On the Expediency and Possibilities of Approximating a Pure Delay Link

Abstract

When solving problems of controlling an object with delay, it is often necessary to approximate a pure delay link with a minimum phase link in order to ensure the possibility of using analytical methods for regulator design. There are many approximation methods based on the Taylor series expansion, as well as modified methods. The most famous one is the Padé approximation method. The known approximation methods have significant drawbacks, which this paper reveals. However, there are other methods of forming other types of filters that can serve as a better approximation in determining the delay relationship, although they are not used for these purposes. In particular, methods of forming the desired differential equation of a locked-loop system of a given order by the method of numerical optimization are known. In this case, the locked-loop system behaves like a filter of the corresponding order, the numerator of which is equal to one, and the specified polynomial is in the denominator. Modeling has shown that such a filter is an effective alternative approximation of the delay link and can be used for the same purposes for which it was supposed to use the Padé approximation. The polynomial coefficients in the literature were calculated only up to the 12th order. The higher the polynomial order is, the more accurate the approximation is.