Detection of oscillations in control loops in irrigation channels

Abstract

Oscillation in irrigation channels have many undesired consequences such as increased erosion on channel banks, reduced level of service to farmers, increased wear and tear on mechanical equipments, etc. It is therefore important to detect oscillations early. In this paper computationally inexpensive algorithms for detection of oscillatory control loops are applied to operational data from six consecutive pools of an irrigation channel. The algorithms performed well and detected the control loops which gave oscillatory responses. Moreover, the controller which caused the oscillations was also identified. As there can be many control loops in an irrigation channel, methods which are able to detect and locate the cause of oscillations are of great value in the operation of irrigation channels.

Introduction

The UN (United Nations) Water Report (2003) states that the Earth is facing a serious water crisis. In Water Report 2 (2006), it is estimated that water globally required for agriculture in 2025 is in the order of $600{\mathrm{km}}^3$, which is more than the estimated requirement for all domestic uses. It is not always the supply of water, but the ability to fully and efficiently utilize the available quantities, which is the problem. It is therefore important to manage the water resources well and minimize the losses. This applies particularly to networks of irrigation channels, where large amounts of water are wasted due to poor management and control. These losses can be reduced by improving the control of the water levels and flows in the channels, and control of irrigation channels is an area which attracts increased attention, see e.g. Malaterre and Baume (1998) and the references therein, Schuurmans, Hof, Dijkstra, Bosgra, and Brouwer (1999), Gomez, Rodellar, and Mantecon (2002), de Halleux, Prieur, Coron, d’Andréa-Novel, and Bastin (2003), Dulhoste, Georges, and Besancon (2004), Mareels et al. (2005), Litrico and Fromion (2006), Litrico, Malaterre, Baume, Vion, and Ribot-Bruno (2007), Cantoni et al. (2007), Li and Cantoni (2008), Weyer (2008) and Ooi and Weyer (2008).

Well tuned controllers lead to improved water management and reduced wastage, but the effects of a badly tuned controller can propagate through the channel network and cause performance degradation. It is therefore important to monitor the performance of the controllers and isolate and retune those which cause unwanted behavior such as large oscillations in water levels. Large oscillations have many undesired consequences such as increased erosion on channel banks, increased risk of flooding, and reduced service to farmers since the flow delivered to farmers will also oscillate. In addition, oscillations will increase the wear and tear on the gates and increase the electric power consumption.

In a network of irrigation channels, the controlled water levels are monitored in order to detect deterioration of closed loop performance. To assist the operators of the channels, alarms are usually raised when water levels fall outside specified limits, i.e. when the water level is too high or too low. However, there are many control loops in a network of irrigation channels, and automatic performance monitoring tools that evaluate the performance of the control loops are of great value in the operation of irrigation channels.

Due to the fact that experimental access is limited, a performance monitoring tool should be able to detect deterioration of closed loop performance using data available from normal day to day operation. The two most common effects of badly tuned controllers in irrigation channels are sluggishness and oscillations. Zhang and Weyer (2005) considered detection of oscillatory and sluggish controllers in irrigation networks based on comparing the actual system output with the output of a reference model. The methods were quite computationally expensive and required that sensible reference models had been established. Methods for detection of sluggish control loops developed in Hägglund (1999) were considered in Ooi and Weyer (2005). However, as observed by Ooi and Weyer (2005) and Hägglund (1999) the methods were unable to distinguish between a well tuned and an oscillatory control loop.

Performance monitoring and assessment of control loops are widely recognized as an important issue, particularly in the area of process control, see e.g. Harris (1996), Huang and Shah (1999), Paulonis and Cox (2003), Huang (2003), Jelali (2006), Thornhill and Horch (2007) and Ordys, Uduehi, and Johnson (2007). Many approaches have been developed to detect oscillating control loops. Ettaleb, Davies, Dumont, and Kwok (1996) developed an off-line procedure to localize the oscillating loops in a multiloop system based on a describing function method. This method uses normal operational data, however it requires the knowledge of the frequencies of the oscillations. In Miao and Seborg (1999) a method was developed to detect excessive oscillation based on computation of the so-called decay-ratio from normal operating data. This method is an off-line approach, and it requires a minimum of five cycles of oscillations in the output data in order to compute the decay ratio.

In Thornhill, Shah, and Huang (2001), principal components analysis (PCA) is applied to the power spectra of the measurements to detect plant-wide oscillations caused by non-linearities. Assuming that the oscillation is a well defined periodic oscillation, a candidate loop causing the oscillations can be identified using either a distortion factor analysis or a non-linear time series analysis. More recently, Jiang, Choudhury, and Shah (2007) detected plant-wide oscillations using a spectral envelope estimated based on the sampled covariance and the periodogram of the measurements. In that paper, the authors also compared their results with those obtained using the detection approach developed in Xia and Thornhill (2005), where spectral independent component analysis (ICA) was utilized to detect multiple plant-wide oscillations.

The approaches based on frequency domain analysis mentioned above are not directly applicable to irrigation channels. This is mainly due to the fact that offtakes of water, which correspond to load disturbances will produce peaks with substantial power at an ambiguous frequencies leading to false alarms. Another important class of methods not directly applicable here are those where the oscillations are caused by stiction, see e.g. Horch (2007, chap. 7) for an overview.

Hägglund (1995) proposed a computationally inexpensive method for detection of an oscillatory control loop based on the zero-crossings of the setpoint error. The integrated absolute error $(\mathit{IAE})$ is computed to determine if a load disturbance has occurred and a control loop is considered oscillatory if too many load disturbances occur in a given period of time. An approximate on-line version was also developed. A modified $\mathit{IAE}$ method was developed in Thornhill and Hägglund (1997). It is an off-line approach and it is useful when the controller integration time is unknown. However, for the detection algorithm to be useful in irrigation channels, it needs to be able to routinely perform analysis, if not in real time, at least every few hours. Moreover, information about the controller parameters are usually available, at least for irrigation channels with modern control modules like the one considered in this paper. Furthermore, the original algorithm based on $\mathit{IAE}$ was applied to irrigation channels using simulated data in Ooi (2003) and the results were promising. Hence, the original algorithm based on $\mathit{IAE}$ proposed in Hägglund (1995) is the main algorithm considered in this paper.

The algorithm in Thornhill, Huang, and Zhang (2003) used zero-crossings of the auto-covariance function $(\mathit{ACF})$ to detect multiple simultaneously present plant-wide oscillations of different frequencies. The advantage over methods based on zero-crossings of the setpoint error is that the influence of noise is reduced. Even though the algorithm proposed in Thornhill et al. (2003) is intended for off-line analysis and for detection of multiple oscillations of different frequencies, the authors have, with some modifications, applied it to irrigation channels and compared the results with those obtained using $\mathit{IAE}$.

The paper is organized as follows. In Section 2, a description of the irrigation channel is given. In the following section, the models and the designed controllers are given. A review of the considered algorithms for detection of oscillatory control loops is given in Section 4. In Section 5, the algorithms are applied to six consecutive pools using operational data from an irrigation channel. Concluding remarks are given in Section 6.