Decentralised PI control of an irrigation channel

• Operation of irrigation channels and control objectives.
  
• Models for control of irrigation channels for control.
  
• Controller configuration.
  
• Field test of controllers at the Haughton main channel.
  
• Responses with and without feedforward.
  
• Conclusions.

Operations of irrigation channels and control objectives

Ideally an irrigation channel should be operated such that one is able to deliver water to farmers when it is needed, and at the same time the wastage of water should be kept to a minimum. Water is usually wasted when it passes the last gate in the channel as there are few opportunities for recapturing unused water.

Fig 1: Top view of irrigation channel.

The two objectives of always being able to supply water on demand and minimising the losses are conflicting and subject to constraints of environmental, economical and political nature. Often irrigation channels are operated on the conservative side with relatively large flows and high water levels. Under such operating conditions, demand can be met most of the time but the wastage of water tends to be large.

Fig2: Irrigation channel with overshot gates

Gates are located along the channel for regulation of flows and water levels, and electric motors move the gates. At each gate we have measurements of the gate position and the upstream water level, and these measurements are sent to other gates and a central computer via a radio network. As offtakes to farms and side channels are gravity fed, the requirement of being able to deliver water on demand has been equated with setpoint regulation.

Fig 3: Water wheels are used as measuring devices for the volume of
water delivered to the farms. They are located just behind the offtake gates

The requirement of minimum wastage means that the flow over the last gate in the channel should be zero. In some cases a constant flow over the last controlled gate is desirable. This is usually the case when there are manually operated gates further downstream of the last gate under automatic control. For overshot gates in free flow a constant flow corresponds a constant head over gate, that is a constant amount of water above the gate.

In addition to the objectives relating to water levels and flows, the controller should also be able to reject disturbances due to offtakes starting and stopping. Although we expect a multivariable controller to give better performance, decentralised PI control has advantages when it comes to ease of design and implementation. As decentralised PI control only requires local information, the communication requirements are much less than for a centralised controller. Moreover, in many systems existing controller configurations are able to realise decentralised PI controllers, so the control strategy can be implemented relatively easily.

Models for control of irrigation channels for control.

From the system identification experiments we have found that a simple linear model is able to track the main trends in the water level in an irrigation channel. We therefore have the following model for pool 8 (the stretch between gate 8 and 9 on Figure 4)

y9 is the downstream water level, and h8 and h9 are the heads over gate 8 and 9 respectively, see Figure 4. Similar models are obtained for the other pools. The parameters are found using system identification . v(t) is a step disturbance due to offtakes starting and stopping, and there is also unmodelled dynamics due to waves in the reach.

 

Fig 4: Side view of irrigation channel.

 

Controller configuration.
The controllers should keep the water levels on setpoint and reject the step disturbances without inducing excessive waves. For demand driven irrigation channels a distant downstream controller configuration as shown on Figure 4 is most suitable.

From equation (1) it is clear that it is advantageous to let head over gate and not gate position be the manipulated variable, since head is directly related to flow.

PI controllers augmented with first order lowpass filters are used in order to ensure low gain at the wave frequencies, i.e.

and improved responses are achieved by introducing feedforward from downstream head over gate.

where F(s) is a lowpass filter and Kff(<=1) is the feedforward gain. With feedforward information about disturbances are transmitted upstream faster. The controllers are easily tuned using standard frequency response methods.

Field test of controllers at the Haughton Main Channel

During the test gate 11 maintained a given head over gate 11. This is equivalent to maintaining a desired flow over the gate. The change in head over gate 11 at time 260 and 600 have the same effect as if an offtake took place. Gate 8, 9 and 10 were controlled by the augmented PI controller with feedforward from the downstream head.

In order to reduce the wear and tear there was a 0.015m dead band on gate position movements, i.e. if the calculated gate position was less than 0.015m away from the current one, the gate did not move. For this reason the water levels do not stabilise exactly on setpoints, and the dead band is also the reason behind the slow oscillations around setpoints which can be observed, particularly in pool 9.

The controllers show excellent performance. The water levels recovers smoothly with no excessive wave motion to their setpoints. The maximum deviation from setpoint is only about 0.05m which is very good. The response times are about twice as fast as the open loop response times.

There is also very good agreement between the actual water levels and the simulated ones. The third order nonlinear system identification models are used for the simulations.

     

Water level in pool 8, 9 and 10 and head over gate 11 over a 24 hours period.

Upstream of gate 10.

Responses with and without feedforward

 

  

Water level in pool 9 and 10 with and without feedforward.

The above figures show the response in pool 9 and 10 for augmented PI controllers with and without feedforward from the downstream head. The initial disturbance is due to that the head over gate 11 was reduced from 0.30m to to 0.12m. The responses are much better with feedforward. It should however be said that the comparison is not 100 % fair since the controller for pool 10 was retuned between the experiments. Another issue which complicates the comparison is that gate 9 saturated in a fully closed position when there was no feedforward (antiwindup was implemented). Despite this, it is clear that the performance is much better with feedforward, and simulation studies have also shown this. The maximum deviation from setpoint is smaller, and the water levels are back on setpoint much quicker.

Conclusions

The main features of the decentralised controllers are

• Head over gate is the manipulated variable.
  
  
• Additional low pass filters have been introduced to ensure low gains at the wave frequencies.
  
  
• Improved responses have been obtained by using feedforward from downstream head over gate.

The experimental results show that there is a large potential for improving water delivery efficiencies by using modern control and system identification techniques, leading to significant environmental benefits.

For further details see E. Weyer (2002). "Decentralised PI control of an open water channel". In proceedings of the 15th World Congress of IFAC, Barcelona, Spain, July 2002.