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.

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.

LQR for State-Bounded Structural Control

1996 ◽  
Vol 118 (1) ◽  
pp. 113-119 ◽  
Author(s):  
C.-H. Chuang ◽  
D.-N. Wu ◽  
Q. Wang
Keyword(s):  
Structural Control ◽  
Vibration Amplitude ◽  
Gain Control ◽  
Linear Quadratic Regulator ◽  
Matching Condition ◽  
High Gain ◽  
Time Instant ◽  
Linear Quadratic ◽  
Earthquake Excitation ◽  
High Gain Control

In order to prevent structural damages, it is more important to bound the vibration amplitude than to reduce the vibration energy. However, in the performance index for linear quadratic regulator (LQR), the instantaneous amplitude of vibration is not minimized. An ordinary LQR may have an unacceptable amplitude at some time instant but still have a good performance. In this paper, we have developed an LQR with adjustable gains to guarantee bounds on the vibration amplitude. For scalar systems, the weighting for control is switched between two values which give a low-gain control when the amplitude is inside the bound and a high-gain control when the amplitude is going to violate the given bound. For multivariable systems, by assuming a matching condition, a similar controller structure has been obtained. This controller is favored for application since the main structure of a common LQR is not changed; the additional high-gain control is required only if the vibration amplitude fails to stay inside the bound. We have applied this controller to a five-story building with active tendon controllers. The results show that the largest oscillation at the first story stays within a given bound when the building is subject to earthquake excitation.

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.

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.

scholarly journals Optimization of parameters of a modal active control in a beam of composite material

2018 ◽  
Vol 211 ◽  
pp. 19002
Author(s):  
Camila Albertin Xavier da Silva ◽  
Erik Taketa ◽  
Edson Hideki Koroishi ◽  
Fabian Andres Lara-Molina ◽  
Albert Willian Faria
Keyword(s):  
Composite Material ◽  
Active Control ◽  
Active Vibration Control ◽  
Linear Quadratic Regulator ◽  
Optimization Methods ◽  
Linear Matrix ◽  
Linear Quadratic ◽  
Electromagnetic Actuators ◽  
Optimization Of Parameters ◽  
The Time Domain

The present work proposes the active vibration control in a beam of composite material, using electromagnetic actuators, in order to obtain a reduction in the response of the displacement of the system associated to a reduction in energy consumption. The control theory used was the linear quadratic regulator solved by linear matrix inequalities. The electromagnetic actuator was then linearized using a methodology similar to that used in magnetic bearings. The work also proposes to study the optimization of parameters applied in this active control, by means of the heuristic optimization methods. From numerical simulations, the system´s response was obtained in the time domain that demonstrated the efficiency of the proposed technique in the active control of vibrations.

System Identification and Robust Controller Design Using Genetic Algorithms for Flexible Space Structures

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Marco P. Schoen ◽  
Randy C. Hoover ◽  
Sinchai Chinvorarat ◽  
Gerhard M. Schoen
Keyword(s):  
Minimum Distance ◽  
Controller Design ◽  
Flexible Structures ◽  
Linear Quadratic Regulator ◽  
Performance Criteria ◽  
Space Structures ◽  
Identification Algorithm ◽  
Robust Controllers ◽  
Linear Quadratic ◽  
Flexible Space Structures

This paper is concerned with the problem of identifying and controlling flexible structures. The structures used exhibit some of the characteristics found in large flexible space structures (LFSSs). Identifying LFSS are problematic in the sense that the modes are of low frequency, lightly damped, and often closely spaced. The proposed identification algorithm utilizes modal contribution coefficients to monitor the data collection. The algorithm is composed of a two-step process, where the input signal for the second step is recomputed based on knowledge gained about the system to be identified. In addition, two different intelligent robust controllers are proposed. In the first controller, optimization is concerned with performance criteria such as rise time, overshoot, control energy, and a robustness measure among others. Optimization is achieved by using an elitism based genetic algorithm (GA). The second controller uses a nested GA resulting in an intelligent linear quadratic regulator/linear quadratic Gaussian (LQR/LQG) controller design. The GAs in this controller are used to find the minimum distance to uncontrollability of a given system and to maximize that minimum distance by finding the optimal coefficients in the weighting matrices of the LQR/LQG controller. The proposed algorithms and controllers are tested numerically and experimentally on a model structure. The results show the effectiveness of the proposed two-step identification algorithm as well as the utilization of GAs applied to the problem of designing optimal robust controllers.

Optimized Near Minimum Time Control of Flexible Structures Using Variable Gain (LQG) Control Strategies

2005 ◽  
Vol 128 (3) ◽  
pp. 402-407 ◽  
Author(s):  
Rajiv Kumar ◽  
S. P. Singh ◽  
H. N. Chandrawat
Keyword(s):  
Control Strategies ◽  
Flexible Structures ◽  
Linear Quadratic Regulator ◽  
Control Voltage ◽  
Control Input ◽  
Linear Quadratic ◽  
Variable Gain ◽  
Time Control ◽  
Present Technique ◽  
Time Optimal

A neural network based time optimal control of flexible structures is presented. The implementation is done on a flexible inverted L structure with surface-bonded piezoceramic sensors/actuators. The state-space presentation, from control input voltages to sensor output voltages is established in multivariable form. A variable gain multi-input multi-output linear quadratic regulator controller is designed and implemented. The controller gains are varied as the modal energy of the system decreases. The gains are varied in such a manner that the system utilizes maximum control energy from fixed amplitude of control voltage. The gains are calculated by solving the Riccatti equation with weightage in performance index that varies according to the states of the system. Thus at periodic intervals, the gains are updated to fully utilize the available control voltage. Comparison of the present technique is done with the classical bang-bang controller.

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.

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