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The paper proposes a new method to tune robust distant downstream proportional integral (PI) controllers for an irrigation canal pool. The method emphasizes the role of gain and phase margins in the controller design, by linking the selection of these robustness indicators to the time domain specifications. This leads to link the frequency domain approach used by automatic control engineers to the time domain approach used by hydraulic engineers. The maximum error corresponding to an unpredicted perturbation is shown to be directly linked to the gain margin and the settling time to the phase margin of the controlled system. The tuning method gives analytical expressions for the controller parameters as function of physical parameters of the canal pool in order to satisfy desired performance requirements. The model is first expressed in terms of dimensionless variables, in order to get generic tuning formulas. The dimensionless PI coefficients are then expressed as functions of time-domain performance requirements. The PI tuning method is evaluated by simulation on a full nonlinear model for a canal pool taken from the ASCE test cases. [ABSTRACT FROM AUTHOR]

Based on the companion paper results, this paper presents a robust tuning method to tune a proportional integral (PI) controller that fulfills the design requirements for a single pool with different hydraulic conditions. The robust PI controller parameters are obtained analytically as a function of the physical parameters of the canal pool. Important implementation issues are also considered. Rules are provided for the sampling time selection in order to recover the continuous-time performance. When the sampling time is imposed, it has to be included in the controller design, by modifying the delay of the system. A simple way is proposed to take account of the gate opening as control action variable, instead of the upstream discharge. This robust PI tuning method is evaluated by simulation on a full nonlinear model of two different canal pools for different flow conditions and different implementations: continuous-time control, discrete-time control, using the discharge or the gate opening as control action variable. Simulation results show that the method leads to efficient realistic PI controllers for a canal pool. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]