Padé approximation of delays in cooperative ACC based on string stability requirements

Cooperative adaptive cruise control (CACC) improves road throughput by employing intervehicle wireless communications. The inherent communication time delay and vehicle actuator delay significantly limit the minimum intervehicle distance in view of string stability requirements. Hence, controller design needs to consider both delays, which result in a nonrational transfer function representation of the CACC-controlled string. Padé approximations can be applied to arrive at a finite-dimensional model, which allows for many standard control methods. Our objective is to provide a method to decide for the lowest possible order of the Padé approximation, which is sufficiently accurate in view of CACC (string) stability analysis. The constant time gap strategy and a one-vehicle look-ahead topology are adopted to develop a CACC stable string. First, based on the stable controller parameter region, a suitable order of Padé approximations of the vehicle actuator delay can been carried out in view of individual vehicle stability. Then, the minimum string-stable time gaps for a CACC system with both exact and approximated delays have been compared. The procedure with a Proportional-derivative controller to choose the approximation order of delays has been given, followed by the time-domain simulation validation.