Chemical processes are inherently nonlinear and their dynamics are naturally described by systems of coupled differential and algebraic equations (DAEs); the differential equations arise from the standard dynamic balances of mass, energy and momentum, while the algebraic equations typically include thermodynamic relations, empirical correlations, quasi-steady-state relations etc. In many cases, the algebraic equations in the DAE model can be readily eliminated to obtain an equivalent ordinary differential equation (ODE) model, which can be used as the basis for controller design. On the other hand, there is a broad class of chemical processes for which the algebraic equations in the DAE models are "singular" in nature, and thus, inhibit a direct reduction of the DAE model into an ODE system. Such DAE systems with singular algebraic equations are said to have a high "index" and they are fundamentally different from ODE systems.
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