Proposal of high backdrivable control using load-side encoder and backlash

Backlash Identification in Two-Mass Systems by Delayed Relay Feedback

“…In the previous subsection, the conditions for a unimodal limit cycle of the system as shown in Fig. 4 were derived, and the characteristic features in terms of the displacement amplitude and period were given by (14) and (15). We note that the limit cycle can appear within the gap mode of backlash, (see section II), provided X ξ < 2β, so that the motor and load remain decoupled (compare with Fig.…”

“…We assume that the backlash itself is sufficiently damped so that the relative displacement between the "impact pair" is not subject to any long-term oscillations when the mechanics engage. Here, we recall that the simplest modeling approach for the backlash in two-mass systems, used for instance in [12,14], applies the dead-zone operator (with δ argument) only, while the dead-zone output is subsequently gained by the stiffness of the link. This arrangement results in a proper backlash behavior merely at lower frequencies, but tends to produce spurious δ-oscillations at higher harmonics.…”

“…Hence, the e parameter should be kept as low-valued as possible, given the system parameters m, M, D and F. This will ensure a displacement of the load which is as low as possible, i.e., X L → 0, induced by the single impulse at impact. Furthermore, low values of e are required firstly to fulfill the necessary and sufficient conditions (10) and (12) of the limit cycle, and secondly to keep the amplitude as low as possible and therefore within the backlash gap (see (14)). Obviously, the maximal load displacement (22) will be induced periodically by the drifting limit cycle, (see section 3.2), each time the impact occurs.…”

“…In addition, the period of the limit cycle 2t * is required to be large enough, with respect to the system sampling rate, so as to ensure a sufficient number of samples per period of the limit cycle. The values computed according to (14) and (15) are X ξ = 0.128 mrad and t * = 2.45 msec respectively. The average X ξ value, determined from the example measurements shown in Fig.…”

Combining Load and Motor Encoders to Compensate Nonlinear Disturbances for High Precision Tracking Control of Gear-Driven Gimbal

“…Therefore, advanced control techniques are necessary to compensate these nonlinear disturbances. Methods of Model-based [ 12 , 13 , 14 ] control to eliminate these disturbances are developed by some authors, but these techniques are deeply dependent on an accurate model. Sensor-less backlash compensation is very interesting [ 15 ].…”