The effects of mechanical response on the dynamics and string stability of a platoon of adaptive cruise control vehicles

•A new formalism treats the general mechanical response of adaptive cruise control vehicles.•String stability of a platoon is necessary but not sufficient for a smooth ride.•A secondary peak in the transfer function due to the delayed response can cause undesirable oscillations.•Frequency-dependent acceleration feedback effectively eliminates oscillations.

The dynamics of a platoon of adaptive cruise control vehicles is analyzed for a general mechanical response of the vehicle. Effects of acceleration-feedback control that were not previously studied are found. For small acceleration-feedback gain, which produces marginally string-stable behavior, the reduction of a disturbance (with increasing car number nn) is found to be faster than for the maximum allowable gain. The asymptotic magnitude of a disturbance is shown to fall off as erf(ct.√n) when n→∞n→∞. For gain approaching the lower limit of stability, oscillations in acceleration associated with a secondary maximum in the transfer function (as a function of frequency) can occur. A frequency-dependent gain that reduces the secondary maximum, but does not affect the transfer function near zero frequency, is proposed. Performance is thereby improved by elimination of the undesirable oscillations while the rapid disturbance reduction is retained.