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.
The temperature sensor for the exchanger is located so that its reading is delayed a few seconds, which introduces the delay term.
This loads the necessary package.
We use the Padé approximation to represent the delay as a polynomial ratio of the order .
This generates an object suitable for analysis with Control System Professional.