Nonlinear modelling and control of a long river stretch

A simple nonlinear model for flow transfer in a river stretch is obtained through several steps: first the diffusive wave model, a quasilinear partial derivative equation, is linearized around equilibrium points, corresponding to the hydraulic equilibrium regimes. Secondly, the moment matching method is used to approximate the linear PDE by a linear ODE with a time delay indexed by the value of the reference discharge. A single nonlinear model is then derived analytically from this family of linear models. The proposed model can reproduce the nonlinear behavior of the time-delay with discharge variations. This simple nonlinear model is inserted into a Internal Model Controller framework in order to obtain a nonlinear controller to control river flow. Simulations demonstrates the performance of the nonlinear controller compared to a linear one.