Proportional and Integral Regulation of Irrigation canal Systems governed by the St Venant Equation

Abstract

The purpose of our paper is to study control and regulation of irrigation canal systems using the St Venant equation. As the linearized models of these systems around equilibrium points are described by symmetric hyperbolic partial differential equations of two independent variables, we consider a class of symmetric hyperbolic systems with boundary observations. We present the exact observability and exponential stability results of Rauch and Taylor in the general case. These results are made explicit by providing estimates of necessary observation length for observability and estimates of exponential decay rate for stability in function of structure parameters. Then, wc apply these results to show that for an one-reach irrigation canal system governed by the St Venant equation, the linearized model around an equilibrium point is exponentially stable for the open loop system. To guarantee a robust regulation arid a robust stability of the dosed loop system wc propose proportional and integral output feedback controllers (PI-Controllers) which assure exponential stabilization of the linearized model and suppress (known or unknown) constant disturbances in the system. The work that we present here brings out a systematic synthesis method for designing boundary stabilizing PI-Controllers for irrigation systems based on linearized models of the St Venant equation