Variable–Domain Fuzzy PI Control Strategy for Variable Speed Limits Independent of Critical Density

Abstract

Variable speed limit (VSL) systems represent a significant strategy for mitigating standing queues at bottlenecks on freeways. However, the implementation of VSL faces three primary challenges: first, fluctuations in VSL metrics; second, the potential for VSL-induced capacity to fall short of free flow capacity; and third, the necessity for manual optimization of VSL controller parameters. This paper addresses these issues by proposing a novel approach. Initially, we introduce a formula for estimating the expected flow rate, utilizing average speed instead of average density. Subsequently, we design a variable domain fuzzy proportional-integral (PI) controller to calculate the optimal speed limit. A scaling factor derived from a proportional exponential function is employed to dynamically adjust the controller’s domain, thereby enhancing the utilization of fuzzy rules, refining the control process, and bolstering the system’s resistance to disturbances. A simulation environment is developed using SUMO and Python, with queue length, average speed, and delay as key evaluation metrics. Comparative analyses are performed under both stable and fluctuating demand scenarios. The results indicate that the proposed variable domain fuzzy PI control strategy significantly improves the average values and stability of the evaluation metrics when contrasted with traditional PI control methods based on critical density.