All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

Abstract

In this paper, a simple derivation for an all-stabilizing proportional controller set for first-order bi-proper systems with time delay is proposed. In contrast to proper systems, an extremely limited number of studies are available in the literature for such bi-proper systems. To fill this gap in the literature, broader aspects of the stabilizing set are taken into consideration. The effect of zero on the stabilizing set is clearly discussed and we also prove that, when their zeros are placed symmetrically to the origin, the stabilizing set of non-minimum phase plant is always smaller than that of the minimum phase one. Moreover, for an open-loop unstable plant, maximum allowable time delay (MATD) is explicitly expressed as a function of the locations of the pole and zero. From that function, it is shown that for a minimum phase plant, the supremum of the MATD is two times that of the time constant of the plant and the infimum of the MATD is the time constant of the plant. We also prove that the supremum is the time constant and the infimum is zero for a non-minimum phase plant.

Robust PID controller design via dominant pole assignment for systems with parametric uncertainties

“…Design of robust PID type controllers for uncertain parameter systems has an important place. Many researchers studied and still continue to study the stabilization of the entire plant using robust PID type controllers [13][14][15][16][17][18][19][20]. Although the robust stability of a closed-loop system is the most important criterion from the control engineering perspective, the robust performance is also crucial.…”

Robust Stabilization of a Servomechanism With Respect To Time-Delay

“…From the mathematical point of view, for Linear Time Invariant (LTI) and Single Input Sıngle Output (SISO) systems, this fact is mostly caused by the fact that time-delay term adds infinite number of poles in the closed-loop. As a result, analysing the performance of time-delay systems, even assessing the stability becomes more complicated in such systems [9][10][11][12][13][14][15][16]. As might be expected from the operational and the mathematical viewpoints and as stated above, the amount of the time-delay may considerably attenuate the overall control performance, even it may lead the system to instability.…”