MPF拓扑下基于观测器的车辆编队控制器的内部稳定性与弦稳定性
Internal and String Stability of an Observer-based Controller for Vehicle Platooning under the MPF Topology
AI总结：
针对MPF拓扑下采用CTHS策略的车辆编队，本文提出基于分布式观测器的控制器，通过简化设计推导弦稳条件，结合启发式搜索与类二分算法求解参数及时距最小值，性能优于传统PID控制器。
摘要：
本文研究了采用恒定时距策略（CTHS）和多前车跟随（MPF）车车信息流拓扑的车辆编队的内部稳定性与弦稳定性。具体而言，我们不同于这类系统传统的比例-积分-微分（PID）控制器设计，提出了一种基于观测器的控制器设计方案。\n在设计该基于观测器的控制器时，我们首先设计了分布式观测器，每辆跟随车可通过该观测器估计自身相对于领航车的位置、速度和加速度误差。观测器通过构建需确定参数的观测器矩阵实现。随后，我们对观测器矩阵的设计进行简化，将设计过程归结为选择单个标量值；这种设计进一步简化了控制器结构，其简洁性使得我们可通过频率响应法推导弦稳定性条件。\n接着，我们将给定时距下的弦稳定性条件转化为控制器参数的约束条件，并通过设计一种新型启发式搜索算法，得到满足稳定性条件的控制器参数。此外，我们结合类二分算法对搜索算法进行扩展，能够在一定偏差容限内得到时距的最小可行值。最后，我们给出了如何通过上述算法确定基于观测器的控制器参数以避免峰值现象的思路。\n我们通过算例验证了所提基于观测器的控制器的性能。此外，与MPF拓扑下广泛使用的PID控制器的对比结果表明，本文提出的基于观测器的控制器具有更优的收敛性能。
英文摘要：
In this paper, we study the internal stability and string stability of a vehicle platoon under the constant time headway spacing (CTHS) policy and the multiple-predecessor-following (MPF) vehicle-to-vehicle information flow topology. More specifically, we depart from the conventional Proportional-Integral-Derivative (PID) controller design for such systems and we propose the design of an observer-based controller. For designing our observer-based controller, we first design a distributed observer, with which each follower estimates their position, speed and acceleration error with respect to the leader. The observer is designed by means of constructing an observer matrix whose parameters should be determined. Next, we simplify the design of the matrix of the observer in such a way that the design boils down to choosing a single scalar value; this design further simplifies the structure of the controller, whose simplicity enables the derivation of string stability conditions by means of a frequency response method. Subsequently, the string stability conditions for a given time headway, are transformed to conditions for the controller parameters. We obtain controller parameters that satisfy the stability conditions by designing a novel heuristic search algorithm. Furthermore, we extend the search algorithm by incorporating a bisection-like algorithm, which allows to obtain (within some deviation tolerance) the minimum available value of the time headway. Finally, we provide insights about how to finalize the observer-based controller parameters from above algorithms to avoid the peaking phenomenon. The performance of the proposed observer-based controller is demonstrated via illustrative examples. Additionally, a comparison with a widely-used PID controller for MPF topology shows that our proposed observer-based controller has better convergence performance.
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