We review error estimation methods for co-simulation, in particular methods that are applicable when the subsystems provide minimal interfaces. By this, we mean that subsystems do not support rollback of time steps, do not output derivatives, and do not provide any other information about their internals besides the output variables that are required for coupling with other subsystems. Such "black-box" subsystems are common in industrial applications, and the ability to couple them and run large-system simulations is one of the major attractions of the co-simulation paradigm. We also describe how the resulting error indicators may be used to automatically control macro time step sizes to strike a good balance between simulation speed and accuracy. The various elements of the step size control algorithm are presented in pseudocode so that readers may implement them and test them in their own applications. We provide practicable advice on how to use error indicators to judge the quality of a co-simulation, how to avoid common pitfalls, and how to configure the step size control algorithm.

翻译：本文回顾了协同仿真的误差估计方法，特别是适用于子系统提供最小接口情况的方法。此处“最小接口”指子系统不支持时间步回滚、不输出导数，且除与其他子系统耦合所需的输出变量外，不提供任何内部信息。此类“黑盒”子系统在工业应用中十分常见，而对其进行耦合并运行大系统仿真的能力正是协同仿真范式的主要吸引力之一。本文还阐述了如何利用所得误差指示器自动控制宏时间步长，以在仿真速度与精度之间实现良好平衡。步长控制算法的各组成部分均以伪代码形式呈现，便于读者在自身应用中实现与测试。我们提供了关于如何使用误差指示器评估协同仿真质量、如何避免常见陷阱以及如何配置步长控制算法的实用建议。