Dynamic Analysis and Control of Nonlinear Processes via Nonlinear Transfer Functions

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Abstract - Palazoglu - 9400304 The majority of chemical processes are inherently nonlinear and the lack of analytical tools for nonlinear systems hampers efforts to establish a comprehensive control paradigm, as has been done with the linear systems. The lack of information regarding the behavior of nonlinear processes results in unnecessarily limiting the region of safe operation; to overdesign in an attempt to soften nonlinearities; or to design conservative control systems such that an acceptable operation is maintained. Such engineering solutions may yield suboptimal plant operations, and more economically favorable regimes may be unnecessarily deemed unsafe or unreliable. The PI is developing a technique for the representation of nonlinear dynamics, a parametrization of the solution of nonlinear dynamic equations, and an analytical solution for the nonlinear feedback control problem. The method is based on a particular operation for nonlinearities that yields nonlinear transfer functions via Laplace-like transformations. This permits the algebraic solution of nonlinear ODEs in the transform domain and subsequent realization in the time domain, quite analogous to linear systems analysis. Such a procedure yields an analytical solution for the nonlinear ODEs. It also provides tools for manipulating nonlinear transfer functions to construct and analyze nonlinear closed-loop control systems. This analytical environment, supported by symbolic computations, has potential in altering previous perceptions about nonlinear systems analysis and paves the way for a new approach for nonlinear control and education.