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This paper proposes a novel and efficient distributed flow control scheme for multirate multicast (MR-M), based on the well-known Proportional Integral and Derivative (PID) controllers. The PID controller at each router computes its expected incoming rate and feed backs this rate to its upstream router, such that the local buffer occupancy can be stabilized at an appropriate value. We give the theoretical analysis of the proposed PID controller in terms of system stability. The proposed MR-M controller achieves the fairness in two aspects: 1) The intrasession fairness, i.e., the receivers from the same source within the same multicast session can receive data at different rates, if they subscribe networks with different capacities; 2) The intersession fairness, i.e., the link bandwidth is fairly shared among multiple multicast sessions from different sources. Extensive simulations have been conducted and the results have demonstrated a superior performance of the proposed scheme in terms of system stability, high link utilization, and high throughput.