Vibrational control of mechanical systems with piecewise linear damping and high-frequency inputs

2019 ◽  
Vol 99 (2) ◽  
pp. 1403-1413
Author(s):  
Sevak Tahmasian ◽  
Atefeh Katrahmani
Author(s):  
Sevak Tahmasian

This paper discusses the averaging, control authority, and vibrational control of mechanical control-affine systems with high-frequency, high-amplitude inputs. The inputs have different frequencies of the same order. This work is an extension of the existing averaging method for high-frequency mechanical systems with single-frequency inputs. Vibrational control authority of mechanical control-affine systems is introduced, and the effects of inputs' waveform and frequency on vibrational control authority are investigated. The results show that, in general, using multifrequency inputs may result in lower control authority of mechanical systems compared to single-frequency inputs, especially when using harmonic inputs. The results on vibrational control authority of the systems with multifrequency inputs are demonstrated using vibrational control of a horizontal pendulum with two inputs. This paper also discusses the averaging of multiple-time-scale control systems.


Author(s):  
Zakia Ahmed ◽  
Sevak Tahmasian ◽  
Craig A. Woolsey

Abstract This paper describes vibrational control and stability of a planar, horizontal 2-link mechanism using translational control of the base pivot. The system is a 3-DOF two-link mechanism that is subject to torsional damping, torsional stiffness, and is moving on a horizontal plane. The goal is to drive the averaged dynamics of the system to a desired configuration using a high-frequency, high-amplitude force applied at the base pivot. The desired configuration is achieved by applying an amplitude and angle of the input determined using the averaged dynamics of the system. We find the range of stable configurations that can be achieved by the system by changing the amplitude of the oscillations for a fixed input angle and oscillation frequency. The effects of varying the physical parameters on the achievable stable configurations are studied. Stability analysis of the system is performed using two methods: the averaged dynamics and averaged potential.


1967 ◽  
Vol 89 (2) ◽  
pp. 357-364
Author(s):  
S. Ochiai ◽  
R. Oldenburger

A derivative of the output of a nonlinear element is taken with respect to the input. For commonly occurring nonlinearities which are piecewise linear, this derivative is sectionally constant with respect to the input. This property of the derivative is used to reduce the computational work required for deriving the describing function. The concept of this derivative is applied to the study of the effect of a high-frequency signal on the input-output relationship of a system containing a limiter with hysteresis. This signal may be regarded as an extra signal introduced into a system to improve the performance of the nonlinear component. The mathematical analysis of the effect is simplified if the extra signal is a triangular wave instead of sinusoidal. The extra triangular signal is applied to removing the jump phenomenon which exists in a feedback control system with a limiter with hysteresis.


Author(s):  
M. R. Brake

Impact is a wide-spread phenomenon in mechanical systems that can have a significant effect on the systems dynamics, stability, wear, and damage. The simulation of impact in complex, mechanical systems, however, is often too computationally intensive for high fidelity finite element analyses to be useful as design tools. As a result, rigid body dynamics and reduced order model simulations are often used, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or penalty stiffness. The effect of epistemic uncertainty in the choice of contact model is investigated in this paper for a representative multiple-degree of freedom mechanical system. Five contact models are considered in the analysis: a constant coefficient of restitution model, a piecewise-linear stiffness and damping (i.e. Kelvin-Voight) model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. The predictions of wear and mechanical failure are assessed for each of the contact models. The ramifications of the choice of the contact model for an optimization study of the system’s geometric design are also presented. These results emphasize the importance of choosing an accurate contact model when simulations are being used to drive the design of a system.


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