In this work, the properties of the class of parallel feedforward compensators to stabilize linear closed-loop systems are studied. The characteristic equation and its root locus behavior, including its asymptotes, are investigated to leave out the compensators that will not result in a stable closed-loop system. Even though there have been numerous studies relevant to parallel feedforward compensation that result in the optimal integration of squared errors (ISE), the broader view of all possible compensators has not been of much interest in the literature. Nevertheless, this study is important because, in the presence of noise and disturbance, an optimal ISE control design for the nominal plant may perform poorly while a finite ISE design may have a robust and efficient performance. One of such class compensators is parallel feedforward compensator with derivative effort (PFCD) that for a vast number of processes can have impressive properties such as no branch comebacks to the right half plane (RHP) of the root locus plot (LHP black hole effect). The example in this paper shows how effectively PFCD can contract the root locus branches into the LHP.

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