A novel approach of the tracking control for synchronizer displacement is introduced in this paper. Based on modeling for the structure of synchronizer and shifting process, a shifting displacement tracking controller is designed by the Udwadia — Kalaba equation. The engagement rule of synchronizer combination sleeve is regarded as the trajectory constraint of the system, certain constraint force is imposed to follow this trajectory constraint, which could be obtained by the Udwadia-Kalaba equation without using Lagrange multiplier or other auxiliary variables. Specific comparative study with conventional PID control is discussed. Simulations and vehicle test results show that the shifting actuator can accurately track the desired trajectory determined by the upper layer control strategy, thus verify the effectiveness of the controller.

中文翻译：

---

基于模型的同步器换挡过程轨迹控制

介绍了一种同步器位移跟踪控制的新方法。在对同步器结构和换挡过程进行建模的基础上，利用Udwadia-Kalaba方程设计了换挡位移跟踪控制器。同步器组合套筒的啮合规则被视为系统的轨迹约束，施加一定的约束力来遵循该轨迹约束，这可以通过Udwadia-Kalaba方程获得，而无需使用Lagrange乘数或其他辅助变量。讨论了与常规PID控制的具体比较研究。仿真和车辆测试结果表明，换档执行器可以准确地跟踪由上层控制策略确定的期望轨迹，从而验证控制器的有效性。