Identification and Adaptive Control for Open Channel Water Flow Systems

Despite the continuous advances in the control design for water flow systems such as irrigation and sewer systems, the design and deployment of efficient water flow control systems requires a careful and efficient fine-tuning of their parameters prior and during the actual system operation. In the majority of water flow control applications, the controller design is based on simplified models (e.g., linear models assuming a fixed time-delay) for the water flow dynamics and as a result the initial controller design calls for a major fine-tuning at the initial deployment of the control system; moreover, the frequent changes in water management commands/needs as well as the severe exogenous disturbances call for a continuous update of the controller parameters. Conventional controller tuning approaches cannot be used for the efficient tuning of the controller parameters in water flow control systems, mainly due to the highly nonlinear dependence of the time-delay with respect to the water flow. In this article, we first introduce and analyze both by means of mathematical analysis and simulation experiments, a computationally simple and efficient methodology for the identification of water flow system dynamics as a State-dependent Delay Difference Equation (sdDDE) model. The main advantage of this methodology is that it can explicitly identify the nonlinear relationship between the water flow system states and the system time-delay. Then, we show that such an sdDDE identification scheme can be used for the efficient adaptive tuning of a general class of water flow control systems. More precisely, by exploiting the knowledge–obtained using the sdDDE identification scheme–regarding the nonlinear characteristics of the time-delay, we come up with a convergent adaptive control scheme, which is able to quickly track rapid changes in setpoint commands and efficiently attenuate severe exogenous disturbances. Simulation results demonstrate that the proposed scheme out-performs significantly existing well fine-tuned linear and nonlinear control schemes.