Polynomial-based Inertia Ratio Controller Design for Vibration Suppression in Two-Mass System

In this paper, a polynomial-based design of inertia ratio controllers is discussed for the vibration suppression in two-mass system. A tradeoff relationship is shown to exist between damping and robustness performances in the control problem. A desirable inertia ratio of 5/16 is derived at which IP control provides a proper damping. Then two approaches for the control of equivalent inertia ratio are discussed without/with load velocity feedback. "Resonance ratio control" is capable of providing a sufficient damping for large inertia ratios by using only drive velocity feedback. However, a negative derivative gain is necessary, which leads to a poor robustness. By using both drive and load velocity feedback, the equivalent inertia ratio can be exactly specified as 5/16. The proposed "inertia ratio controller" design shows an obvious improvement in terms of both damping and robustness performances. All the experimental results validate the polynomial-based theoretical analysis and controller design. The demonstrated generality and the explicit expression of damping indicate the promising prospect of the polynomial-based controller design for solving more complicated control problems.