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On Internet servers, there is an increasing demand for provisioning of fine-grained quality of service (QoS). Feedback control provides a sound way for such QoS provisioning by amortizing the effect of disturbances from unpredictable and dynamic server workloads. The performance of a feedback control approach is dependent on its agility to the workload changes. Queueing-model based prediction is effective in improving the agility. In this paper, we present a feedback control approach to manage the processing rate on Internet servers for QoS provisioning with respect to slowdown. Slowdown is the ratio of a request's queueing delay to its service time and reflects the requirement that all requests should be treated equally regardless of their resource requirements. The approach adjusts the processing rate of a class using an integral feedback controller according to measured deviations from the target slowdown ratios. For agility, a queueing-model based predictor is integrated to periodically estimates the processing rate of the class. The experimental results under various environment settings demonstrate the approach's effectiveness, robustness, and agility in providing proportional slowdown differentiation services.