Robust pole-placement based on convex $D_R$-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant.

中文翻译：

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磁悬浮装置的离散时间极区鲁棒控制器

基于凸面的稳健极点布置 $d_{\mathrm{[R}}$区域属于实际系统的有效控制设计技术，可提供易于计算的极点布置设计算法。当规定了相对阻尼时，在离散时域中会出现问题，因为相应的离散时域是非凸的，呈“心形”形状。在本文中，我们进一步开发了关于心形件的内凸近似值的最新结果，对它的设计参数及其对相应闭环性能的影响进行了系统分析（通过绝对误差的标准积分（IAE）和总方差标准衡量） ）。在实际的实验室磁悬浮厂中，对鲁棒控制器的应用进行了说明，并对其进行了评估，该鲁棒控制器具有拟议的离散时间极点区域的凸近似值。