Analysis of a Simplified Predictive Function Control Formulation Using First Order Transfer Function for Adaptive Cruise Control

Abstract

This paper presents a formulation and analysis of a low computation Predictive Functional Control (PFC), which is a simplified version of the more advanced Model Predictive Control (MPC) for an Adaptive Cruise Control (ACC) system by using a representation of first order closed-loop transfer function. In this work, a non-linear mathematical model of vehicle longitudinal dynamics is considered as a control plant. Then, a simple Proportional Integral (PI) controller is employed as an inner loop to identify the first-order relationship between its actual and desired trajectory speed according to the reasonable time constant based on the logical response of pedals pressing. To directly control the whole plant, the PFC is formulated as an outer loop to track the desired speed together with the convergence rate based on a user preference while satisfying constraints related to acceleration and safe distancing. Since PFC is formulated based on the first-order transfer function, the prediction and tuning processes are straightforward and specific to this system. The simulation results confirm that the proposed controller managed to track the desired speed while maintaining a comfortable driving response. Besides, the controller also can retain safe distancing during the car following application, even in the presence of unmeasured disturbance. In summary, this framework can avoid the need to formulate an inverse non-linear model that is typically used when deploying a hierarchical control structure to compute the throttle and brake pedals pressing as it has been replaced with an inner loop PI controller. The performance also is comparable yet more conservative due to the simplification. These findings can become a good reference for designing and improving the ACC controller, as the framework can be easily generalized for any type of vehicle for future work.