Stable Predictive Control of Open‐Channel Flow

This paper presents an algorithm for automatic control of open‐channel flow. The design of a control algorithm is essentially conditioned by two features of the open‐channel dynamics: (1) The time‐inverse propagation process is ill‐posed—thus arise problems to get stable control and assymptotical convergence of the output to the demanded setpoint; and (2) the complete description of the propagation process is mathematically complex, requiring the use of a couple of nonlinear hyperbolic partial differential equations and a posteriori linearization around the steady state. Instead of the complete equations, the control algorithm proposed in this paper uses a simplified model of the unsteady flow to describe the openchannel behavior. This model is used in conjunction with a predictive control strategy, resulting in a control algorithm with guaranteed stability and setpoint convergence as well as mathematical simplicity. Numerical examples illustrate the effectiveness of the control algorithm.