Scheduled System Maintenance:
Some services will be unavailable Sunday, March 29th through Monday, March 30th. We apologize for the inconvenience.
By Topic

Relation between structural compliance and allowable friction in a servomechanism

Sign In

Full text access may be available.

To access full text, please use your member or institutional sign in.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Biernson, George ; Sylvania Electric Products Inc., Waltham, MA, USA

In a great many control systems, error is primarily caused by transient load torques, often the result of static friction. To keep the error due to transient load torques small a high output inertia, and high values of gain crossover frequencies are required in the control loops. Integral networks that increase the static stiffness of the control system generally have negligible effect against transient load torques. The maximum error produced by a step of torque is approximately as follows for a rate feedback system: \theta_{e} = frac{T}{J \omega _{c}\omega _{r}} (1) where T is the magnitude of the step of torque, J is the output intertia, ωc, is the gain-crossover frequency of the position loop, and \omega {r} is the gain-crossover frequency of the rate loop. Thus, if the error is to be kept within a given bound \theta_{e} , the maximum allowable friction torque Tfis given by T_{f} \leq \theta_{e}J\omega _{c}\omega _{r} (2) Structural compliance is a severe limitation upon the allowable values of gain-crossover frequency. The maximum value of rate loop gain-crossover frequency ωrin practice is usually about half the natural frequency of the structure ωn. The position loop gain-cross-over frequency is usually at least a factor of three below that of the rate loop. Therefore one can assume that \omega _{r} \leq frac{\omega _{n}}{2} (3) \omega _{c} \leq frac{\omega _{r}}{3} \leq frac{\omega _{n}}{6} (4) Substituting (3) and (4) into (2) gives T_{f} \leq (1/12)J\omega _{n}^{2}\theta_{e} (5) Equation (5) shows that regardless of the type of control system used, there is a maximum possible value of friction torque that is related only to the allowable error, the output inertia, and the structural natural frequency. Although this limitation is derived in terms of a specific servo configuration, it also holds approximately for other configurations, and cannot be improved by integral networks.

Published in:

Automatic Control, IEEE Transactions on  (Volume:10 ,  Issue: 1 )