Robust Active Vibration Control of Smart Structures; a Comparison between Two Approaches: µ-Synthesis & LMI-Based Design

Abstract

The purpose of this paper is comparing the performance of two robust control designing approaches in smart structures. First, an accurate model of a homogeneous plate with special boundary conditions is derived by using of modal analysis. Then, some primitive p late's modes are considered as nominal system and the remaining modes are left as a mu ltip licat ive unstructured modelling uncertainty. Next, t wo robust controller are designed using µ-Synthesis & LMI-Based Design approaches based on the augmented plant composed of the nominal model and its accompanied uncertainty. Finally, the robustness of two uncertain closed-loop models and the d ifference between t wo controller performances has been investigated. Obtained results show the higher performance of LMI-Based Design approach in rejection of random disturbances.

Multiple-input multiple-output robust vibration control for constrained gyroelastic solar panel considering parametric and un-modeled dynamic uncertainties

“…Based on the principle of minimizing the scaled infinite norm of the system (Balas and Doyle, 1994; Zhou et al, 1996), μ-synthesis breaks through H∞ control’s conservative limitation and can effectively solve the robust controller design problem with structured uncertainties. In the previous study, μ-synthesis is generally used to suppress the vibration of the flexible structure with piezoelectric actuators (Hu and Xu, 2013; Khushnood et al, 2018; Kumar, 2013; Li et al, 2003; Oveisi and Gudarzi, 2012), and there are few researches on its application for gyroelastic body. In addition, although the selection method of design weights for SISO system is studied by Atif (Khushnood et al, 2018), MIMO system still needs to be further study.…”

Active vibration control of a blade element with uncertainty modeling in PZT actuator force

“…Control effectiveness in flexible systems with piezoelectric actuation depends on the applied control methods. Many types of controller design methods, such as robust mixed H2/H∞ (Bolat and Sivrioglu, 2017; Oveisi and Nestorović, 2018), adaptive feedforward control (Zhu et al., 2017), quantitative robust linear parameter varying H∞ control (Zhang et al., 2015), adaptive robust sliding mode control (Wang et al., 2014), robust adaptive vibration control (Moradi Maryamnegari and Khoshnood, 2019), robust µ-synthesis and linear matrix inequalities (LMI)-based design (Oveisi and Gudarzi, 2012), velocity feedback control (Omidi and Mahmoodi, 2016), and gain-scheduled control (Becker et al., 2017), have been studied for different PZT bonded flexible systems.…”

Vibration attenuation of spacecraft in the presence of parametric and unmodeled dynamics uncertainties using collocated and noncollocated control: A comparative study

“…µ-synthesis is a control technique that offers the advantage of maintaining robust performance and stability in the presence of plant uncertainties. However, relatively few studies have employed it for suppressing vibration through piezoelectric actuators (Li et al., 2003; Oveisi and Gudarzi, 2012; Hu and Xu, 2013; Kumar, 2013); also, the guidelines for selecting design weights are vague. In this paper, expressions relating the 2-norm of the vector of regulated outputs and closed-loop modal damping to the weights used for µ-control synthesis are derived.…”