Time-delay estimation for nonlinear systems with piecewise-constant input
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NOTICE: This is the author’s version of a work that was accepted for publication in Applied Mathematics and Computations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published Applied Mathematics and Computations, Vol. 219, Issue 7. (2013). doi: 10.1016/j.amc.2013.03.015
We consider a general nonlinear time-delay system in which the input signal is piecewise-constant. Such systems arise in a wide range of industrial applications, including evaporation and purification processes and chromatography. We assume that the time-delays—one involving the state variables and the other involving the input variables—are unknown and need to be estimated using experimental data. We formulate the problem of estimating the unknown delays as a nonlinear optimization problem in which the cost function measures the least-squares error between predicted and measured system output. The main difficulty with this problem is that the delays are decision variables to be optimized, rather than fixed values. Thus, conventional optimization techniques are not directly applicable. We propose a new computational approach based on a novel algorithm for computing the cost function’s gradient. We then apply this approach to estimate the time-delays in two industrial chemical processes: a zinc sulphate purification process and a sodium aluminate evaporation process.
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