Tracking performance limitations in a linear feedback system with remote sensors

This paper studies tracking performance limitations for a networked feedback control system. In the system, the plant is a linear time invariant (LTI) SISO system and the measurement signal is received from a remote site through a network. The reference signal in the tracking problem is a step signal. The tracking performance is measured by an integral square error between the output of the plant and the reference signal. To transmit the measurement signal through a network, this signal is quantized and then certain information which the original signal possesses could be lost. The major issue which we study in this paper is: How does a logarithmic quantization law constrain the best attainable tracking performance of the feedback system? Here the quantization error is modeled as a product of the original signal and a bounded nonlinear function. An upper bound of the best attainable tracking performance of the system is presented in terms of the quantization error model and the characteristics of the plant. It is also found that, if the nonlinear function in the quantization error model is an Hinfty norm-bounded uncertainty, this upper bound is the tracking performance limit of the feedback system under the worst uncertainty. In the case where the quantizer and network are not used in the system, the upper is equal to the tracking performance limit of the LTI system.