String stable integral control design for vehicle platoons with disturbances

Abstract: This paper presents a control design with integral action for vehicle platoons with disturbance that ensures string stability of the closed loop and disturbance rejection. The addition of integral action and a coordinate change allows to develop sufficient smoothness conditions on the closed loop system to ensure that the closed loop system using the proposed controller is string stable in the presence of time-varying disturbances and able able to reject constant disturbances. In addition, bounds for the tracking error of the platoon configuration are also given. Further, a case study is considered together with a suitable controller structure, which satisfies the required smoothness conditions. Simulation results illustrate the performance of the closed loop.

• The paper introduces an integral control design that ensures disturbance rejection and string stability in vehicle platoons using bidirectional communication.
• It employs a transformation matrix and symmetric coupling functions to optimize controller gains and reject constant disturbances.
• Simulation results demonstrate reduced state error norms and improved transient behavior in heterogeneous vehicle systems.

String Stable Integral Control Design for Vehicle Platoons with Disturbances

Introduction

The paper "String stable integral control design for vehicle platoons with disturbances" (2002.09666) addresses the challenge of ensuring string stability in vehicle platoons subjected to time-varying and constant disturbances. Vehicle platooning is a technique employed in intelligent transportation systems with benefits such as increased traffic throughput and reduced fuel consumption. However, string stability is essential as it ensures disturbances are attenuated along the vehicle string regardless of its length, preventing amplification of errors.

Previous research identified the need for stability properties such as string stability in automated vehicle systems, introduced as early as the 1960s. The paper advances the string stability discourse by introducing integral control actions that provide robustness against constant disturbances while maintaining string stability across longitudinal vehicle formations.

Controller Design and Problem Formulation

The central contribution of the paper is a control design encompassing integral action for vehicle platoons with a bidirectional communication framework. This design ensures disturbance string stability (DSS) and constant disturbance rejection, utilizing smoothness conditions imposed through coordinate changes.

The mathematical formulation considers a system of interconnected agents, described by differential equations incorporating state vectors, control inputs, and disturbances. The controller design features a structured approach with symmetry considerations and dynamic adjustments for disturbances. The sufficient conditions for DSS involve interaction between coupling functions in the control law and symmetry parameters, ensuring the attenuation of disturbances.

Sufficient conditions for DSS are proposed and derived based on previous work, extending the framework to include constant disturbance rejection via integral action. The controller is optimized through a transformation matrix approach and considers heterogeneous vehicle dynamics.

Numerical Example and Simulation

Simulations are conducted on a heterogeneous car platoon system to evaluate the controller's performance. The results demonstrate that the inclusion of integral action compensates effectively for constant disturbances, showing reduced state error norms and convergence toward desired inter-vehicle distances. The controller design achieves improved transient behavior and effectively manages uncertainty in vehicle masses.

The numerical results corroborate the theoretical expectations, illustrating the capability of the proposed controller to maintain string stability and reject constant disturbances. Conditions for suitable controller gains are identified through convex optimization, verified through simulations.

Conclusion

The research illustrates the efficacy of integral control actions in vehicle platooning, with sustained disturbance rejection and string stability. The theoretical framework and sufficient conditions provided pave the way for robust control solutions in platoon systems, addressing both time-varying and persistent disruptions. Future work is suggested to extend controller formulations for decentralized settings without global reference information.

In summary, this paper contributes significantly to the development of stable, disturbance-resistant control strategies for vehicle platooning, enhancing the robustness and reliability of intelligent transportation systems.