We give a concrete description of a controlled quantum stochastic dynamical model corresponding to a quantum system (a cavity mode) undergoing continual quadrature measurements, with a PID controller acting on the filtered estimate for the mode operator. The control has three feedback paths: P (proportional), I (integral) and D (derivative) of the error signal. Central use is made of the input and output pictures when constructing the model: these unitarily equivalent pictures are presented in the paper, and used to transfer concepts relating to the controlled internal dynamics to those relating to measurement output, and vice versa. The approach shows the general principle for investigating mathematically and physically consistent models in which standard control theoretic methods are to be extended to the quantum setting.

中文翻译：

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基于量子卡尔曼滤波器的 PID 控制器

我们给出了一个受控量子随机动力学模型的具体描述，该模型对应于进行连续正交测量的量子系统（腔模式），PID 控制器作用于模式算子的滤波估计。该控制具有三个反馈路径：误差信号的 P（比例）、I（积分）和 D（微分）。在构建模型时集中使用输入和输出图片：这些统一等效的图片在论文中呈现，用于将与受控内部动力学相关的概念转移到与测量输出相关的概念，反之亦然。该方法显示了研究数学和物理一致模型的一般原则，其中标准控制理论方法将扩展到量子设置。