S. Nima Mahmoodi

Active Vibration Control With Modified Positive Position Feedback

A novel active vibration control technique based on positive position feedback method is developed. This method, which is a modified version of positive position feedback, employs a first-order compensator that provides damping control and a second-order compensator for vibration suppression. In contrast, conventional positive position feedback uses a single second-order compensator. The technique is useful for strain-based sensors and can be applied to piezoelectrically controlled systems. After introducing the concept of modified positive position feedback, this paper investigates the stability of the new method for locating gain limits. Stability conditions are global and independent of the dynamical characteristics of the open-loop system. Using root locus plots, proper compensator frequency is identified and damping of the closed-loop system is studied. The performance of the modified positive position feedback for both steady-state and transient dynamic control is studied. The experimental and numerical results show that the proposed method is significantly more effective in controlling steady-state response and slightly advantageous for transient dynamics control, as compared with conventional positive position feedback.

Modified acceleration feedback for active vibration control of aerospace structures

An acceleration feedback control method suggested in several past studies is modified to include two compensators, one first order and another second order, to separately control the closed-loop system stiffness and damping. The second order compensator has a damping ratio that is as low as that of the flexible structure in order to provide periodic vibration control. The first order compensator is used to provide the necessary damping, simultaneously. Employing two separate compensators allow us to provide stiffness and damping control in a dynamically decoupled manner. The new controller is readily applicable to a strain-based sensing and actuating approach, such as piezoelectrically controlled systems. Control gains are obtained through a stability analysis that is described in detail in the paper. The effectiveness of the controller is verified experimentally using a test setup that includes a flexible plate. The plate includes two small piezoelectric patches that are used as control actuators. Ten miniature size accelerometers are mounted on the plate for measuring plate vibrations. Two piezoelectric actuators in different positions are used for vibration control of the plate and the results are compared with the condition in which only one actuator is used. In addition, the results confirm that the new controller is able to effectively control more than one frequency simultaneously.

Adaptive Modified Positive Position Feedback for Active Vibration Control of Structures

The modified positive position feedback (MPPF) 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 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 broadband 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 broadband vibrations. The experimental results show that the frequency adaptation 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.

Coupled Flexural-Torsional Nonlinear Vibrations of Piezoelectrically Actuated Microcantilevers With Application to Friction Force Microscopy

The problem of vibrations of microcantilevers has recently received considerable attention due to its application in several nanotechnological instruments, such as atomic force microscopy, nanomechanical cantilever sensors, and friction force microscopy. Along this line, this paper undertakes the problem of coupled flexural-torsional nonlinear vibrations of a piezoelectrically actuated microcantilever beam as a typical configuration utilized in these applications. The actuation and sensing are both facilitated through bonding a piezoelectric layer (here, ZnO) on the microcantilever surface. The beam is considered to have simultaneous flexural, torsional, and longitudinal vibrations. The piezoelectric properties combined with nonlinear geometry of the beam introduce both linear and nonlinear couplings between flexural vibration as well as longitudinal and torsional vibrations. Of particular interest is the inextensibility configuration, for which the governing equations reduce to coupled flexural-torsional nonlinear equations 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. Both linear and nonlinear simulation results are compared to the experimental results and it is observed that nonlinear modeling response matches the experimental findings very closely. More specifically, the softening phenomenon in fundamental flexural frequency, which is due to nonlinearity of the system, is analytically and experimentally verified. It is also disclosed that the initial twisting in the microcantilever can influence the value ofthe flexural vibration resonance. The experimental results from a macroscale beam are utilized to demonstrate such twist-flexure coupling. This unique coupling effect may lead to the possibility of indirect measurement of small torsional vibration without the need for any angular displacement sensor. This observation could significantly extend the application of friction force microscopy to measure the friction of a surface indirectly.

Vibration control of collocated smart structures using H ∞ modified positive position and velocity feedback

In this paper, H∞ modified positive position feedback (HMPPF) and H∞ modified positive velocity feedback (HMPVF) controllers are developed as two innovative controllers for active vibration reduction in flexible collocated structures. The controllers use the concept of modified positive feedback and are enhanced by the H∞ feedback design to provide effective vibration suppression of multiple modes. An aluminum cantilever beam is used to experimentally evaluate the performance of the two controllers. The objective of the HMPPF controller is to suppress vibration displacement when all of the fundamental modes are excited. In this case which considers the first three modes of the flexible structure, overall vibration displacement is reduced to 38% of the uncontrolled value. The HMPVF, on the other hand, uses the control energy to reduce the vibration velocity to the lowest possible value. Vibration velocity amplitude using the HMPVF approach was reduced more than displacement, which makes this controller more effective for fatigue failure prevention purposes.

Nonlinear vibrations of microcantilevers subjected to tip-sample interactions: Theory and experiment

Improvement of microcantilever-based sensors and actuators chiefly depends on their modeling accuracy. Atomic force microscopy (AFM) is the most widespread application of microcantilever beam as a sensor, which is usually influenced by the tip-sample interaction force. Along this line of reasoning, vibration of AFM microcantilever probe is analyzed in this paper, along with analytical and experimental investigation of the influence of the sample interaction force on the microcantilever vibration. Nonlinear integropartial equation of microcantilever vibration subject to the tip-sample interaction is then derived and multiple time scales method is utilized to estimate the tip amplitude while it is vibrating near the sample. A set of experiments is performed using a commercial AFM for both resonance and nonresonance modes, and the results are compared with the theoretical results. Hysteresis, instability and amplitude drop can be identified in the experimental curves inside the particle attraction domain. Th...

Analytical solution for nonlinear free vibrations of viscoelastic microcantilevers covered with a piezoelectric layer

Nonlinear vibrations of viscoelastic microcantilevers with a piezoelectric actuator layer on the top surface are investigated. In this work, the microcantilever follows a classical linear viscoelastic model, i.e., Kelvin–Voigt. In addition, it is assumed that the microcantilever complies with Euler–Bernoulli beam theory. The Hamilton principle is used to obtain the equations of motion for the microcantilever oscillations. Then, the Galerkin approximation is utilized for separation of time and displacement variables, thus the time function is obtained as a second order nonlinear ordinary differential equation with quadratic and cubic nonlinear terms. Nonlinearities appear in stiffness, inertia and damping terms. Using the method of multiple scales, the analytical relations for nonlinear natural frequency and amplitude of the vibration are derived. Using the obtained analytical relations, the effects of geometric factors and material properties on the free nonlinear behavior of this beam are investigated. The results are also verified by numerical analysis of the equations.

Implementation of modified positive velocity feedback controller for active vibration control in smart structures

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.

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

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.© 2013 ASME

Active vibration control of aerospace structures using a modified Positive Position Feedback method

A Positive Position Feedback controller is modified and a new active vibration control technique is developed. Unlike the conventional Positive Position Feedback, the new controller separates the damping and stiffness control using two parallel first order and second order compensators. The second order compensator has a damping ratio as low as the damping of flexible structure to provide periodic vibration control. Simultaneously, the high damping is made available through a first order compensator. The new controller is applicable to a strain-based sensing/actuating approach and can be extensively applied to piezoelectrically controlled systems. Control gains are obtained by performing the stability analysis. The controller is verified experimentally using a plate vibration suppression setup. The plate is controlled through two piezoelectric patches and its vibrations are monitored by ten sensors mounted on the surface of the plate. The results confirm that the new controller is able to provide good vibration reduction, with the ability to be used to simultaneously control more than one natural frequency.