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.

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.

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.

Independent Modal Space Control With Positive Position Feedback

1992 ◽  
Vol 114 (1) ◽  
pp. 96-103 ◽  
Author(s):  
A. Baz ◽  
S. Poh ◽  
J. Fedor
Keyword(s):  
Control System ◽  
Active Control ◽  
Complex Structure ◽  
Flexible Structures ◽  
Optimal Time ◽  
Time Sharing ◽  
Positive Position Feedback ◽  
Position Feedback ◽  
Active Control System ◽  
Modal Space

This study presents an Independent Modal Space Control (IMSC) algorithm whose modal control forces are generated based on a Positive Position Feedback (PPF) strategy. This is in contrast to conventional modal controllers that rely in their opeation on negative feedback of the modal position and velocity. The proposed algorithm combines the attractive attributes of both the IMSC and the PPF. It maintains the simplicity of the IMSC as it designs the controller of a complex structure at the uncoupled modal level. At the same time, it utilizes only the modal position signal to provide a damping action to undamped modes. The paper presents the theory behind this algorithm when using first order filters to achieve the PPF effect. The optimal time constants of the filters are determined. The performance of the algorithm is enhanced by augmenting it with a “time sharing” strategy to share a small number of actuators between larger number of modes. The effectiveness of the algorithm in damping out the vibration of flexible structures is validated experimentally. A simple cantilevered beam is used as an example of a flexible structure whose multi-modes of vibration are controlled by a single actuator. A piezo-electric actuator is utilized, in this regard, as a part of a computer-controlled active control system. The performance of the active control system is determined in the time and the frequency domains. The results are compared with those obtained when using the IMSC, PPF with second order filters, the Psuedo-Inverse (PI) and a Modified Independent Modal Space Control (MIMSC). The experimental results suggest the potential of the proposed method as a viable means for controlling the vibration of large flexible structures.

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 nano-beam based on capacitive acoustic sensors

2020 ◽  
Vol 64 (1-4) ◽  
pp. 421-429
Author(s):  
Lei Wan ◽  
Canchang Liu ◽  
Weixu Kong ◽  
Yingchao Zhou ◽  
Chicheng Ma
Keyword(s):  
Vibration Control ◽  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Graphene Film ◽  
Primary Resonance ◽  
High Sensitivity ◽  
Vibration Signal ◽  
System Stability ◽  
Acoustic Sensors ◽  
Nonlinear Vibration Control

The nonlinear vibration control of the Euler–Bernoulli beam is studied based on capacitive micro-mechanical acoustic sensors The graphene film has the characteristics of high sensitivity and high accuracy which can be applied to sense the vibration signal. Capacitive micro-mechanical acoustic sensors can be used to detect the acoustic signal of the vibration of the nano-beam. The nonlinear vibration control equation of nano-beam can be established with the displacement and velocity voltage feedback controller based on capacitive micro-mechanical acoustic sensors. The amplitude-frequency response equation of the primary resonance of nano-beam can be gotten by using the multiple scales method. The relationship between the nonlinear vibration of nano-beam and system parameters is investigated. The influencing factors of how to weak system nonlinearity and enhance system stability are analyzed. The static bifurcation behavior of the system is discussed. The numerical results show that the nonlinearity of vibration can be reduced and the stability of the system can be improved by selecting the appropriate control gains and appropriately reducing the amplitude of DC and AC excitation voltages.

Determination of optimal positive position feedback parameters by using nonsmooth H∞ synthesis

2020 ◽  
pp. 107754632094379
Author(s):  
Bin E ◽  
Jinjun Shan ◽  
Muhammad Atif Khushnood ◽  
Xiaogang Wang ◽  
Naigang Cui
Keyword(s):  
Control Structure ◽  
Multiple Input Multiple Output ◽  
Flexible Structures ◽  
Optimal Parameters ◽  
Feedback Controllers ◽  
Positive Position Feedback ◽  
Multiple Input ◽  
Position Feedback ◽  
Input Multiple Output ◽  
Fixed Order

This article presents a method for determining optimal parameters of positive position feedback controllers used for suppressing vibration of flexible structures. The method is based on solving the H∞ synthesis problem with additional constraints on the controller structure. The method allows for independent control of damping added to each mode. Moreover, optimal parameters for both simple input simple output and multiple input multiple output control formulations can be obtained. The effectiveness of the method is shown by comparing the results of both multiple input multiple output and simple input simple output positive position feedback controllers designed by the proposed method, with the simple input simple output positive position feedback controller designed by analytically derived optimal parameters. Moreover, results of controllers designed with the fixed-order transfer function control structure are also presented to emphasize the advantages offered by the positive position feedback control structure.

Sign in / Sign up

Export Citation Format

Share Document