The paper studies robustness with respect to time-sampling of the energy regulation for one-dimensional sine–Gordon system. Such a problem is a new to control of invariants for hyperbolic partial differential equations (PDEs). In the absence of analytic results, the problem is studied numerically. The properties of four sampled-data algorithms are computationally studied with respect to three performance criteria. The four speed gradient algorithms are the “proportional”, “relay”, “adaptive-relay” and combined ones, by using state feedback with in-domain actuators. The three performance criteria are limit error, transient time, and threshold of stability for the sampling interval. An unexpected result is that the best performance for all three criteria was exhibited by the simplest, speed-gradient-proportional, algorithm. Simulation results are also presented for other energy tracking controllers to add insight into the parameter choice for improving the closed-loop robustness in the PDE setting over sampled-data algorithms.

本文研究了一维正弦-戈登系统的能量调节时间采样的鲁棒性。这样的问题对于控制双曲偏微分方程 (PDE) 的不变量来说是一个新问题。在没有分析结果的情况下，对该问题进行了数值研究。四个采样数据算法的属性针对三个性能标准进行了计算研究。四种速度梯度算法是“比例”、“中继”、“自适应中继”和组合算法，通过使用域内执行器的状态反馈。三个性能标准是采样间隔的极限误差、瞬态时间和稳定性阈值。一个意想不到的结果是，最简单的速度梯度比例算法展示了所有三个标准的最佳性能。