Backlash, also known as mechanical play, is a piecewise differentiable nonlinearity which exists in several actuated systems, comprising, e.g., rack-and-pinion drives, shaft couplings, toothed gears, and other elements. Generally, the backlash is nested between the moving elements of a complex dynamic system, which handicaps its proper detection and identification. A classical example is the two-mass system which can approximate numerous mechanisms connected by a shaft (or link) with relatively high stiffness and backlash in series. Information about the presence and extent of the backlash is seldom exactly known and is rather conditional upon factors such as wear, fatigue and incipient failures in components. This paper proposes a novel backlash identification method using one-side sensing of a twomass system. The method is based on the delayed relay operator in feedback that allows stable and controllable limit cycles to be induced, operating within the unknown backlash gap. The system model, with structural transformations required for the one-side backlash measurements, is given, along with the analysis of the delayed relay in velocity feedback. Experimental evaluations are shown for a two-inertia motor bench with gear coupling, with a low backlash gap of about one degree.

Backlash Identification in Two-Mass Systems by Delayed Relay Feedback

Relay feedback systems belong, since long, to rather classical topics of the control theory and engineering. While they were first used as robust and simple switching elements in the automatic control, over time, they experienced different periods of renewed interest regarding both the theoretical analysis and applications. Examples here are the automatic tuning of the simple feedback controllers, delta-sigma modulators for analog-digital converters, robust relaybased controls, nonlinear systems analysis and identification, and others. One of the remarkable features when using relays in feedback is appearance of the stable limit cycles. The structural and parametric conditions for the stable limit cycles, their prediction, and controllability of magnitude and frequency already found answers, to the large part, in the former research, driven by both theoretical curiosity and application requirements. This brief tutorial paper is summarizing the basic principles of relay feedback systems, discuss several characteristics interesting for applications, and address some perspectives of further use for the system identification. A case-specific study of estimating the unknown backlash, hidden within two-mass systems, is demonstrated along with experimental example, based on provoking the controllable drifting limit cycles by the non-ideal relay in the velocity feedback loop.

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Relay feedback systems - established approaches and new perspectives for application

Although inception of the measurement of astronaut body mass measurement was as old as Skylab era, progress in the field has not been as expected. There are fundamental physical difficulties as well as program management issues. New mass measurement systems with the current sensor technologies should be prepared, and the new sensor system could be expanded for “Drop Tower” in space.

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Issues with Body Mass Measurement on the International Space Station (ISS)

A review of mass measurement devices developed by the author is presented. According to the measurement principles, the treated devices are classified into two types. The first type uses a dynamic vibration absorber as a device for both mass measurement and vibration control. The main advantage is no vibration transmitted into the surrounding structures during measurement. The second type uses relay feedback. The advantages are simpler mechanism and robustness against disturbances. In this article, the principles of measurement of each type are presented.

Development of Mass Measurement Devices for Zero-Gravity Experiments

Abstract This paper treats a relay-feedback mass measurement system that uses a relay with hysteresis and feeds back the velocity of the object. The measurement system has an on-off relay with hysteresis and switches force acting on the object in relation to its velocity. Such nonlinear control induces a limit cycle. The mass of the object is determined from the period of this cycle. In previous study, the actual trajectory of the limit cycle was different in shape from the theoretical one so that the prerequisites of the estimation formula were not satisfied. The delay of the velocity sensor is a main factor of such degradation. In this paper, the effect of the delay on mass estimation is investigated experimentally and analytically. In addition, an estimating equation including this effect is derived. Experimental result supports the validity of the derived estimating equation.

Study on the delay of velocity detection and derivation of a correction formula in mass measurement using relay feedback

Mass measurement using a relay feedback system was studied experimentally. The measurement system has an on-off relay with hysteresis and switches force acting on the object in relation to its velocity. Such nonlinear control induces a limit cycle in the feedback system. The mass of the object is determined from the period of this limit cycle. The apparatus manufactured for experimental study uses two voice coil motors (VCM's), one of which is for driving the object and the other is for generating prescribed disturbances. The effects of system parameters and disturbances on measurement accuracy were examined experimentally.

Takahiro Adachi

Papers

Mass Measurement System Using Relay Feedback with Hysteresis