Ever-increasing demands from the industry require better performance out of the same system to achieve a competitive advantage. In systems functioning at different operating points, a fundamental trade-off between robustness and performance can limit the achieved performance. Linear Parameter Varying (LPV) controller synthesis can overcome this issue by adapting the controller parameters with the operating points. This requires a parametric LPV model of the system, which in many cases is difficult or costly to obtain. Recently, LPV controller design methods based on the frequency-domain data in different operating points have shown to result in great performance without the need of a parametric LPV model. In these approaches, however, the scheduling parameters are assumed to be measured exactly. In this paper, a new approach is proposed to design LPV controllers with slowly varying uncertain scheduling parameters, using only the frequency response data of a SISO system around different operating points. The proposed approach is applied on a rotary table, a machine used in the manufacturing industry. The dynamics of the rotary table depend on the inertia of the object mounted on- top which cannot be directly measured. Since the scheduling parameter cannot be measured, it is estimated using a short sequence of data that leads to an inexact estimation with interval uncertainty. For the system considered, the LPV controller designed by the proposed approach shows clear improvement over the state-of-the-art robust controller synthesis approaches.