A Comparison of Recursive Least Squares Estimation and Kalman Filtering for Flow in Open Channels


Abstract: An integrated approach to the design of an automatic control system for canals using a Linear Quadratic Gaussian regulator based on recursive least squares estimation was developed. The one-dimensional partial differential equations describing open channel flow (Saint-Venant) equations are linearized about an average operating condition of the canal. The concept of optimal control theory is applied to drive a feedback control algorithm for constant-level control of an irrigation canal. The performance of state observers designed using the recursive least squares technique and the Kalman filtering technique is compared with the results obtained using a full-state feedback controller. An example problem with a multi-pool irrigation canal is considered for evaluating the techniques used to design an observer for the system. Considering the computational complexity and accuracy of the results obtained, the recursive least squares technique is found to be adequate for irrigation canals. In addition, the recursive least squares algorithm is simpler than the Kalman technique and provides an attractive alternative to the Kalman filtering.

Keywords: Optimal control, Least squares estimation, Kalman filters, Open-channel flow

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