Discontinuity analysis for the treatment of nonlinear lumped-parameter systems for singular inputs
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Different approaches suggested for the treatment of nonlinear systems subjected to singular inputs are either approximate or difficult to apply. In this paper, discontinuity analysis is used for this treatment, and is found to represent a good compromise between accuracy and ease of applicability. An example of non-isothermal CSTR representing nonlinear lumped-parameter chemical engineering systems is considered for the treatment. In the treatment, the integration of a model is carried out across the time of jump discontinuity by including singularity in the cause. This allows a priori estimation of initial conditions. The estimated initial conditions are then used for the initialization of the numerical solution of the model, whose singular input variables are set at their pre-initial values. The accuracy of the procedure in providing a reliable estimation of the system behavior is quantified by comparison with the numerical solutions initialized through the application of physical balances to the initial effects of singularity on the system, and with the numerical solutions obtained through pulse approximation for impulse. The procedure has simple and uniform applicability in comparison to the application of physical balances, and is substantially accurate than the commonly used pulse approximation method.
KeywordsDynamic simulation Impulse Nonlinear Process modeling Systems analysis
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