Membrane technology is one of the most reliable and efficient separation processes for water treatment. However, one of the main limiting factors in the membrane filtration process is fouling, which is the deposition or adsorption of contaminants on the membrane surface or inside the membrane pores. In this paper, induced-vibrations is proposed as a cleaning-aid by preventing and reducing membrane fouling. The response of the membrane to periodic displacement at its boundaries is found mathematically and experiments are performed using a tabletop shaker to verify the model. Humic Acid (HA), a common water foulant in filtration systems, are distributed on the surface and their motion is observed at various forcing frequencies. Here we aim to utilize induced vibrations to excite the membrane’s resonances and take advantage of the spatial non-uniformity of the resulting mode shapes. In these modes, there will be regions of the membrane which vibrate out-of-phase with one another, potentially reducing the deposition of particles on the membrane surface (fouling) further by creating instability in the fluid near the membrane surface. Because the amplitude of vibration varies across the membrane surface, the deposition of foulants will also occur unevenly. These uneven patterns of fouling may be able to be removed from the membrane more easily during subsequent cleaning.
Atomic Force Microscopy (AFM) uses a scanning process performed by a microcantilever beam to create a three dimensional image of a nano-scale physical surface. AFM includes a microcantilever probe with a tip at the end that is controlled in order to keep the force between the tip and the surface constant by changing the distance of the microcantilever from the surface. Some microcantilevers have a layer of piezoelectric material on one side of the microcantilever for actuation purpose. An accurate understanding of the microcantilever motion and tip-sample force is needed to generate accurate imaging. In this paper, the equations of motion for an AFM piezoelectric microcantilever probe are derived for a nonlinear contact force. The analytical expressions for natural frequencies and mode shapes are determined. Then, the analytical frequency response of the piezoelectric probe is found using the method of multiple scales. The effects of nonlinear excitation force on the microcantilever probe’s frequency and amplitude have been analytically studied. The force nonlinearities lead to a frequency shift in the response. Accurately modeling this frequency shift during contact mode of the AFM probe is a significant consideration for the generation of more accurate imaging.
This paper introduces the Modified Positive Velocity Feedback (MPVF) controller as an alternative to the conventional Positive Position Feedback (PPF) controller, with the goal of suppressing unwanted resonant vibrations in smart structures. The MPVF controller uses two parallel feedback compensators working on the fundamental modes of the structure. The vibration velocity is measured by a sensor or state estimator and is fed back to the controller as the input. To control n-modes, n sets of parallel compensators are required. MPVF controller gain selection in multimode cases highly affects the control results. This problem is resolved using the Linear Quadratic Regulator (LQR) and the M-norm optimization method, which are selected to form the desired performance of the MPVF controller. First, the controller is simulated for the two optimization approaches, and then, experimental investigation of the vibration suppression is performed. The LQR-optimized MPVF provides a better suppression in terms of vibration displacement. The M-normoptimized MPVF controller focuses on modes with higher magnitudes of velocity and provides a higher level of vibration velocity suppression than LQR-optimized method. Vibration velocity attenuation can be very important in preventing fatigue failures due to the fact that velocity can be directly related to stress.
The modified positive position feedback controller, an active vibration control method that uses
collocated piezoelectric actuator actuators and sensors, is developed using an adaptive controller.
The adaptive mechanism consists of two main parts: 1) Frequency adaptation mechanism, and 2)
Adaptive controller. Frequency adaptation only tracks the frequency of vibrations using Fast
Fourier Transforms. The obtained frequency is then fed to MPPF compensators and the adaptive
controller. This provides a unique feature for MPPF, by extending its domain of capabilities from
controlling tonal vibrations to broad band disturbances. The adaptive controller mechanism
consists of a reference model that is of the same order as the MPPF system and its compensators.
The adaptive law provides the additional control force that is needed for controlling frequency
changes caused by broad band vibrations. The experimental results show that the frequency
tracking method that is derived has worked quite well. The results also indicate that the MPPF
can provide significant vibration reduction on a cantilever beam that is used throughout the
experiments.
Modified acceleration feedback (MAF) control, an active vibration control method that uses collocated piezoelectric
actuator actuators and sensors is improved using an optimal controller. The controller consists of two main parts: 1)
Frequency adaptation that uses Adaptive Line Enhancer (ALE), and 2) an optimal controller. Frequency adaptation
tracks the frequency of vibrations using ALE. The obtained frequency is then fed to MPPF compensators and the optimal
controller. This provides a unique feature for MAF, by extending its domain of capabilities from controlling tonal
vibrations to broad band disturbances. The optimal controller consists of a set of optimal gains for wide range of
frequencies that is provided, related to the characteristics of the system. Based on the tracked frequency, the optimal
control system decides to use which set of gains for the MAF controller. The gains are optimal for the frequencies close
to the tracked frequency. The numerical results show that the frequency tracking method that is derived has worked quite
well. In addition, the frequency tracking is fast enough to be used in real-time controller. The results also indicate that the MAF can provide significant vibration reduction using the optimal controller.
KEYWORDS: Vibration control, Control systems, Feedback control, Active vibration control, Actuators, Control systems design, Solids, Safety, Microelectromechanical systems, Micromirrors
The vibration control of microelectromechanical structures is an interesting and challenging
research area that is extensively applicable in micro-mass measurement, micro-sensors and
micro-mirror control. An active vibration control technique based on positive position feedback
method is constructed in this paper. This method is used to control the vibration of
microcantilevers through actuation of a piezoelectric layer that covers one side of the
microcantilever. The modified version of positive position feedback used in this paper, employs
a second order compensator for vibration suppression, and a first order compensator provides
damping. Since the positive position feedback control is based on strain sensing approach, it is
extensively applied to piezoelectrically controlled microcantilevers. Similar to conventional
positive position feedback, stability conditions are global and independent of the dynamical
characteristics of the open-loop system. Root locus diagrams are used to find proper compensator
frequency and damping of the closed loop system. A numerical simulation is performed to
evaluate the performance of the modified positive position feedback for both steady-state and
transient dynamic control. The results indicate that the proposed method is more effective in
controlling both steady-state and transient dynamics than conventional positive position feedback.
In this paper the problem of coupled flexural-torsional nonlinear vibrations of a piezoelectrically-actuated
microcantilever beam is investigated considering beam's simultaneous flexural, torsional and longitudinal vibrations.
Application of such problem is utilized in several nanotechnological instruments such as atomic force microscopy,
nanomechanical cantilever sensors and friction force microscopy. The actuation and sensing are both facilitated through
bonding a piezoelectric layer (here, ZnO) on the microcantilever surface. The piezoelectric properties combined with
nonlinear geometry of the beam introduce both linear and nonlinear coupling between flexural vibration as well as
longitudinal and torsional vibrations. The governing equations of motion are obtained with piezoelectric nonlinearity
appearing in quadratic form while inertia and stiffness nonlinearities as cubic. An experimental setup consisting of a
commercial piezoelectric microcantilever installed on the stand of an ultramodern laser-based microsystem analyzer is
designed and utilized to verify the theoretical developments. First and second flexural natural frequencies are both
experimentally and numerically obtained and are shown to be in good agreement. Both linear and nonlinear simulation
results are compared with experimental results and it is observed that nonlinear modeling response matches the
experimental findings very closely.
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