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Local Linearization of Nonlinear SystemsOverview

11.2 Rational Polynomial Approximations

Another approach to obtaining the linear time-invariant (LTI) approximation to a nonlinear system involves the approximation of a nonlinear transfer function by a polynomial ratio. Corresponding functions are provided with standard Mathematica packages and represent Padé, economized rational, general rational, and minimax approximations. The first two are in the context Calculus`Pade`, and the others are in NumericalMath`Approximations`. Note that the built-in function InterpolatingPolynomial may be useful for some approximations, too.

Here is the transfer function describing some ideal heat exchanger.

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The temperature sensor for the exchanger is located so that its reading is delayed a few seconds, which introduces the delay term.

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This loads the necessary package.

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We use the Padé approximation to represent the delay as a polynomial ratio of the order .

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This generates an object suitable for analysis with Control System Professional.

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Local Linearization of Nonlinear SystemsOverview