Canal controller design. A multivariable approach using H∞

In this paper, H
_∞
approach is applied in order to design robust controllers for irrigation canals. From an automatic control point of view, an irrigation canal is a strongly coupled multi-variable system. More precisely, it is a cascade of sub-systems (pools) where the control input of each sub-system perturbs the previous sub-system. Control laws are usually obtained by designing monovariable controllers for each subsystem with some ad hoc improvements in order to take into account coupling effects. In this paper, we propose to formulate the design objectives as a weighted H
_∞
optimization problem. To this purpose, we propose a simple guideline for writing a weighted H
_∞
optimization problem taking into account design objectives. The monovariable case is first considered, that is, the control of one sub-system. The obtained H
_∞
controller is then compared to a classical PID-like controller. Second, the same approach is applied to the multivariable case. The obtained controller, which is indeed multivariable, is then analyzed and tested in the non-linear case.