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The notion of service times is of such fundamental importance in the analysis of queues that it has long been taken for granted. Intuitively, it is used to represent the time interval that a server is capable of completing a dispatched job. However, actual measurements of service times under simple queues in production lines have encountered practical difficulties, in spite of its seemingly deterministic nature.

This paper proposes two frequency-domain design techniques for rate and amplitude saturation compensators formulated as three degrees of freedom controllers. For single constraint systems, it shows an equivalence between the a posteriori compensator design and the a priori controller synthesis proposed by Horowitz. For rate and amplitude constrained systems, the three degrees of freedom controller is a special case of the general saturation compensator. Through multivariable frequency domain analysis of the compensators, hidden properties of the three degrees of freedom controller are revealed. These inherent properties are utilized in compensator designs by techniques shaping the characteristic loci and speci® cation of singular values. Simulated examples illustrate the success of the design methods.

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