Non-minimum-phase property of N-trailer kinematics resulting from off-axle interconnections

Off-axle interconnections between segments of N-trailer vehicles may imply specific oscillatory behaviour of trailers during vehicle manoeuvres. The paper reveals that this kind of oscillations is a direct consequence of the non-minimum-phase property of vehicle kinematics resulting from application of off-axle interconnections between vehicle segments. First we show the non-minimum-phase property for dynamics of a single pair of interconnected segments, and then how it propagates along the N-trailers equipped with arbitrary number of off-axle interconnections. By referring to available results for linear systems, we locally analyse linearly approximated vehicle kinematics around selected steady-motion conditions. We focus on the time-response effects like undershooting, zero-crossing, and overshooting caused by off-axle interconnections. We show how the number and type of interconnections influence the non-minimum-phase effects. Numerical results obtained for three-trailer kinematics validate theoretical considerations providing some quantitative view of the problem. Short discussion has been provided on the possible control-level consequences resulting from the non-minimum-phase property of N-trailers.