Search

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. [DOI: 10.1115/1.3089565] Keywords: active control vibration compensation, positive position feedback, first-order compensator, second-order compensator

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 of the 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. [DOI: 10.1115/l.2948379] Keywords: nonlinear vibration of microcantilever beams, coupled flexural-torsional vibrations, piezoelectrically-actuated microcantilevers, friction force microscopy

The equations of motion for a piezoelectric microcantilever are derived for a nonlinear contact force. The analytical expressions for natural frequencies and mode shapes are obtained. Then, the method of multiple scales is used to analyze the analytical frequency response of the piezoelectric probe. The effects of nonlinear excitation force on the microcantilever beam's frequency and amplitude are analytically studied. The results show a frequency shift in the response resulting from the force nonlinearities. This frequency shift during contact mode is an important consideration in the modeling of AFM mechanics for generation of more accurate imaging. Also, a sensitivity analysis of the system parameters on the nonlinearity effect is performed. The results of a sensitivity analysis show that it is possible to choose parameters such that the frequency shift minimizes. Certain parameters such as tip radius, microcantilever beam dimensions, and modulus of elasticity have more influence on the nonlinearity of the system than other parameters. By changing only three parameters--tip radius, thickness, and modulus of elasticity of the microbeam--a more than 70% reduction in nonlinearity effect was achieved. [ABSTRACT FROM AUTHOR]

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. They are likely related to the interaction force between the tip and sample as well as the ever-present water layer during the experiments. A fair agreement is observed between the theoretical simulations and experimental findings, which obviously demonstrates the effectiveness and applicability of the developed model. [ABSTRACT FROM AUTHOR]

This paper proposes a new leader–follower-based consensus vibration controller to actively suppress unwanted oscillations in distributed-parameter flexible structures. Actuation and sensing is performed via piezoelectric layers in a collocated sense. The actuator/sensor patches for the vibration control system are considered to collaborate in a network, and follow a virtual leader which is accessible to all agents. Hence, a vibration controller law is defined, to remove disagreement between agents and force the agents to follow the virtual leader. The proposed approach is an observer-based design, in which an optimal consensus state estimator is initially designed. Stability of the closed-loop system is investigated and the optimality conditions of the system are derived. Although the designed vibration controller could be implemented for suppression tasks in different distributed-parameter systems, a flexible clamped-clamped beam is used here for equation derivation and numerical performance verification. According to the results, the optimal observer estimates the system states in a finite time, as expected, and the vibration controller suppresses unwanted oscillations, either in resonant or arbitrary form, to a much lower level; while the disagreement between agents converges to zero. Additionally, suppression performance and robustness of the controller to failure in control system elements is investigated in comparison with a conventional positive position feedback controller, and its superiority is illustrated and discussed. [ABSTRACT FROM AUTHOR]

A new multi-piezoelectric microcantilever sensor is introduced in this article for replacing laser sensors in atomic force microscopes. This microcantilever consists of multiple piezoelectric layers over its surface, and a consensus algorithm is designed to provide a robust and accurate estimation of the deflections at the tip of the microcantilever. The dynamic equation set of the microcantilever is developed first and then the consensus observer is designed. A set of Riccati equations is used to obtain the optimal gains for the observer, and the robustness of the microcantilever is considered by designing a H∞ norm constraint. A set of numerical simulations is conducted to evaluate the performance of the microcantilever. Results show that the consensus-based multi-piezoelectric microcantilever can successfully provide an accurate estimation of the deflections at the tip of the microcantilever. It is also shown that the robustness of the design can positively improve the estimation performance in the presence of noise. Additionally, a comparison with a single-layered design shows the advantages of the new sensor. [ABSTRACT FROM AUTHOR]