Decomposition of the Equations of Motion in the Analysis of Dynamics of a 3-DOF Nonideal System

The dynamic response of a nonlinear system with three degrees of freedom, which is excited by nonideal excitation, is investigated. In the considered system the role of a nonideal source is played by a direct current motor, where the central axis of the rotor is not coincident with the axis of rotation. This translation generates a torque whose magnitude depends on the angular velocity. During the system operation a general coordinate assigned to the nonideal source grows rapidly as a result of rotation. We propose the decomposition of the equations of motion in such a way to extract the solution which is directly related to the rotation of an unbalanced rotor. The remaining part of the solution describes pure oscillation depending on the dynamical behaviour of the whole system. The decomposed equations are solved numerically. The influence of selected system parameters on the rotor vibration is examined. The presented approach can be applied to separate vibration and rotation of motions in many other engineering systems.

On Lugre Friction Model to Mitigate Nonideal Vibrations

In this paper, a nonideal mechanical system with the LuGre friction damping model is considered. The mechanical model of the system is an oscillator not necessarily linear connected with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper. The mathematical model of the system is represented by coupled nonlinear differential equations. The identification of some interesting nonlinear phenomenon in the transient and steady state motion of the system during the passage through resonance (using applied voltages at dc motor as control parameter) is investigated in detail using numerical simulation.

An Energetic Control Methodology for Exploiting the Passive Dynamics of Pneumatically Actuated Hopping

This paper presents an energetically derived control methodology to specify and regulate the oscillatory motion of a pneumatic hopping robot. An ideal lossless pneumatic actuation system with an inertia is shown to represent an oscillator with a stiffness, and hence frequency, related to the equilibrium pressures in the actuator. Following from an analysis of the conservative energy storage elements in the system, a control methodology is derived to sustain a specified frequency of oscillation in the presence of energy dissipation. The basic control strategy is to control the pressure in the upper chamber of the pneumatic cylinder to specify the contact time of the piston, while controlling the total conservative energy stored in the system to specify the flight time and corresponding flight height of the cylinder. The control strategy takes advantage of the natural passive dynamics of the upper chamber to provide much of the required actuation forces and natural stiffness, while the remaining forces needed to overcome the energy dissipation present in a nonideal system with losses are provided by a nonlinear control law for the charging and discharging of the lower chamber of the cylinder. Efficient hopping motion, relative to a traditional nonconservative actuator, is achieved by allowing the energy storing capability of a pneumatic actuator to store and return energy to the system at a controlled specifiable frequency. The control methodology is demonstrated through simulation and experimental results to provide accurate and repeatable hopping motion for pneumatically actuated robots in the presence of dissipative forces.