A modified form of first-order perturbation theory, called phase-space interpolated perturbation theory (PSIPT), was developed to more accurately model families of perturbations where changes are intermediate to defined reference and bounding configurations. PSIPT can thus be used on any application where the range of change to the system is known a priori but the magnitude of change is not known. PSIPT is demonstrated for several applications, notably the position of the outer shim control cylinders (OSCCs) at the Advanced Test Reactor (ATR). The current method used for calculating the OSCC positions during a cycle startup utilizes a heuristic trial-and-error approach that is impractical with advanced computationally intensive reactor physics tools. PSIPT is implemented into a method to automate shim rotation prediction for startup.