LQ control of an irrigation channel

In this paper we consider LQ control of an irrigation channel in which the water levels are controlled using overshot gates located along the channel. Traditionally, irrigation channels have been modelled using the St. Venant equations which are partial differential equation, and hence quite difficult to use for control design. Here we base the design on simple system identification models which capture the relevant dynamics of the irrigation channel, and moreover they are easy to use for control design. It is shown that a quadratic criterion as minimised in LQ control makes sense for the physical control problem at hand. Auxiliary states are included in the state space model in order to achieve zero steady state error and to avoid inducing large waves. As expected, the LQ controller shows better performance than decentralised PI controllers. The water levels recover smoothly from disturbances without excessive oscillations, and the deviations from setpoints are small. Moreover the controller is robust against input uncertainties and unmodelled high frequency dynamics. However, much more effort has to go into the design of an LQ controller than of decentralised PI controllers, and whether the improved performance is worth the additional effort is something that has to be assessed on a case by case basis.