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Research Papers

# A Mechanical Approach to the Design of Independent Modal Space Control for Vibration Suppression

[+] Author and Article Information
S. Cinquemani

Assistant Professor
e-mail: simone.cinquemani@polimi.it

F. Resta

Professor
e-mail: ferruccio.resta@polimi.it
Dipartimento di Meccanica, Campus Bovisa Sud,
Politecnico di Milano,
Via la Masa 1,
Milano 20156, Italy

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 21, 2011; final manuscript received May 6, 2012; published online June 18, 2013. Assoc. Editor: Jeffrey Vipperman.

J. Vib. Acoust 135(5), 051002 (Jun 18, 2013) (12 pages) Paper No: VIB-11-1087; doi: 10.1115/1.4024509 History: Received April 21, 2011; Revised May 06, 2012

## Abstract

Many systems have, by their nature, a small damping and therefore they are potentially subjected to dangerous vibration phenomena. The aim of active vibration control is to contain this phenomenon, improve the dynamic performance of the system, and increase its fatigue strength. A way to reach this goal is to increase the system damping, preferably without changing its natural frequencies and vibration modes. In the past decades this has been achieved by developing the well-known independent modal space control (IMSC) technique. The paper describes a new approach to the synthesis of a modal controller to suppress vibrations in structures. It turns from the traditional formulation of the problem and it demonstrates how the performance of the controller can be evaluated through the analysis of the modal damping matrix of the controlled system. The ability to easily manage this information allows us to synthesize an efficient modal controller. Furthermore, it enables us to easily evaluate the stability of the control, the effects of spillover, and the consequent effectiveness in reducing vibration. Theoretical aspects are supported by experimental applications on a large flexible system.

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## Figures

Fig. 1

(a) Reduced model, (b) real system (optimized), (c) real system (nonoptimized)

Fig. 2

Suspended plate

Fig. 3

The plate

Fig. 5

Experimental modal shapes of modeled modes and their corresponding natural frequencies and modal damping ratios

Fig. 6

Experimental setup

Fig. 4

Blocked response transfer functions and mechanical impedance of inertial actuators (normalized with respect to their natural frequency f0)

Fig. 7

Test 1: independent modal control on all the modeled modes. Modal velocities (r¯1 = 1.26 N s/m, r¯2 = 4.21 N s/m, r¯3 = 1.3 N s/m).

Fig. 8

Test 1: independent modal control on all the modeled modes. Accelerations measured by sensors (r¯1 = 1.26 N s/m, r¯2 = 4.21 N s/m, r¯3 = 1.3 N s/m).

Fig. 10

Test 3: independent modal control on the first modeled modes. Accelerations measured by sensors (r¯1 = 0.86 N s/m, r¯2 = 3.22 N s/m, r¯3 = 0.99 N s/m).

Fig. 11

Test 4: independent modal control on the first modeled modes. Modal velocities (r¯1 = 1.26 N s/m, r¯2 = 0 N s/m, r¯3 = 0 N s/m).

Fig. 12

Test 4: independent modal control on the first modeled modes. Accelerations measured by sensors (r¯1 = 1.26 N s/m, r¯2 = 0 N s/m, r¯3 = 0 N s/m).

Fig. 9

Test 3: independent modal control on the first modeled modes. Modal velocities (r¯1 = 0.86 N s/m, r¯2 = 3.22 N s/m, r¯3 = 0.99 N s/m).

Fig. 13

Test 5: independent modal control on the first modeled modes. Acceleration measured by a fourth sensor (r¯1 = 1.26 N s/m, r¯2 = 4.21 N s/m, r¯3 = 1.3 N s/m).

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