网络化系统周期信号的跟踪
The tracking problem in networked systems with periodic signal reference input

研究线性时不变、单变量、离散网络化系统对周期信号的跟踪问题. 与现有文献考虑的参考输入信号大都为常 见的能量信号所不同的是, 本文参考输入信号是离散时间周期方波功率信号. 相应地, 研究系统对基于功率谱的参考输 入信号功率的响应, 系统的跟踪性能通过输入信号与受控对象输出之差的功率来衡量, 而最优跟踪性能采用跟踪误差的 平均功率来度量. 考虑的网络化控制系统仅上行通道存在丢包误差的影响, 把丢包过程看作两个信号的合成, 一是确定 性信号, 二是随机过程, 进而丢包误差描述为源信号和白噪声之间乘积. 根据被控对象和随机过程的性质, 采用 Parseval等式、维纳–辛钦定理和范数矩阵理论得到该系统跟踪性能极限的下界表达式. 仿真结果表明, 所设计的控制器 能实现对周期信号的有效跟踪, 进而验证了结论的正确性.
The tracking problem in linear time invariant SISO discrete-time networked systems with periodic signal reference input is studied. The most important difference between the exist works on the tracking problem and this paper is that the reference input signal considered in the latter is a discrete-time periodic square wave power signal, whereas the reference input signal considered in most of the former is the common energy signal. Accordingly, we study the system response to the power of input signal based on power spectrum. The tracking performance is measured by the power of the tracking error between the plant output and the reference and the optimal tracking performance is thus measured by the mean power of the tracking error. We consider this case for which there may be packet dropouts only in the forward channel in the communication network. Subsequently, the packet dropouts may be described by a certain type of signal and an uncertain type of signal, the error in packet dropouts is assumed to be a product of the original signal and a white noise. By applying Parseval identity and Wiener-Khinchin theorem as well as norm matrix theory, the lower bound of the performance in tracking is derived in terms of the characteristics of the plant and the uncertain type of signal. Numerical simulation results demonstrate the effectiveness in tracking periodic signal under the control of optimal tracking controller presented in this study. Consequently, it demonstrates the correctness of our result.