Input-output feedback linearization control of a tractor with n-trailers mechanism considering the path curvature

Abstract

In this paper, an observer-based proportional-integral-derivative (PID) controller is proposed for an autonomous tractor with n-trailer units with prescribed transient and steady-state performances by compensating the negative effect of the path curvature during the turning of the trailers. The control objective is to place the position of the last trailer on a desired trajectory without any deviation in the course of its turning. Since the curvature of the trajectory causes a remarkable unwanted deviation of the trailers’ positions from the path, an input-output model is derived for the tractor with n-trailers based on the extended look-ahead control concept which employs a corrective angle to compensate the path curvature. A nonlinear transformation is employed to transform constrained errors into unconstrained ones and to obtain an open-loop error dynamic model in terms of the unconstrained errors. Then, a neural network adaptive PID output-feedback linearization-based controller is proposed to force the tracking errors to the zero neighbourhood with a guaranteed prescribed performance with preferable overshoot/undershoot, convergence speed and final tracking accuracy. The Kalman–Yakobovich (KY) lemma is employed to prove the closed-loop stability of the observer-controller system strongly. Numerical simulations are given to show the controller’s effectiveness in practice.