth variations at the downstream end. Some knowledge of the canal pool characteristics are needed to determine the amount of flow change and its duration. Auto tune variation (ATV) is one method for determining the duration of these step tests. Pools that are under backwater over their entire length tend to exhibit oscillations attributable to resonance waves. Random Binary Sequence (RBS) tests have been used to determine the resonance frequency of such pools, for which step tests with different durations are used. RBS tests are difficult to implement in practice and may not provide the resonance frequency. The intent of this paper is to demonstrate on a real canal that the ATV method can determine both the resonance frequency and the resonance-peak height for canal pools whose water levels oscillate.

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.

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.

Centralized controller for the Narmada main canal

The current challenge facing irrigation networks is to find ways to improve their operational performance. Control system design and implementation is considered as one of the most assured ways to achieve this aim. In this paper, a downstream water-level controller is presented for the first nine pools of the Narmada main canal in India. The control system consists of a remote downstream proportional-integral (PI) feedback controller with feedforward control. In this controller, each water-level regulator is adjusted based on water levels of all the pools of the canal. A linear model of the canal pool response, the integrator-delay model, is applied to define the state transitions. To evaluate the control system potential, performance criteria were considered. The results show that the designed controller has considerable potential to closely match the discharges at the downstream outlets/offtakes with those ordered by water users while maintaining the water levels throughout the length of the canal. This result is achieved providing that the estimated delay times used in the feedforward controller are varied depending on the flow rate. Copyright © 2005 John Wiley & Sons, Ltd.

Simplified Modeling of Irrigation Canals for Controller Design

The integrator delay zero (IDZ) model presented by Litrico and Fromion is a simple way to model a canal for control purposes that extends the classical integrator delay model. This analytical model gives a very good frequency domain approximation of the Saint-Venant transfer matrix for a pool possibly in backwater conditions. The present paper shows how this model can be used to model an irrigation canal for control design. The IDZ model is analyzed and its accuracy evaluated in the frequency and time domain on two ASCE test canals for high and low flow conditions.

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.