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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]

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. [ABSTRACT FROM AUTHOR]

The nonlinear vibrations of the tapping-mode atomic force microscopy probe are investigated due to both nonlinearity in tip–sample contact force and curvature of the microcantilever probe. The nonlinear equations of motion for vibrations of the probe are obtained using Hamilton’s principle. In this work, the contact force is considered to be more dominant while previous works only consider Van der Waals force. The nonlinear contact force is expanded using a Taylor series to provide a polynomial with coefficients that are functions of the tip–sample distance. The outcome of this work allows the proper distance to be chosen before scanning to avoid instability in the response. Instability regions must be avoided for accurate imaging. The results show that initial tip–sample distance has a major effect on the stability of the frequency response and force response curves. For analytical investigation, the mode shapes of the atomic force microscopy probe are derived based on the presence of the nonlinear contact force as a boundary condition at the free end of the probe. The frequency response curve is obtained using the method of multiple scales. The results show that the effects of the nonlinearities due to probe geometry and contact force can be minimized. Minimizing the effects of nonlinearities allows for less cumbersome and calculation intensive software packages for atomic force microscopies. This research shows that one possible method of decreasing the nonlinearity effect is increasing the excitation force; however, this can increase the contact region and is not the best solution for canceling the nonlinearity effect. The superior method which is the major contribution of this paper is to find the optimal initial tip–sample distance and excitation force that minimize the nonlinearity effect. It is shown that at a certain tip–sample distance the quadratic and cubic nonlinearities cancel each other and the system responds linearly. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]