Recently, applications of control theory to avoid overload conditions have been studied. But, in conventional feedback theory, control input is determined by an error between a reference value of a controlled signal and its current value. In real-time systems, a set of active tasks may be time-varying so that the reference value may change according to the set. In this paper, we proposed a novel control method for a fair resource allocation and QoS levels of tasks are used as controlled signals. The proposed adaptation controller allocates a CPU utilization factor to each task with on-line search for the fair QoS level, and the proposed control rule is based on errors between the current QoS levels and their average. Its computation time is small so that it does not yield a heavy overhead.