Abstract
It is known that the transfer function of sampled-data system has so-called intrinsic and discretization zeros, the latter of which are often unstable and have no counterpart for the original continuous-time system; moreover have no closed expression in terms of the continuous-time zeros and the sample time. This fact limits the application range of inversion-based feedforward compensation for digital control systems because the stability of the feedforward controller essentially depends on the stability of the sampled zeros. Fortunately, recent research has revealed that discretization zeros of sampled-data systems tend to zeros of the so-called Euler-Frobenius polynomial, the location of which has a regularity. Based on this fact and the computing power of recently emerging symbolic mathematics software, this paper presents polynomial expression formulas of all discretization zeros with respect to the sample time for general sampled-data systems. The result is applied to developing a method to relocate the zeros of sampled-data systems and stabilize inversion-based feedforward controllers.
