Abstract
This paper studies linear time-invariant systems with an input delay and only real open-loop poles. The systems in discussion have one unstable pole but no zeros. To design P, PD, PI and PID-controllers, the closed-loop system eigenvalue-loci are constructed with respect to the controller gains, like the root-locus for non-delay systems. Via the concept of leading locus, stability criteria are derived for the controllers, and performances of output responses are analyzed. Finally the proposed methods are tested with examples to illustrate the application process and demonstrate the effectiveness.
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