基于量化控制信号的线性系统的跟踪性能极限

研究基于量化控制信号的线性系统的跟踪性能极限. 所研究的被控对象是稳定的线性时不变(LTI)系统, 参考跟踪信号是阶跃信号. 跟踪性能通过对象输出与参考信号之差的能量来衡量. 为了达到渐近跟踪, 提出了一个新的量化方案. 方案包括两部分: 一部分是在初始时刻将控制信号的稳态值通过网络传输给被控对象并且存储在其输入端; 另一部分则是通过对数量化器, 对控制信号的瞬态部分(即控制信号与其稳态值之差)进行量化, 然后传输给被控对象. 最后该量化信号与稳态控制信号相加后作用于被控对象. 这里, 假设对数量化误差是

The performance limit in tracking of a linear system with a quantized control signal

The performance limit in tracking a step signal by a stable and linear time-invariant(LTI) system with a quantized control signal is studied. The tracking performance is measured by the energy of the error between the plant output and the reference. To achieve the asymptotic tracking, a new quantization scheme is proposed. To the plant, this scheme initially sends the quantized value of the steady-state control signal, and continuously sends the logarithmically quantized value of the error between the control signal and its steady-state value. The error in the logarithmic quantization is assumed to be a product of the original signal and a white noise with a uniform distribution over a given range. The lower bound of the performance in tracking is derived in terms of the characteristics of the plant and the quantizer. This result answers, in an average sense, the question in networked control system of how large quantization error is allowed in a step tracking with a given tracking error energy level.