On Pole-Zero Assignment of Vibratory Systems by Multi-Input Feedback Control

TL;DR

This paper introduces a novel multi-step, two-stage feedback control method for assigning poles and zeros in vibratory systems, improving control precision through a reformulated approach and linear matrix inequalities.

Contribution

It presents a new multi-input pole-zero assignment technique that reformulates the problem into a single-input scenario and employs linear matrix inequalities for enhanced control.

Findings

Effective pole-zero assignment demonstrated through numerical examples

Reformulation simplifies multi-input problems into manageable single-input steps

Linear matrix inequalities improve the accuracy of pole placement

Abstract

In this paper, we consider the pole-zero assignment problem for vibratory systems via multi-input feedback control. We propose a multi-step two-stage approach for solving the multi-input pole-zero assignment problem. We first reformulate the assignment problem as a multi-step single-input pole-zero assignment problem. Then, in each step, we propose a two-stage approach for solving the single-input pole-zero assignment problem. In the first stage, based on the measured receptances, we replace the selected zeros of the prescribed open-loop point receptance to the desired locations, where we need to solve a small underdetermined linear equation for finding the corresponding columns of the feedback matrices. In the second stage, by using linear matrix inequalities, the complete closed-loop poles are assigned to the prescribed subregion of the complex left-hand plane. Finally, we give some numerical examples to demonstrate the effectiveness of our method.