Adaptive Switch Timing Control Law for Optimal Displacement Reduction via SSDI

2016 ◽  
Author(s):  
Christopher R. Kelley ◽  
Jeffrey L. Kauffman
Keyword(s):  
Electromechanical Coupling ◽  
Excitation Frequency ◽  
Resonance Excitation ◽  
Piezo Actuator ◽  
Control Law ◽  
Timing Control ◽  
Modal Damping ◽  
Switch Time ◽  
Control Framework ◽  
Adaptive Switch

In the conventional implementation of synchronized switch damping (SSD), the switches are intended to occur at every displacement extrema. However, recent work reveals that switching at the vibration peaks is only optimal for displacement reduction under resonance excitation. In general, the optimal switch timing is dependent on the excitation frequency along with the electromechanical coupling and modal damping of the structure. This work seeks to develop a control framework that searches through the possible switch times to find the optimal switch time for synchronized switch damping on an inductor (SSDI) under steady state excitation. The control law does not need any knowledge of the system, only requiring the voltage of the piezo actuator to develop a displacement estimate that is minimized by adjusting the switch timing. Furthermore, the controller naturally senses changes in the excitation and adapts the switch timing to best reduce displacement under the new excitation.

Switch Triggers for Optimal Vibration Reduction Via Resonance Frequency Detuning

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Garrett K. Lopp ◽  
Jeffrey L. Kauffman
Keyword(s):  
Resonance Frequency ◽  
Coupling Coefficient ◽  
Electromechanical Coupling ◽  
Vibration Reduction ◽  
Excitation Frequency ◽  
Electromechanical Coupling Coefficient ◽  
Peak Strain ◽  
Frequency Detuning ◽  
Response Dynamics ◽  
Modal Damping

Resonance frequency detuning (RFD) reduces vibration of systems subjected to frequency sweep excitation by altering the structural stiffness state as the excitation frequency passes through resonance. This vibration reduction technique applies to turbomachinery experiencing changes in rotation speed, for example, on spool-up and spool-down, and can be achieved through the inclusion of piezoelectric material and manipulation of its electrical boundary conditions. Key system parameters—the excitation sweep rate, modal damping ratio, electromechanical coupling coefficient, and, most importantly, the switch trigger that initiates the stiffness state switch (represented here in terms of excitation frequency)—determine the peak response dynamics. This paper exploits an analytical solution to a nondimensional single degree-of-freedom equation of motion to provide this blade response and recasts the equation in scaled form to include the altered system dynamics following the stiffness state switch. An extensive study over a range of sweep rates, damping ratios, and electromechanical coupling coefficients reveals the optimal frequency switch trigger that minimizes the peak of the blade response envelope. This switch trigger is primarily a function of the electromechanical coupling coefficient and the phase of vibration at which the switch occurs. As the coupling coefficient increases, the frequency-based switch trigger decreases, approximately linearly with the square of the coupling coefficient. Furthermore, as with other state-switching techniques, the optimal stiffness switch occurs on peak strain energy; however, the degradation in vibration reduction performance associated with a switch occurring at a nonoptimal phase is negligible for slow sweep rates and low modal damping.

scholarly journals On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Saad Ilyas ◽  
Feras K. Alfosail ◽  
Mohammad I. Younis
Keyword(s):  
Analytical Solution ◽  
Multiple Scales ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Equation Of Motion ◽  
Higher Order ◽  
Resonance Excitation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Electrostatically Actuated

We investigate modeling the dynamics of an electrostatically actuated resonator using the perturbation method of multiple time scales (MTS). First, we discuss two approaches to treat the nonlinear parallel-plate electrostatic force in the equation of motion and their impact on the application of MTS: expanding the force in Taylor series and multiplying both sides of the equation with the denominator of the forcing term. Considering a spring–mass–damper system excited electrostatically near primary resonance, it is concluded that, with consistent truncation of higher-order terms, both techniques yield same modulation equations. Then, we consider the problem of an electrostatically actuated resonator under simultaneous superharmonic and primary resonance excitation and derive a comprehensive analytical solution using MTS. The results of the analytical solution are compared against the numerical results obtained by long-time integration of the equation of motion. It is demonstrated that along with the direct excitation components at the excitation frequency and twice of that, higher-order parametric terms should also be included. Finally, the contributions of primary and superharmonic resonance toward the overall response of the resonator are examined.

scholarly journals A Human-Robot Cooperative and Personalized Compliant Joint Controller for Upper-Limb Rehabilitation Robots: The Elbow Joint Validation

2021 ◽  
Author(s):  
Stefano Dalla Gasperina ◽  
Valeria Longatelli ◽  
Francesco Braghin ◽  
Alessandra Laura Giulia Pedrocchi ◽  
Marta Gandolla
Keyword(s):  
Upper Limb ◽  
Human Robot Interaction ◽  
Control Law ◽  
Robot Interaction ◽  
Activation Patterns ◽  
Upper Limb Rehabilitation ◽  
Control Framework ◽  
High Level ◽  
Limb Rehabilitation ◽  
Muscular Activation

Abstract Background: Appropriate training modalities for post-stroke upper-limb rehabilitation are key features for effective recovery after the acute event. This work presents a novel human-robot cooperative control framework that promotes compliant motion and renders different high-level human-robot interaction rehabilitation modalities under a unified low-level control scheme. Methods: The presented control law is based on a loadcell-based impedance controller provided with positive-feedback compensation terms for disturbances rejection and dynamics compensation. We developed an elbow flexion-extension experimental setup, and we conducted experiments to evaluate the controller performances. Seven high-level modalities, characterized by different levels of (i) impedance-based corrective assistance, (ii) weight counterbalance assistance, and (iii) resistance, have been defined and tested with 14 healthy volunteers.Results: The unified controller demonstrated suitability to promote good transparency and render compliant and high-impedance behavior at the joint. Superficial electromyography results showed different muscular activation patterns according to the rehabilitation modalities. Results suggested to avoid weight counterbalance assistance, since it could induce different motor relearning with respect to purely impedance-based corrective strategies. Conclusion: We proved that the proposed control framework could implement different physical human-robot interaction modalities and promote the assist-as-needed paradigm, helping the user to accomplish the task, while maintaining physiological muscular activation patterns. Future insights involve the extension to multiple degrees of freedom robots and the investigation of an adaptation control law that makes the controller learn and adapt in a therapist-like manner.

ANALYTICAL RANDOM VIBRATION ANALYSIS OF BOUNDARY-EXCITED THIN RECTANGULAR PLATES

2013 ◽  
Vol 13 (03) ◽  
pp. 1250062 ◽  
Author(s):  
ASHKAN HAJI HOSSEINLOO ◽  
FOOK FAH YAP ◽  
NADER VAHDATI
Keyword(s):  
Random Vibration ◽  
Printed Circuit Boards ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Jet Impingement ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Frequency Range ◽  
Modal Damping Ratio ◽  
Modal Damping

Fatigue life, stability and performance of majority of the structures and systems depend significantly on dynamic loadings applied on them. In many engineering cases, the dynamic loading is random vibration and the structure is a plate-like system. Examples could be printed circuit boards or jet impingement cooling systems subjected to random vibrations in harsh military environments. In this study, the response of thin rectangular plates to random boundary excitation is analytically formulated and analyzed. In the presented method, closed-form mode shapes are used and some of the assumptions in previous studies are eliminated; hence it is simpler and reduces the computational load. In addition, the effects of different boundary conditions, modal damping and excitation frequency range on dynamic random response of the system are studied. The results show that increasing both the modal damping ratio and the excitation frequency range will decrease the root mean square acceleration and the maximum deflection of the plate.

Attitude Protection Control for Side Stick-Operated Aircraft

2013 ◽  
Vol 846-847 ◽  
pp. 77-85
Author(s):  
Yi Qun Dong ◽  
Li Dong Zhang ◽  
Yi Jun Zhang ◽  
Jian Liang Ai
Keyword(s):  
Predictive Control ◽  
Control Strategy ◽  
Ground Control ◽  
Control Law ◽  
Euler Angles ◽  
Simulation Test ◽  
Rolling Angle ◽  
Control Framework ◽  
Control Work

A control framework to limit aircraft Euler angles (pitch/rolling) under adverse side stick command adding is introduced. Attitude envelope of the aircraft pitch/rolling angle is discussed based on geometrical position of the aircraft relative to the ground. Control law of is established by using linearized predictive control strategy. The simulation test presents the performance of attitude protection restricting the Euler angles within the required envelop at 1,000m. Based on the test work discussed herein, the control work proposed in this paper is believed to be applicable.

Response Measurement Accuracy for Off-Resonance Excitation in Atomic Force Microscopy

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
R. Parker Eason ◽  
Andrew J. Dick
Keyword(s):  
Atomic Force Microscopy ◽  
Measurement Accuracy ◽  
Excitation Frequency ◽  
Operating Conditions ◽  
Laser Spot ◽  
Resonance Excitation ◽  
Force Microscopy ◽  
Atomic Force ◽  
Mode Behavior ◽  
Tip Mass

Displacement measurement in atomic force microscopy (AFM) is most commonly obtained indirectly by measuring the slope of the AFM probe and applying a calibration factor. Static calibration techniques operate on the assumption that the probe response approximates single mode behavior. For off-resonance excitation or different operating conditions the contribution of higher modes may become significant. In this paper, changes to the calibrated slope-displacement relationship and the corresponding implications on measurement accuracy are investigated. A model is developed and numerical simulations are performed to examine the effect of laser spot position, tip mass, quality factor and excitation frequency on measurement accuracy. Free response conditions and operation under nonlinear tip-sample forces are considered. Results are verified experimentally using a representative macroscale system. A laser spot positioned at a nominal position between x = 0.5 and 0.6 is determined to minimize optical lever measurement error under conditions where the response is dominated by contributions from the first two modes, due to excitation as well as other factors.

Topological Optimization of Piezoelectric Transducers for Vibration Reduction of Bladed Disks

2021 ◽  
Author(s):  
Y. Fan ◽  
H. Y. Ma ◽  
Y. G. Wu ◽  
L. Li ◽  
K. Y. Tian ◽  
...  
Keyword(s):  
Electromechanical Coupling ◽  
Piezoelectric Materials ◽  
Damping Ratio ◽  
Added Mass ◽  
Topological Optimization ◽  
Fe Model ◽  
Bladed Disks ◽  
Multiple Modes ◽  
Bladed Disk ◽  
Modal Damping

Abstract In this work, we develop a numerical method to determine the best distribution of piezoelectric materials on a given bladed disk, so as to minimize the added mass of shunted piezoelectric dampers. There is no constrain on the shape of piezoelectric materials, and only the overall mass is limited. The method can be applied to a single mode or several modes from the same or different modal groups. The method is based on the fact that the modal damping is solely determined by the modal electromechanical coupling factor (MEMCF) which is related to the modal stress field and the geometric of the piezoelectric materials only. A linear weighting of stress components is proposed as the criterion to determine the priority of locations for piezoelectric materials. The piezoelectric materials are introduced to the FE model by modifying the type and materials parameters of elements if they are embedded to the bladed disks; or by creating an additional layers of elements if they are bonded to the bladed disks. Details for considering multiple modes, handling polarization direction and electrode connection are also presented. The proposed procedure is applied to an empirical bladed disk with NASA-ROTOR37 profile. Results show that 12% damping ratio can be achieved for multiple modes simultaneously, if we locate piezoelectric materials on the blade with 10% added mass. When locate the piezoelectric materials on the disk and the added mass is only 5%, up to 13% modal damping ratio for the disk dominant modes can be achieved.

Exploiting the Subharmonic Parametric Resonance of a Bi-Stable Beam for Energy Harvesting

2017 ◽  
Author(s):  
Samir A. Emam ◽  
Meghashyam Panyam ◽  
Mohammed F. Daqaq
Keyword(s):  
Electromechanical Coupling ◽  
Vibration Mode ◽  
Fiber Composite ◽  
Excitation Frequency ◽  
Energy Harvesters ◽  
Buckled Beam ◽  
Transverse Vibrations ◽  
Stable Equilibria ◽  
Theoretical Results ◽  
Good Agreement

We investigate the potential of harvesting vibration energy via a bi-stable beam subjected to subharmonic parametric excitations. The vibrating structure is a buckled beam with two stable equilibria separated by a potential barrier. The beam is subjected to a superposition of a static axial load beyond its critical buckling load and a harmonic axial excitation which frequency is around twice the frequency of the first vibration mode. A micro-fiber composite (MFC) is attached to one side of the beam to convert the strain energy resulting from the beams oscillation into electricity. The study considers two regimes of excitations: an amplitude sweep and a frequency sweep. In the first regime, the amplitude of excitation is varied while the excitation frequency is tuned at twice the natural frequency of the first vibration mode. In the second regime, the excitation frequency is swept forward and backward around the subharmonic resonant frequency while the amplitude of excitation is kept constant. A theoretical model which governs the electromechanical coupling of the transverse vibrations of the beam and the output voltage is used to monitor the response as the excitation parameters are changed. An experimental setup is built and a series of tests is performed. The theoretical results are in good agreement with their experimental counterparts. The experiment also shows that this type of bi-stable energy harvesters exhibits a broadband frequency response as compared to the classical linear harvesters.

scholarly journals Reorientation of Asymmetric Rigid Body Using Two Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Donghoon Kim ◽  
James D. Turner ◽  
Henzeh Leeghim
Keyword(s):  
Numerical Simulation ◽  
Underactuated System ◽  
Control Law ◽  
System Control ◽  
Control Torque ◽  
Start Time ◽  
Control Laws ◽  
Switch Time ◽  
Simulation Results ◽  
Asymmetric Rigid Body

Most spacecrafts are designed to be maneuvered to achieve pointing goals. This is accomplished usually by designing a three-axis control system, which can achieve arbitrary maneuvers, where the goal is to repoint the spacecraft and match a desired angular velocity at the end of the maneuver. New control laws are required, however, if one of the three-axis control actuators fails. This paper explores suboptimal maneuver strategies when only two control torque inputs are available. To handle this underactuated system control problem, the three-axis maneuver strategy is transformed to two successive independent submaneuver strategies. The first maneuver is conducted on one of the available torque axes. Next, the second maneuver is conducted on the torque available plane using two available control torques. However, the resulting control law is more complicated than the general three-axis control law. This is because an optimal switch time needs to be found for determining the end time for the single-axis maneuver or the start time for the second maneuver. Numerical simulation results are presented that compare optimal maneuver strategies for both nominal and failed actuator cases.

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