Multiple Mode Spatial Vibration Reduction in Flexible Beams Using H2- and H∞-Modified Positive Position Feedback

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Ehsan Omidi ◽  
S. Nima Mahmoodi
Keyword(s):  
Cantilever Beam ◽  
Vibration Amplitude ◽  
Vibration Suppression ◽  
Controller Design ◽  
Flexible Structures ◽  
Laser Vibrometer ◽  
Beam Vibration ◽  
Spatial Vibration ◽  
Positive Position Feedback ◽  
Position Feedback

This paper develops H2 modified positive position feedback (H2-MPPF) and H∞-MPPF controllers for spatial vibration suppression of flexible structures in multimode condition. Resonant vibrations in a clamped–clamped (c–c) and a cantilever beam are aimed to be spatially suppressed using minimum number of piezoelectric patches. These two types of beams are selected since they are more frequently used in macro- and microscale structures. The shape functions of the beams are extracted using the assumed-modes approach. Then, they are implemented in the controller design via spatial H2 and H∞ norms. The controllers are then evaluated experimentally. Vibrations of multiple points on the beams are concurrently measured using a laser vibrometer. According to the results of the c–c beam, vibration amplitude is reduced to less than half for the entire beam using both H2- and H∞-MPPF controllers. For the cantilever beam, vibration amplitude is suppressed to a higher level using the H2-MPPF controller compared to the H∞-MPPF method. Results show that the designed controllers can effectively use one piezoelectric actuator to efficiently perform spatial vibration control on the entire length of the beams with different boundary conditions.

Positive Position Feedback Vibration Control of a Composite I-Beam With Fuzzy Gain Tuning

2002 ◽  
Author(s):  
H. Gu ◽  
G. Song
Keyword(s):  
Vibration Control ◽  
Least Squares ◽  
Fuzzy System ◽  
Vibration Suppression ◽  
Active Vibration Control ◽  
Flexible Structures ◽  
Training Data ◽  
Sensors And Actuators ◽  
Positive Position Feedback ◽  
Position Feedback

Positive position feedback (PPF) control is widely used in active vibration control of flexible structures. To ensure the vibration is quickly suppressed, a large PPF scalar gain is often applied in a PPF controller. However, PPF control with a large scalar gain causes initial overshoot, which is undesirable in many situations. In this paper, a fuzzy gain tuner is proposed to tune the gain in the positive position feedback control to reduce the initial overshoot while still maintaining a quick vibration suppression. The fuzzy system is trained by the desired input-output data sets by batch least squares algorithm so that the trained fuzzy system can behave like the training data. A 3.35 meter long I-beam with piezoceramic patch sensors and actuators is used as the experimental object. The experiments include the standard PPF control, standard PPF control with traditional fuzzy gain tuning, and PPF control with batch least squares fuzzy gain tuning. Experimental results clearly demonstrate that PPF control with batch least squares fuzzy gain tuner behaves much better than the other two in terms of successfully reducing the initial overshoot and quickly suppressing vibration.

Multimode Modified Positive Position Feedback to Control a Collocated Structure

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Ehsan Omidi ◽  
S. Nima Mahmoodi
Keyword(s):  
Vibration Amplitude ◽  
Flexible Structures ◽  
Low Frequency ◽  
Linear Quadratic Regulator ◽  
Optimization Methods ◽  
Piezo Actuator ◽  
Linear Quadratic ◽  
Positive Position Feedback ◽  
Resonance Frequencies ◽  
Position Feedback

Multimode modified positive position feedback (MMPPF) is proposed to suppress vibrations at multi-resonance frequencies in flexible collocated structures. Typically, flexible structures have large numbers of active modes in low frequency bandwidths, which make them susceptible to multi-frequency resonant vibrations. Hence, it is essential for the controller to have effective suppression on all participating modes. The MMPPF controller consists of a first- and a second-order compensator for each mode, as they are all set parallel for all active modes. Because of suppression performance sensitivity to controller gain parameters, proper gain selection is essential. Here, the linear quadratic regulator (LQR) approach and a proposed method called M-norm are used for gain optimization of the MMPPF controller. The optimized controller is then evaluated experimentally using a cantilever beam, enhanced by a piezoelectric actuator. According to the obtained results, the MMPPF controller reduces vibration amplitudes to the expected lower level, under both LQR and M-norm optimization methods. In some cases, vibration amplitude at the place of piezo-actuator is reduced to even less than the vibration amplitude level of the disturbance input at clamped end.

Nonlinear Vibration Control of Flexible Structures Using Nonlinear Modified Positive Position Feedback Approach

2014 ◽  
Author(s):  
Ehsan Omidi ◽  
S. Nima Mahmoodi
Keyword(s):  
Multiple Scales ◽  
Flexible Structures ◽  
Primary Resonance ◽  
Oscillatory System ◽  
Parameter Analysis ◽  
Superior Performance ◽  
Closed Loop System ◽  
Positive Position Feedback ◽  
Position Feedback ◽  
Nonlinear Vibration Control

A new Nonlinear Modified Positive Position Feedback (NMPPF) controller is proposed in this paper to suppress the nonlinear resonant vibrations in flexible structures. The NMPPF uses a nonlinear second-order feedback compensator to overcome the vibrations at exact primary resonance frequency, and a first-order integrating term to lower the remaining peak amplitudes in the frequency domain. For the closed-loop system, an innovative implementation of the Method of Multiple Scales is employed to obtain the modulation equations. Results demonstrate the superior performance of the NMPPF controller compared to the conventional approach i.e. Positive Position Feedback (PPF), as the suppression performance is improved by 62% in the peak amplitude reduction. The presented parameter analysis of the NMPPF controller also proposes the optimal controller parameters to provide the highest suppression level in the nonlinear oscillatory system.

Active Vibration Control of Resonant Systems via Multivariable Modified Positive Position Feedback

2013 ◽  
Author(s):  
Ehsan Omidi ◽  
S. Nima Mahmoodi
Keyword(s):  
Vibration Control ◽  
Vibration Suppression ◽  
Active Vibration Control ◽  
Optimization Method ◽  
Resonant Structures ◽  
Distributed Structure ◽  
Positive Position Feedback ◽  
Lqr Problem ◽  
Position Feedback ◽  
Resonant Systems

One of the predominant difficulties in the theory of distributed structure control systems comes from the fact that these resonant structures have a large number of active modes in the working band-width. Among the different methods for vibration control, Positive Position Feedback (PPF) is of interest, which uses piezoelectric actuation to overcome the vibration as a collocated controller. Modified Positive Position Feedback (MPPF) is later presented by adding a first-order damping compensator to the conventional second-order compensator, to have a better performance for steady-state and transient disturbances. In this paper, Multivariable Modified Positive Position Feedback (MMPPF) is presented to suppress the unwanted resonant vibrations in the structure. This approach benefits the advantages of MPPF, while it controls larger number vibration modes. An optimization method is introduced, consisting of a cost function that is minimized in the area of the stability of the system. LQR problem is also used to optimize the controller performance by optimized gain selection. It is shown that the LQR-optimized MMPPF controller provides vibration suppression in more efficiently manner.

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