Digital Effects and Delays in Connected Vehicles: Linear Stability and Simulations

To improve the ride quality in connected vehicle platoons, information about the motion of the leader can be transmitted using vehicle-to-vehicle (V2V) communication and such information can be incorporated in the controllers of the following vehicle. However, according to the current V2V standards, dedicated short range communication (DSRC) devices transmit information every 100 ms which introduces time delays into the control loops. In this paper we study the effects of these time delays on the dynamics of vehicle platoons subject to digital control and derive conditions for plant stability and string stability. It is shown that when the time delay exceeds a critical value, no gain combination can stabilize the system. Our results have important implications on connected vehicle design. INTRODUCTION Recent decades have witnessed a growing interests in increasing the safety and throughput of vehicular traffic by using different control strategies [1]. One way to achieve this goal is improving the performance of autonomous cruise control (ACC) [2,3] devices by incorporating signals received from other vehicles via vehicle-to-vehicle (V2V) communication [4]. This is often referred as cooperative autonomous cruise control (CACC) [5]. Indeed these controllers use finite sampling time. For standard (radar-based) ACC the sampling time is in the range of 50 ms but dedicated short range communication devices (DSRC) only broadcast a packet every 100ms and the effective sampling time may be multiples of this when packets are lost [4]. When combining this with the zero-order hold (ZOH) [6] used in digital controllers, a hybrid system is obtained where the continuoustime dynamics is subject to piece-wise constant inputs. This introduces time-dependent time delays into the vehicle dynamics [7] that can significantly influence the limitations of the controllers. In this paper we investigate a nonlinear physics-based model that is controlled by a nonlinear digital controller [8]. Of particular interest is the stability of the system. Apart from the ability to be able to follow a leader traveling with a constant speed (called plant stability) we also require attenuations of disturbances along platoons (called string stability [9]) in order to ensure smooth traffic flow. Here, for the first time, we derive such conditions for digitally controlled vehicles by transforming the continuoustime system to a discrete time system with discrete delay. We analyze the dynamics at the linear level in the vicinity of the uniform flow equilibrium and draw stability charts for the plant and string stability of the system which can inform designers how to select feedback gains. Our results indicate that the digital effects have significant impacts on the available control gains and there exists a critical sampling time, beyond which no gain combinations can be found that ensure string stability. We validate our linear design by numerical simulations using the nonlinear model. NONLINEAR CAR-FOLLOWING MODEL In this section, we construct a nonlinear vehicle model and propose a nonlinear controller that can maintain a desired distance-dependent equilibrium velocity. To model the longitudinal vehicle dynamics, we consider no slip condition on the wheels and neglect the flexibility of the tires and the suspension which results in meffv̇ =−mgsinφ− γmgcosφ− k(v+ vw) + η R Ten , (1) 1 Copyright © 2013 by ASME Proceedings of the ASME 2013 Dynamic Systems and Control Conference DSCC2013 October 21-23, 2013, Palo Alto, California, USA