Broadband Multi-Mode Vibration Suppression Using an LQR-Controlled Active Dynamic Vibration Absorber

Abstract

Structural vibration remains a critical challenge in modern mechatronic systems, particularly in lightweight structures, precision machinery, robotic platforms, aerospace components, and smart manufacturing equipment. This paper presents an optimal control strategy for broadband suppression of multi-mode structural vibrations using an Active Dynamic Vibration Absorber (ADVA) regulated by a Linear Quadratic Regulator (LQR) controller. A multi-degree-of-freedom (MDOF) structural model representing a three-storey flexible system subjected to base excitation is developed and integrated with an active absorber capable of generating control forces through actuator action. The coupled structure–absorber dynamics are formulated in state-space form to support feedback-based controller design. The LQR controller is designed by minimizing a quadratic performance index that balances vibration attenuation and actuator control effort. Numerical simulations are performed to evaluate the proposed mechatronic vibration control system under broadband excitation conditions. Frequency response analysis and floor-wise vibration responses are used to compare the uncontrolled structure, passive ADVA, and LQR-controlled ADVA configurations. The proposed controller achieved peak vibration reductions of 28.21%, 27.05%, and 24.90% for Floors 1, 2, and 3, respectively, demonstrating effective broadband vibration suppression and improved closed-loop dynamic performance. Results demonstrate that the LQR-controlled ADVA provides significant attenuation of resonance peaks across multiple vibration modes and achieves superior broadband vibration suppression compared with passive absorption methods. The proposed approach improves dynamic response and closed-loop stability, making it a promising solution for active vibration mitigation in flexible mechatronic and structural systems.