Class of Stabilizing Parallel Feedforward Compensators for Nonminimum-Phase Systems

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.

Analytical Statistical Study of Linear Parallel Feedforward Compensators for Nonminimum-Phase Systems

In this work, a new parallel feedforward compensator for the feedback loop of a linear nonminimum-phase system is introduced. Then, analytical statistical arguments between the existing developed methods and the innovated method are brought. The compelling arguments suggest the parallel feedforward compensation with derivative (PFCD) method is a strong method even though at its first survey it seems to be optimistic and not pragmatic. While most of the existing methods offer an optimal integral of squared errors (ISE) for the closed-loop response of the nominal plant, the PFCD offers a finite ISE; in reality, typically, the nominal plant is not of main concern in the controller design and the performance in the presence of mismatch model, noise, and disturbance has priority. In this work, there are several arguments brought to bold the importance of the innovated PFCD design. Also, there is a closed-loop design example to show the PFCD effectiveness in action.