Adaptive PID feedback control for the longitudinal dynamics of driver-assisted vehicles in mixed traffic

Vehicles equipped with varying levels of automation and connection are starting to share the road with conventional vehicles. This provides new opportunities to design and test systems to control the acceleration dynamics of those equipped vehicles in mixed traffic environment contexts, with the global aim to globally reduce traffic congestion and increase traffic safety. Recent work has been focusing on proposing solutions to this problem by applying modern control theory, such as optimal control, ℋ
_∞
control. However, such approaches tend to be computationally expensive or do not take into account the actuators limitations and the safety constraints. For this reason, as well as for the sake of simplicity, in this paper we investigate the design of classic PID controllers to control the acceleration of vehicles equipped with Automated Driving Systems. We consider that each vehicle updates its acceleration according to a car-following model with specific behavioural parameters, thereby accounting for the variability of drivers' behaviours, and we assume that the longitudinal acceleration dynamics of only a proportion of vehicles can be controlled. After linearising the system about its equilibrium state, we show that each vehicle speed to acceleration transfer function reduces to a second order system written as a function of the equilibrium state and the behavioural parameters of the vehicle. We validate this formulation in simulation considering PBRS acceleration inputs. Selecting the set point as the equilibrium speed, an adaptive PID controller is then derived for each vehicle, considering the behavioural parameters. We then discuss set point weighting to avoid propagation of measurement errors, integrator wind-up to consider limitations of the actuators and safety constraints, and tuning of the controllers. Simulations highlight that the designed controllers are able to remove traffic flow instabilities even with a low proportion of equipped vehicles in the traffic flow.