1 A SINGULAR VALUE DECOMPOSITION BASED KALMAN FILTERING FOR CONTROL OF IRRIGATION CANALS

Abstract:- A discrete-time linear Kalman filtering algorithm based on singular value decomposition (SVD) technique is applied to the control of irrigation canals. The Saint-Venant equations of open-channel flow are linearized using the Taylor series and a finite difference approximation of the original nonlinear, partial differential equations. Using the linear optimal control theory, a Linear Quadratic Gaussian (LQG) controller is designed for an irrigation canal with 6 gates and 5 pools. The Kalman state estimator in the LQG controller is designed using both conventional and singular value decomposition (SVD) techniques. The results from both techniques are compared to observe the performance of state variables estimation for an irrigation canal. The singular value decomposition (SVD) based Kalman filter formulation has a good numerical stability and can handle correlated measurement noise without any additional transformation. In conventional Kalman filter applications, measurements are generally designed to be uncorrelated; and this may be a large source of error. The results of this study show that a SVD based Kalman filter for irrigation canals offers an alternative to conventional Kalman filter when the flow depth measurements in the canal are correlated