Torsional Oscillations and the Antiresonant Controller

Abstract

This chapter explains the mechanical resonance and torsional oscillations within mechanical structures of the motion-control systems. Their impact on closed-loop performance is predicted and evaluated. The cases are distinguished where the lowest resonance frequency remains well beyond the desired bandwidth and where the resonant modes can be neglected as secondary phenomena. For applications where the resonance phenomena overlap with the frequency range of interest, passive and active antiresonant In Chapter 1, the mechanical part of a motion-controlled system has been modeled as a concentrated inertia J with friction coefficient B and with an external load torque disturbance T L. When the servo motor is coupled to the load by means of a rigid shaft, the motor and load positions are the same, and the inertia coefficient corresponds to the sum of the load inertia J L and the inertia of the rotor J M (J = J L + J M). In cases when a stiff shaft connects several revolving objects, the equivalent inertia J EQ is obtained as a sum, while the transfer function of the control object remains W P (s) = 1/(J EQ s + B). connection between mechanical elements. Therefore, the control object is considered and modeled as a concatenated inertia, comprising the rotor, load, and the equivalent inertia of all the moving elements. Mechanical structures, joints, and couplings within a motion-control system have a finite stiffness: that is, transmission elements such as shafts do not ensure equal positions at the shaft ends. Even a small flexibility results in certain torsion Δθ of the shaft, proportional to the applied torque. In cases when the shaft couples two revolving parts, each one with a distinct inertia J, the two inertias and the shaft constitute a resonant subsystem. For example, when a step in the driving torque is applied, the speed and position at both ends of the shaft exhibit poorly damped oscillations. Oscillating phenomena involving the speed, torque, and position of revolving objects are referred to as torsional oscillations. In cases where the translation The analysis and discussion in the preceding chapters assume a rigid control actions are devised and evaluated. An insight is given into designing and using antiresonant controllers by means of simulation and experiments.