Tray indexing driven by timing belt actuator is widely used in the industry, where high-precision profile tracking is essential to guarantee good production quality. To avoid humming sound and chip dislodged, an autonomous S-curve trajectory is used as the reference profile and the jerk resulting from the control input chattering needs to be well controlled. To implement the optimal tracking control with respect to an S-curve profile and maintain a guaranteed adequate level of performance towards the perturbation, the composite system is constructed by augmenting the S-curve trajectory with the system model and an $\mathcal {H}_2$ guaranteed cost optimization problem is formulated. The system performance in terms of tracking accuracy and jerk minimization is quantified as the $\mathcal {H}_2$-norm, and it aims to minimize the upper bound to the $\mathcal {H}_2$-norm over the uncertain domain. However, due to structural constraints on the composite gain matrix as well as robustness requirement, the algebraic Riccati equations cannot be used. This article presents the theoretical results where all the stabilizing constrained gain matrices can be parameterized over an extended matrical set. Efficient numerical procedures are developed to obtain the $\epsilon$-optimum with guaranteed robustness by linear programming and outer linearization in an iterative framework. Numerical optimization and experiments are conducted to validate the theoretical results and the practical appeal of the proposed approach.

中文翻译：

---

面向约束控制器设计的参数空间优化与托盘索引的应用

由同步带执行器驱动的托盘分度在行业中得到广泛应用，高精度的轮廓跟踪对于保证良好的生产质量至关重要。为避免嗡嗡声和芯片脱落，使用自主 S 曲线轨迹作为参考轮廓，并且需要很好地控制由控制输入颤动引起的急动。为了实现关于 S 曲线轮廓的最佳跟踪控制并在扰动方面保持足够的性能水平，复合系统是通过用系统模型和一个增强 S 曲线轨迹来构建的$\mathcal {H}_2$保证成本优化问题被公式化。系统在跟踪精度和加加速度最小化方面的性能被量化为$\mathcal {H}_2$-norm，它旨在最小化 $\mathcal {H}_2$- 不确定域上的范数。然而，由于复合增益矩阵的结构限制以及稳健性要求，不能使用代数 Riccati 方程。本文介绍了所有稳定约束增益矩阵都可以在扩展矩阵集上参数化的理论结果。开发了有效的数值程序以获得$\epsilon$- 在迭代框架中通过线性规划和外线性化保证鲁棒性的最优。进行数值优化和实验以验证理论结果和所提出方法的实际吸引力。