Linear-like discrete-time fuzzy control in the regulation of irrigation canals

A linear-like discrete-time fuzzy controller was designed to control and stabilize a single-pool irrigation canal. Saint Venant equations for open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear partial differential equations. Using the linear optimal control theory, a traditional linear quadratic regulator (LQR) was first developed for an irrigation canal with a single-pool, and the results were observed. Then a linear-like global system representation of a discrete-time fuzzy system was proposed by viewing a discrete-time fuzzy system in a global concept and unifying the individual matrices into synthetic matrices. This linear-like representation aided development of a design scheme for a global optimal fuzzy controller in the way of the general linear quadratic approach. Based on this kind of system representation, a discrete-time optimal fuzzy control law that can achieve global minimum effect was developed. An example problem with a single-pool was considered for evaluating the performance of the discrete-time optimal fuzzy controller in the control of irrigation canals. The results obtained with the optimal fuzzy controller were compared to the results obtained with a traditional linear quadratic regulator. The discrete-time fuzzy controller was the best for the operation of the canal system, reaching the optimal performance index under unknown demands.