Cubic-spline identification of distributed-parameter systems

The use of doubly cubic splines is presented for the identification of a general second-order distributed-parameter system. The application of doubly cubic splines is shown to result in a system of linear algebraic equations that may be solved for the unknown process parameters in an on-line recursive manner. Due to the advantageous properties of splines, the approximation of partial derivatives is shown to incorporate temporal and spatial smoothing, an important feature when process data is subject to random disturbances. Coefficients of extraneous terms in the assumed model are also correctly identified. A comparison of the spline technique with other identification schemes in current use indicates that the spline application is consistently superior with regard to accuracy of estimation and rate of convergence.