Control of Transient Response via Polynomial Method ⋆

In this paper, a general discussion on the controller design for transient response control is first conducted based on the polynomial method. It is shown for general all-pole close-loop systems, their step responses have zero or nearly zero overshoot under the nominal characteristic ratio assignment [2.5, 2, 2, . . .]; while the time constant τ determines the speed of response. The control of the classical benchmark two-mass system is introduced as a case study, in which the m-IPD control configuration is adopted. It is found the time constant τ cannot be arbitrarily specified under the m-IPD control configuration and the nominal characteristic ratio assignment. The designed m-IPD controller demonstrates a sufficient damping performance. Meanwhile, the large and negative derivative gain designed under the nominal characteristic ratio assignment leads to a poor robustness. Through the complementary sensitivity function analysis, the robustness of the polynomial-based m-IPD controller design is found to depend on the term of (K∗ ds ∗2 + K∗ ps ∗ + K∗ i ); while the characteristic ratio assignment and the time constant determine the nominal time response of the close-loop control system.