Traditional codes for initial-value problems adapt to changing conditions by varying the stepsize as the integration progresses. The aim is to keep the local truncation error close to a user-supplied tolerance. Since the revolutionary work of Gustafsson, Lundh, and Söderlind [1], this process has been looked at from the point of view of control theory, and the use of proportional integral (PI) controllers has led to improved computational behavior. This paper reinterprets this work in terms of digital filter theory. Specifically, the aim is to study how the logarithms of the stepsize and the local error estimates respond to varying behavior in the logarithm of the principal error coefficient for certain controllers. A particular difficulty with some controllers is that noise in the input leads to irregular behavior in the outputs. Hence, controllers with the ability to filter out high frequencies will lead to better performance. A number of new and existing controllers are analyzed, and this leads to recommendations depending on the problem class.